text:
James Anthony Bailey

James Anthony Bailey (July 4, 1847 – April 11, 1906) (né McGinnis), was an American owner and manager of several 19th-century circuses, including The Barnum and Bailey Greatest Show on Earth.

Early life
James Anthony McGinnis was born July 4, 1847 to Edward and Hannora McGinnis in Detroit, Michigan. Edward McGinnis died in October, 1849 of cholera and in 1855, James was orphaned when his mother died. James then went to live with his older sister, Catherine Gordon.

Life with Catherine was difficult as she tended to be overbearing and harsh. Sometime between 1859 and 1860, James ran away from Catherine's home and found a job and a place to stay on a farm about 10 miles outside the city of Pontiac, Michigan. Finding life on the farm unrewarding, 13-year old James wandered into Pontiac where he found work at the Hodges House Hotel.

After working at the hotel for a time, he was discovered by Colonel Frederic Harrison Bailey, a nephew of circus pioneer Hachaliah Bailey, and an advance man for John Robinson and Bill Lake's traveling circus. F.H. Bailey gave McGinnis a job as his assistant, and the two traveled together for many years. McGinnis eventually adopted F.H. Bailey's surname to become James A. Bailey.

Circus life
In his diary, James' brother-in-law Joe McCaddon writes that Bailey recounted stories of how he left the circus world at age 16 and went to work as clerk to a sutler during the Civil War.

In 1866, with the war over, he went back to work for Bill Lake, who now owned his own circus with his wife Agnes Lake Thatcher. During this time, James met Ruth Louisa McCaddon of Zanesville, Ohio. James and Ruth became friends, fell in love, and were married in December 1868. The very next year in Granby, Missouri, Bill Lake was shot and killed. With her husband dead, Agnes Lake became the first woman in the United States to own a circus (Agnes Lake would later marry famous gunfighter Wild Bill Hickok, who worked for a short time with Buffalo Bill Cody, whose Wild West Show James A. Bailey would one day manage).

Bailey later associated with James E. Cooper, and by the time he was 22, he was manager of the Cooper and Bailey circus. He then met with P.T. Barnum, and together they established Barnum and Bailey's Circus (for which Bailey was instrumental in obtaining Jumbo the Elephant) in 1880, with their combined show opening the following spring in Madison Square Garden.

Barnum was the face of the circus, but James Bailey was the hard worker who insisted on staying behind the scenes. Barnum once wrote to him that James managed the show “ten times better than I could.”

Equestrienne Josie Demott Robinson wrote in her autobiography that, “Mr. Barnum was the advertiser, who loved the limelight, who rode around in the ring, and announced who he was. But Mr. Bailey was the businessman, content to be invisible...and interested only in the success of the show.”

Bailey was considered by many to be a genius at logistics. His organizational skills for transporting people, animals, and equipment was copied by the military of more than one country.

He hired Pinkerton Detectives to travel with the show and protect circusgoers from grifters and thieves.

He established “Orphan Day”, one day a year when orphans could attend the circus for free. He was often known to carry children who couldn't walk into the circus tent and find them a seat away from the crush of the crowd.

Following Barnum's death in 1891, Bailey managed not only The Barnum and Bailey Greatest Show on Earth, but in 1894, took on the management of Buffalo Bill’s Wild West Show.

Death and legacy
Bailey died of erysipelas in 1906 at age 58 at his home in Mount Vernon, NY. He is buried in Woodlawn Cemetery, in The Bronx, New York City. His widow subsequently sold the circus to the Ringling brothers in 1907, who eventually merged the rival operations in 1919.

In his book about the circus, Earl Chapin May wrote, “Probably...no circus owner and manager left more sincere mourners than the thin little magnate known to millions as James A. Bailey.”

Taped beneath a photo of James Bailey in the scrapbook of employee Harrison Gunning is a small scrap of paper that reads, “P.T. Barnum was the great showman, but Mr. Bailey was the supreme of all circus managers, past and present.”

James A. Bailey was inducted into the International Circus Hall of Fame in 1960 and into the Circus Ring of Fame in Sarasota, Florida in 1990.

title: James Anthony Bailey


text:
Magic carpet (disambiguation)

A magic carpet is a mythological flying (or "teleporting") rug.

Magic carpet may also refer to:

Film, video, music and print media

 * The Magic Carpet, 1930s pulp magazine originally called Oriental Stories
 * IMAX Magic Carpet, large format film system in 1990
 * Magic Carpet (Aladdin), silent character featured in 1992 Disney film Aladdin and its franchise
 * Magic Carpet (video game), 1994 first person shooter game from Bullfrog Productions
 * Early form of "Extreme Gear" (type of racing vehicle) in the 2006 video game, Sonic Riders
 * "Magic Carpet" (song), 1963 song by English performer Billy J. Kramer
 * Magic Carpet (band), English psychedelic folk band during 1970s
 * The Magic Carpet (film), a 1951 American adventure film

Military operations

 * Magic Carpet, slang term for Malta convoy supply runs from Alexandria to Malta by British submarines during the Siege of Malta during World War II
 * Operation Magic Carpet, post-World War II U.S. Navy military operation
 * Operation Magic Carpet (Yemen), joint effort by UK and U.S. to airlift Yemeni Jews to Israel 1949–50

Transportation

 * Magic carpet (ski lift), type of surface lift found at ski areas
 * Cessna Experimental Magic Carpet, light aircraft research project

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Magic carpet (disambiguation)


text:
Pfaffian

In mathematics the determinant of an m×m skew-symmetric matrix can always be written as the square of a polynomial in the matrix entries, a polynomial with integer coefficients that only depends on m. When m is odd, the polynomial is zero. When m is even, it is a nonzero polynomial of degree m/2, and is unique up to multiplication by ±1. The convention on skew-symmetric tridiagonal matrices, given below in the examples, then determines one specific polynomial, called the Pfaffian polynomial. The value of this polynomial, when applied to the entries of a skew-symmetric matrix, is called the Pfaffian of that matrix. The term Pfaffian was introduced by, who indirectly named them after Johann Friedrich Pfaff.

Explicitly, for a skew-symmetric matrix $$A$$,
 * $$ \operatorname{pf}(A)^2=\det(A),$$

which was first proved by, who cites Jacobi for introducing these polynomials in work on Pfaffian systems of differential equations. Cayley obtains this relation by specialising a more general result on matrices that deviate from skew symmetry only in the first row and the first column. The determinant of such a matrix is the product of the Pfaffians of the two matrices obtained by first setting in the original matrix the upper left entry to zero and then copying, respectively, the negative transpose of the first row to the first column and the negative transpose of the first column to the first row. This is proved by induction by expanding the determinant on minors and employing the recursion formula below.

Examples

 * $$A=\begin{bmatrix} 0 & a \\ -a & 0  \end{bmatrix}.\qquad\operatorname{pf}(A)=a.$$

 * $$B=\begin{bmatrix}  0     & a & b \\ -a & 0        & c  \\   -b      &  -c       & 0 \end{bmatrix}.\qquad\operatorname{pf}(B)=0.$$

(3 is odd, so the Pfaffian of B is 0)

 * $$\operatorname{pf}\begin{bmatrix}   0     & a & b & c \\ -a & 0        & d & e  \\   -b      &  -d       & 0& f    \\-c &  -e      & -f & 0 \end{bmatrix}=af-be+dc.$$

The Pfaffian of a 2n × 2n skew-symmetric tridiagonal matrix is given as
 * $$\operatorname{pf}\begin{bmatrix}

0 & a_1 & 0 & 0\\ -a_1 & 0 & 0 & 0\\ 0 & 0 &0 & a_2 \\ 0 & 0 & -a_2 &0&\ddots\\ &&&\ddots&\ddots& \\ &&&& &0&a_n\\ &&&&&-a_n&0 \end{bmatrix} = a_1 a_2\cdots a_n.$$ (Note that any skew-symmetric matrix can be reduced to this form; see Spectral theory of a skew-symmetric matrix.)

Formal definition
Let A = (aij) be a 2n × 2n skew-symmetric matrix. The Pfaffian of A is explicitly defined by the formula

 * $$\operatorname{pf}(A) = \frac{1}{2^n n!}\sum_{\sigma\in S_{2n}}\operatorname{sgn}(\sigma)\prod_{i=1}^{n}a_{\sigma(2i-1),\sigma(2i)} \,, $$

where S2n is the symmetric group of order (2n)! and sgn(σ) is the signature of σ.

One can make use of the skew-symmetry of A to avoid summing over all possible permutations. Let Π be the set of all partitions of $\{1, 2, ..., 2n\}$ into pairs without regard to order. There are (2n)!/(2nn!) = (2n − 1)!! such partitions. An element α ∈ Π can be written as
 * $$\alpha=\{(i_1,j_1),(i_2,j_2),\cdots,(i_n,j_n)\}$$

with ik < jk and $$i_1 < i_2 < \cdots < i_n$$. Let
 * $$\pi_\alpha=\begin{bmatrix} 1 & 2 & 3 & 4 & \cdots & 2n -1 & 2n \\ i_1 & j_1 & i_2 & j_2 & \cdots & i_n & j_{n} \end{bmatrix}$$

be the corresponding permutation. Given a partition α as above, define
 * $$ A_\alpha =\operatorname{sgn}(\pi_\alpha)a_{i_1,j_1}a_{i_2,j_2}\cdots a_{i_n,j_n}.$$

The Pfaffian of A is then given by
 * $$\operatorname{pf}(A)=\sum_{\alpha\in\Pi} A_\alpha.$$

The Pfaffian of a n×n skew-symmetric matrix for n odd is defined to be zero, as the determinant of an odd skew-symmetric matrix is zero, since for a skew-symmetric matrix, $$\det\,A = \det\,A^\text{T} = \det\left(-A\right) = (-1)^n \det\,A,$$ and for n odd, this implies $$\det\,A = 0$$.

Recursive definition
By convention, the Pfaffian of the 0×0 matrix is equal to one. The Pfaffian of a skew-symmetric 2n×2n matrix A with n > 0 can be computed recursively as
 * $$\operatorname{pf}(A)=\sum_{{j=1}\atop{j\neq i}}^{2n}(-1)^{i+j+1+\theta(i-j)}a_{ij}\operatorname{pf}(A_{\hat{\imath}\hat{\jmath}}),$$

where the index i can be selected arbitrarily, $$\theta(i-j)$$ is the Heaviside step function, and $$A_{\hat{\imath}\hat{\jmath}}$$ denotes the matrix A with both the i-th and j-th rows and columns removed. Note how for the special choice $$i=1$$ this reduces to the simpler expression:
 * $$\operatorname{pf}(A)=\sum_{j=2}^{2n}(-1)^{j}a_{1j}\operatorname{pf}(A_{\hat{1}\hat{\jmath}}).$$

Alternative definitions
One can associate to any skew-symmetric 2n×2n matrix A = (aij) a bivector
 * $$\omega=\sum_{i<j} a_{ij}\;e_i\wedge e_j ,$$

where $\{e_{1}, e_{2}, ..., e_{2n}\}$ is the standard basis of R2n. The Pfaffian is then defined by the equation
 * $$\frac{1}{n!}\omega^n = \operatorname{pf}(A)\;e_1\wedge e_2\wedge\cdots\wedge e_{2n},$$

here ωn denotes the wedge product of n copies of ω.

Equivalently, we can consider the bivector (which is more convenient when we do not want to impose the summation constraint $$i < j$$): $$\omega'=2 \omega = \sum_{i, j} a_{ij}\;e_i\wedge e_j,$$ which gives $$\omega'^n = 2^n n! \operatorname{pf}(A)\;e_1\wedge e_2\wedge\cdots\wedge e_{2n}.$$

A non-zero generalisation of the Pfaffian to odd-dimensional matrices is given in the work of de Bruijn on multiple integrals involving determinants. In particular for any $$m\times m$$-matrix A, we use the formal definition above but set $$n = \lfloor m/2\rfloor $$. For m odd, one can then show that this is equal to the usual Pfaffian of an $$(m+1) \times (m+1)$$-dimensional skew symmetric matrix where we have added an $$(m+1)$$th column consisting of m elements 1, an $$(m+1)$$th row consisting of m elements −1, and the corner element is zero. The usual properties of Pfaffians, for example the relation to the determinant, then apply to this extended matrix.

Properties and identities
Pfaffians have the following properties, which are similar to those of determinants. Using these properties, Pfaffians can be computed quickly, akin to the computation of determinants.
 * Multiplication of a row and a column by a constant is equivalent to multiplication of the Pfaffian by the same constant.
 * Simultaneous interchange of two different rows and corresponding columns changes the sign of the Pfaffian.
 * A multiple of a row and corresponding column added to another row and corresponding column does not change the value of the Pfaffian.

Miscellaneous
For a 2n × 2n skew-symmetric matrix A
 * $$\operatorname{pf}(A^\text{T}) = (-1)^n\operatorname{pf}(A).$$
 * $$\operatorname{pf}(\lambda A) = \lambda^n \operatorname{pf}(A).$$
 * $$\operatorname{pf}(A)^2 = \det(A).$$

For an arbitrary 2n × 2n matrix B,
 * $$\operatorname{pf}(BAB^\text{T})= \det(B)\operatorname{pf}(A).$$

Substituting in this equation B = Am, one gets for all integer m
 * $$\operatorname{pf}(A^{2m+1})= (-1)^{nm}\operatorname{pf}(A)^{2m+1}.$$

$$

$$

Derivative identities
If A depends on some variable xi, then the gradient of a Pfaffian is given by
 * $$\frac{1}{\operatorname{pf}(A)}\frac{\partial\operatorname{pf}(A)}{\partial x_i}=\frac{1}{2}\operatorname{tr}\left(A^{-1}\frac{\partial A}{\partial x_i}\right),$$

and the Hessian of a Pfaffian is given by
 * $$\frac{1}{\operatorname{pf}(A)}\frac{\partial^2\operatorname{pf}(A)}{\partial x_i\partial x_j}=\frac{1}{2}\operatorname{tr}\left(A^{-1}\frac{\partial^2 A}{\partial x_i\partial x_j}\right)-\frac{1}{2}\operatorname{tr}\left(A^{-1}\frac{\partial A}{\partial x_i}A^{-1}\frac{\partial A}{\partial x_j}\right)+\frac{1}{4}\operatorname{tr}\left(A^{-1}\frac{\partial A}{\partial x_i}\right)\operatorname{tr}\left(A^{-1}\frac{\partial A}{\partial x_j}\right).$$

Trace identities
The product of the Pfaffians of skew-symmetric matrices A and B can be represented in the form of an exponential
 * $$\textrm{pf}(A)\,\textrm{pf}(B) = \exp(\tfrac{1}{2}\mathrm{tr}\log(A^\text{T}B)).$$

Suppose A and B are 2n × 2n skew-symmetric matrices, then
 * $$ \mathrm{pf}(A)\,\mathrm{pf}(B) = \tfrac{1}{n!} B_n(s_1, s_2, \ldots, s_n), \qquad \mathrm{where} \qquad s_l = - \tfrac{1}{2}(l - 1)!\,\mathrm{tr}((AB)^l)$$

and Bn(s1,s2,...,sn) are Bell polynomials.

Block matrices
For a block-diagonal matrix
 * $$A_1\oplus A_2=\begin{bmatrix} A_1 & 0 \\ 0 & A_2 \end{bmatrix},$$
 * $$\operatorname{pf}(A_1\oplus A_2) =\operatorname{pf}(A_1)\operatorname{pf}(A_2).$$

For an arbitrary n × n matrix M:
 * $$\operatorname{pf}\begin{bmatrix} 0 & M \\ -M^\text{T} & 0  \end{bmatrix} =

(-1)^{n(n-1)/2}\det M.$$

It is often required to compute the pfaffian of a skew-symmetric matrix $$ S $$ with the block structure

S = \begin{pmatrix} M & Q\\-Q^\mathrm{T} & N \end{pmatrix}\, $$ where $$ M $$ and $$ N $$ are skew-symmetric matrices and $$ Q $$ is a general rectangular matrix.

When $$ M $$ is invertible, one has

\operatorname{pf}( S) = \operatorname{pf}( M)\operatorname{pf}( N+ Q^\mathrm{T}   M^{-1}  Q). $$ This can be seen from Aitken block-diagonalization formula,
 * $$\begin{pmatrix}M& 0\\ 0 & N+Q^\mathrm{T} M^{-1} Q\end{pmatrix} = \begin{pmatrix}I& 0\\ Q^\mathrm{T} M^{-1} & I\end{pmatrix}\begin{pmatrix} M& Q\\ -Q^\mathrm{T} & N\end{pmatrix} \begin{pmatrix}I& -M^{-1} Q\\ 0& I \end{pmatrix}.$$

This decomposition involves a congruence transformations that allow to use the pfaffian property $$ \operatorname{pf}(BAB^\mathrm{T}) = \operatorname{det}(B)\operatorname{pf}(A)$$.

Similarly, when $$ N $$ is invertible, one has

\operatorname{pf}( S) = \operatorname{pf}(N)\operatorname{pf}( M+ Q N^{-1} Q^\mathrm{T}), $$ as can be seen by employing the decomposition
 * $$\begin{pmatrix}M+Q N^{-1} Q^\mathrm{T}& 0\\ 0 & N\end{pmatrix} = \begin{pmatrix}I& -Q N^{-1}\\ 0 & I\end{pmatrix}\begin{pmatrix} M& Q\\ -Q^\mathrm{T} & N\end{pmatrix} \begin{pmatrix}I& 0\\ N^{-1} Q^\mathrm{T}& I \end{pmatrix}.$$

Calculating the Pfaffian numerically
Suppose A is a 2n × 2n skew-symmetric matrices, then
 * $$\textrm{pf}(A) = i^{(n^2)} \exp\left(\tfrac{1}{2}\mathrm{tr}\log((\sigma_y\otimes I_n)^\mathrm{T}\cdot A)\right), $$

where $$\sigma_y$$ is the second Pauli matrix, $$I_n$$ is an identity matrix of dimension n and we took the trace over a matrix logarithm.

This equality is based on the trace identity
 * $$\textrm{pf}(A)\,\textrm{pf}(B) = \exp\left(\tfrac{1}{2}\mathrm{tr}\log(A^\text{T}B)\right)$$

and on the observation that $$\textrm{pf}(\sigma_y\otimes I_n)=(-i)^{n^2}$$.

Since calculating the logarithm of a matrix is a computationally demanding task, one can instead compute all eigenvalues of $$((\sigma_y\otimes I_n)^\mathrm{T}\cdot A)$$, take the log of all of these and sum them up. This procedure merely exploits the property $$\operatorname{tr}{\log{(AB)}} = \operatorname{tr}{\log{(A)}} + \operatorname{tr}{\log{(B)}} $$. This can be implemented in Mathematica with a single statement:

However, this algorithm is unstable when the Pfaffian is large. The eigenvalues of $$(\sigma_y\otimes I_n)^\mathrm{T}\cdot A $$ will generally be complex, and the logarithm of these complex eigenvalues are generally taken to be in $$ [-\pi, \pi] $$. Under the summation, for a real valued Pfaffian, the argument of the exponential will be given in the form $$ x + k\pi/2 $$ for some integer $$k$$. When $$x$$ is very large, rounding errors in computing the resulting sign from the complex phase can lead to a non-zero imaginary component.

For other (more) efficient algorithms see.

Applications

 * There exist programs for the numerical computation of the Pfaffian on various platforms (Python, Matlab, Mathematica).
 * The Pfaffian is an invariant polynomial of a skew-symmetric matrix under a proper orthogonal change of basis. As such, it is important in the theory of characteristic classes. In particular, it can be used to define the Euler class of a Riemannian manifold that is used in the generalized Gauss–Bonnet theorem.
 * The number of perfect matchings in a planar graph is given by a Pfaffian, hence is polynomial time computable via the FKT algorithm. This is surprising given that for general graphs, the problem is very difficult (so called #P-complete). This result is used to calculate the number of domino tilings of a rectangle, the partition function of Ising models in physics, or of Markov random fields in machine learning, where the underlying graph is planar. It is also used to derive efficient algorithms for some otherwise seemingly intractable problems, including the efficient simulation of certain types of restricted quantum computation. Read Holographic algorithm for more information.

title: Pfaffian


text:
Mount Suribachi

Mount Suribachi (摺鉢山) is a 169 m-high mountain on the southwest end of Iwo Jima in the northwest Pacific Ocean under the administration of Ogasawara Subprefecture, Tokyo Metropolis, Japan.

The mountain's name derives from its shape, resembling a suribachi or grinding bowl. It is also known as "Mount Pipe" (パイプ山), since the volcanic gas and water vapor that rolls in from the summit, alongside the rest of the island, give the appearance of a smoking pipe when viewed from the sea.

Joe Rosenthal's iconic World War II photograph, Raising the Flag on Iwo Jima, depicting United States Marines raising an American flag, was taken at the mountain's peak during the Battle of Iwo Jima in 1945. Ammunition ship USS Suribachi was named after this mountain.

Geology
Geologically, the mountain is a cinder cone of andesite, formed by volcanic activity. It is thought that the mountain is a dormant vent to a still active volcano (designated Iō-tō, the name of the island as a whole). From 1889 to 1957, the Japanese government recorded sixteen eruptions on the peak. One eruption lasted for sixty-five minutes, and created a crater with a diameter of 35 meters and a depth of fifteen meters on the runway near the former airfield from World War II. The Japanese Meteorological Agency reported that on May 2, 2012, a small eruption caused water discoloration to the northeast, and confirmed the appearance of a new fumarole.

History
During World War II, the Japanese built tunnel and bunker systems in and on Mount Suribachi. In February 1945, United States Marines invaded the island and initiated a major battle. For the United States, Iwo Jima was an important strategic point between the United States and mainland Japan, needed for its close proximity to Japan as an airstrip for supporting aircraft in Japanese mainland bombing operations but became useful for damaged B-29s returning to the Mariana Islands from bombing Japan, a status that resulted in severe fighting that led to over 20,000 American casualties and close to 20,000 Japanese killed.

In popular culture

 * During the Battle of Iwo Jima, Marines captured Mount Suribachi and raised a small American flag. Their officers ordered it replaced with a larger one, and photographer Joe Rosenthal took his famous picture, Raising the Flag on Iwo Jima. The photograph has become an iconic image and is depicted as a large statue at the Marine Corps War Memorial.
 * The 1949 film Sands of Iwo Jima, directed by Allan Dwan and starring John Wayne, follows a United States Marine rifle squad preparing for battle at Iwo Jima. The 2006 films Letters from Iwo Jima and Flags of Our Fathers, directed by Clint Eastwood, treat the theme of this Pacific battle and present the positions of both belligerents in this conflict.

title: Mount Suribachi


text:
Talk:Josip Štolcer-Slavenski

Untitled
What does "new secvence of the universal time" mean? Elf | Talk 05:51, 16 Mar 2004 (UTC)

As I see it, his music expresses the timelessness of traditional life - a deeper rhythm of life.

serbian and german?
he never considered himself a serb, and is a croat by birth, his family stemming from germany but being in međimurje for generations at the time of his birth; so i see no need for the old introduction. —Preceding unsigned comment added by 78.0.210.39 (talk) 10:36, 25 October 2010 (UTC)

External links modified
Hello fellow Wikipedians,

I have just modified one external link on Josip Štolcer-Slavenski. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive https://web.archive.org/web/20090616074614/http://www.m-i-c.rs/slavenskien.html to http://www.m-i-c.rs/slavenskien.html

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

Cheers.— InternetArchiveBot  (Report bug) 02:08, 28 April 2017 (UTC)

title: Talk:Josip Štolcer-Slavenski


text:
Talk:Gauss–Bonnet theorem

What about the generalized version?
I have started Pfaffian, so maybe someone can do Generalized Gauss-Bonnet theorem??? Tosha 05:52, 16 Mar 2004 (UTC)

A and s
What is A and what is s in the formula?

A is a differential-2-form, which represents the "surface" of the manifold M. Simililarly, s is a one-form (also called Pfaffian form), which represents the border of M (which is one-dimensional).

Orientable?
Does the manifold really have to be orientable? AxelBoldt 01:07, 21 April 2006 (UTC)
 * I don't think so. AFAIK, it just must be able to be triangulated (to get the Euler characteristic), but other than that there are no requirements on the surface. cBuckley (Talk • Contribs) 17:37, 21 April 2006 (UTC)
 * The Russians also don't mention orientability, so I'll make the change. AxelBoldt 01:06, 23 April 2006 (UTC)
 * Orientability is related to the existence of a metric. For example, a projective space has no metric, and is also unorientable.  In the absence of a metric, the boundary integral of the theorem has no meaning.  Nevertheless, the requirement that the manifold be Riemannian necessarily implies the use of the Riemannian metric.  Therefore, the manifold must be orientable.  Specifying that it must be so is therefore unnecessary, but it does contribute to clarity of exposition, which is, after all, one goal of a wikipedia article.  6 October 2008

—Preceding unsigned comment added by 75.134.153.115 (talk) 17:35, 6 October 2008 (UTC)

 * Any paracompact differentiable manifold has a metric, regardless of its orientability or lack thereof. The statement of the theorem still holds for non-orientable manfolds.  In most formulations of the theorem, the integrals require only the surface measure to be well-defined (which only needs the metric, not an orientation).  Some versions of the theorem, however, involve the Pfaffian of the curvature, and these require orientability.   siℓℓy rabbit  (  talk  ) 19:57, 6 October 2008 (UTC)

Move application section?
It seems to me the application section should be moved since it's really just an application of Euler's formula. The Gauss–Bonnet theorem is only used to show that the Euler characteristic of the sphere is 2 and there are much more elementary ways of doing that. --RDBury (talk) 01:37, 29 February 2008 (UTC)

Agreed. It makes no sense to use Euler's formula once then purposefully avoid it to compute chi of a sphere via Gauss-Bonnet. Instead of deleting this section, I'm moving it to the page on Euler characteristic. Jjauregui (talk) 02:49, 10 April 2009 (UTC)

Where is proof?
It would be great to provide the proof either in the article directly or via references. --Wladik Derevianko (talk) 20:49, 29 December 2009 (UTC)

Assessment comment
Substituted at 02:08, 5 May 2016 (UTC)

Example in 3-D
I'm not at all familiar with the subject matter, but I feel like an excellent addition to this page would be a description of how this theorem could be applied to a surface in 3D, which would make it a lot more intuitive. I'm not sure if the cited textbooks give any such examples. Wiki47222 (talk) 19:37, 24 October 2022 (UTC)

title: Talk:Gauss–Bonnet theorem


text:
TDT

TDT may refer to:
 * Digital terrestrial television
 * TDT (TV station), a digital television station in Tasmania, Australia
 * TDT (Portugal), digital terrestrial television in Portugal
 * TDT (Spain), digital terrestrial television in Spain
 * TDT Band (The Down Troddence), a six piece Indian thrash metal band
 * TDT Banda or Thamar Dillon Thomas Banda (fl. 1957–1962), Nyasaland politician
 * Terminal deoxynucleotidyl transferase, a specialized DNA polymerase expressed in immune cells
 * Terrestrial Dynamical Time, an obsolete name for Terrestrial Time
 * The Damned Things, an American heavy metal supergroup
 * Time domain transmissometry, a method of testing transmission lines
 * Toronto Dance Theatre, a Canadian modern dance company based in Toronto, Ontario
 * Tracing Debugging Technique, an early debugger by DEC
 * Transmission disequilibrium test, a family-based genetic association test
 * The Dark Tower (series), a book series written by Stephen King.

title: TDT


text:
Antonio Lamer

Joseph Antonio Charles Lamer (July 8, 1933 – November 24, 2007) was a Canadian lawyer, jurist and the 16th Chief Justice of Canada.

Career
Lamer practised in partnership at the firm of Cutler, Lamer, Bellemare and Associates and was a full professor in the Faculty of Law, Université de Montréal, where he was also a lecturer in criminology.

On December 19, 1969, at the age of 36, he was appointed to the Quebec Superior Court and to the Queen's Bench (Crown Side) of the province of Quebec. In 1978, he was elevated to the Quebec Court of Appeal and was appointed to the Supreme Court of Canada in 1980. Brian Mulroney named Lamer as Chief Justice on July 1, 1990.

On January 7, 2000, Lamer took an unexpected early retirement after having served as chief justice for ten years. Several years after his death, former judges spoke about the situation surrounding his retirement. According to a 2011 article in The Globe and Mail, in February 1999, a "delegation of three veteran judges" including former Supreme Court judge John C. Major, selected by their colleagues met with Lamer to tell him that "his performance was not what it had been up until this time." To which he immediately responded, "Well, then I'll resign." Lamer finally agreed to resign following a second meeting with Justices Major, Peter Cory and Charles Gonthier in the spring of 1999. He announced in an August 1999 talk to the Canadian Bar Association, that he would be resigning from the Supreme Court in January 2000.

After he retired, Lamer joined a large law firm, Stikeman Elliott, in a senior advisory role and was appointed associate professor of law at the Université de Montréal in 2000. He was appointed Communications Security Establishment Commissioner on June 19, 2003, a position he held until August 1, 2006. He also served as honorary colonel of the Governor General's Foot Guards.

In a CBC interview, Lamer described how the Supreme Court of Canada was transformed following the 1982 Canadian Charter of Rights and Freedoms under then Prime Minister Pierre Trudeau which expanded the role of the judiciary. Lamer described it as "somewhat of a shock to see their job description changed so fundamentally." Eugene Meehan, who was Lamer's first executive legal officer at the Supreme Court of Canada described Lamer as "a foundational builder", who was "one of the key architects of how courts interpret" the 1982 Charter" ..."building on the work of his predecessor as chief justice, Brian Dickson."

In March 2003, the government of Newfoundland and Labrador asked Lamer to head a high-profile inquiry into several wrongful convictions in Newfoundland specifically to oversee an inquiry into how the criminal justice system dealt with three discredited murder convictions. The hearings lasted about three years. Lamer was tasked to conduct an investigation into the death of Catherine Carroll and the circumstances surrounding the resulting criminal proceedings against Gregory Parsons, and an investigation into the death of Brenda Young and the circumstances surrounding the resulting criminal proceedings against Randy Druken. Lamer was also asked to inquire as to why Ronald Dalton's appeal of his murder conviction took eight years before it was brought on for a hearing in the Court of Appeal.

Personal life
Born in Montreal, Quebec, Lamer served in the Royal Canadian Artillery from 1950 to 1954 and in the Canadian Intelligence Corps from 1954 to 1960. In 1956, he graduated in law from the Université de Montréal and was called to the Bar of Quebec in 1957.

In 1987, he married Danièle Tremblay-Lamer, who was later appointed a judge on the Federal Court.

During his tenure he was well known among the bench to be a frequent consumer of alcohol, especially wine, and have various drug prescriptions to deal with his declining health. Various commentators and even other judges have vocally critiqued these habits of his as reason for him to resign from the court.

He died in Ottawa of a cardiac condition on November 24, 2007, and was entombed at the Notre Dame des Neiges Cemetery in Montreal.

Recognition
He was a Companion of the Order of Canada. He received honorary degrees from the Université de Moncton, University of Ottawa, Université de Montréal, University of Toronto, University of New Brunswick, Dalhousie University, University of British Columbia, and Saint Paul University.

From 1992 to 1998, Chief Justice Lamer was Honorary Lieutenant Colonel of the 62nd (Shawinigan) Field Artillery Regiment, RCA.

title: Antonio Lamer


text:
Genesee Community College

Genesee Community College (GCC) is a public community college with its main campus in Batavia, New York. It has campus centers in Albion, Medina, Warsaw, Dansville, Arcade, Lima (previously Lakeville), New York. Thus, the college covers areas not only inside of Genesee County but also in Orleans County, Livingston County and Wyoming County. This two-year college also offers housing facilities to out-of-area students, although the school is attended primarily by commuters. Additionally, GCC offers some degree and certificate programs online.

History
Genesee Community College was founded in 1966 as part of the State University of New York system. On September 27, 1967, Genesee Community College officially opened classes to full and part-time students. In January 1972, Genesee Community College relocated to its current permanent address on One College Road in the town of Batavia.

In 1991, GCC would see expansion with the addition of the Stuart Steiner Theatre, which houses a theater and stage, as well as expanded classrooms for the various arts programs. In 2000, the Conable Technology Building was added to the main campus facilities, a two-story 42000 sqft annex that is the center for most of GCC's technological programs and apparatus. In January 2006, GCC expanded again, adding the Wolcott J. Humphrey III Student Union, a central location for student affairs and organizations.

In February 2009, the plans for another campus center in Lima was announced, which will replace the Lakeville satellite campus and in June 2009, construction of the campus was completed. The 9000 sqft campus features two modern computer labs and a state-of-the-art science lab, five to seven classrooms, a lobby and reception area, as well as faculty, staff, advisor, and administrative offices.

Academics
Genesee Community College offers over 60 associate degree and certificate programs. Many students of the associate degree programs eventually transfer to four-year schools to complete their degree. College-ready students can complete their choice of 16 fully online programs at GCC.

Athletics
Genesee Community College currently has 14 intercollegiate men's and women's teams in basketball, baseball, lacrosse, soccer, softball, golf, swimming, cheerleading, and volleyball. Collectively, they are known as the Cougars, and their colors are blue and gold.

Roz Steiner Gallery
The Roz Steiner Gallery is Genesee Community College's (GCC) only gallery and is located in Batavia, New York, United States. The gallery is located in GCC's Center for the Arts, to the east of the Stuart Steiner Theatre lobby. The Roz Steiner Gallery opened in spring 2011. While the Steiner Gallery does not house a permanent collection, it typically features three professional exhibitions and two student-work exhibitions each academic year. The gallery was financed with funding from the State University of New York Construction Fund, and gifts from the Genesee Community College Foundation and Genesee Community College Association.

Media
GCC also has a radio station called The Music. It can be heard on 90.7 FM and online. It broadcasts to an approximately 25 mi radius of the school.

title: Genesee Community College


text:
Hachaliah Bailey

Hachaliah Lyman Bailey (pronounced heck-a-LIE-uh; July 31, 1775 – September 2, 1845) was the founder of one of America's earliest circuses. In 1808, he purchased an Indian elephant which he named "Old Bet" and which was one of the first such animals to reach America. With "Old Bet" as its main attraction, he formed the Bailey Circus, which also included a trained dog, several pigs, a horse and four wagons. This was the impetus for what in time evolved into the Bailey component of what became the Ringling Bros. and Barnum & Bailey Circus.

Between 1820 and 1825, Bailey built the Elephant Hotel in Somers, New York. The hotel was designated a National Historic Landmark in 2005. Bailey also served two terms in the New York State legislature.

In 1837, Bailey sold the hotel and moved to Northern Virginia, bought the land surrounding the intersection of Leesburg Pike and Columbia Pike in Fairfax County, Virginia near Falls Church, Virginia, and gave Bailey's Crossroads his name. The Crossroads then became the winter quarters for his circus.

In 1845 Hachaliah returned to Somers for a visit and died from the kick of a horse while there. He is buried in Somers' Ivandell Cemetery.

Several of the next generation of Baileys performed in circuses. Hachaliah Bailey served as a role model to a young P.T. Barnum, who wrote of meeting him when Hachaliah visited Barnum's store in Bethel, Connecticut. In 1888, Barnum lent his name to a partnership with James Anthony Bailey, who had adopted the surname of Frederick Bailey, a nephew of Hachaliah's, to form the Barnum and Bailey Circus.

Early career
Hachaliah Bailey was born in the small village of Somers, New York on July 31, 1775. His parents were James Bailey and Anne Brown Bailey. Hachaliah was one of six children, Mary Bailey, Stephen Bailey, Lewis Bailey, Jane Bailey and Anna Bailey Owens.

Like his father, Hachaliah became a farmer where he farmed land and raised cattle. Hachaliah married Mary Purdy and they had five children. Hachaliah Bailey was also known for finding other ways to make an income. He became one of the directors of the Croton Turnpike Company, this eventually turned into a toll road through the middle of Somers where it became a major route. This route was used to transport cattle to the Hudson. Another way Hachaliah made a profit was by becoming a part-owner of a sloop which was used to transport farm animals.

Hachaliah and many locals frequented a bar called the Bull Head Tavern. This is where Hachaliah bought his elephant Old Bet for only $1,000. Old Bet's name drew from Hachaliah's daughter Elizabeth whose nickname was Young Beth. Old Bet was the second elephant ever to be brought to the United States. Hachaliah brought the elephant to Hudson Valley in 1805 and then New York City in 1806. Old Bet was originally supposed to be used as a draft animal, however, it didn't take long for Hachaliah to realize the rising interest that Americans had for exotic animals. Hachaliah then used this intrigue and began traveling at night so no one could get a glimpse of the animal and he would charge 25 cents per person to see Old Bet.

Hachaliah then decided to showcase Old Bet in a small circus. After Hachaliah's neighbors saw the booming success the exotic creature brought to Hachaliah, most of his neighbors started buying and showcasing exotic animals. Soon after Somers became known for its intriguing animals. By 1808 Hachaliah took on two partners Benjamin Lent and Andrew Brunn each paying $1200 for one/third of the interest on Old Bet. Hachaliah also owned two more elephants after Old Bet was shot on tour by a local farmer who was angry with the amount of money and attention that was being spent on an elephant. Hachaliah then memorialized Old Bet by creating the Elephant Hotel and building a statue in her honor.

Marriages and children
Hachaliah Bailey married his wife Mary Purdy when she was fourteen years old and he was twenty-three years old. Together they had five children:
 * Calista Bailey (1800-1879)
 * Lewis Bailey (1803-1870)
 * Jane Bailey (1808-1882)
 * Joseph Turk Bailey (1810-1881)
 * Stephen Bailey (1814-1863)

Hachaliah Bailey then would split with Mary and later marry his wife Ruth Ferris Bailey where they had no children.

title: Hachaliah Bailey


text:
Port of Houston

The Port of Houston is one of the world's largest ports and serves the metropolitan area of Houston, Texas. The port is a 50 mi complex of diversified public and private facilities located a few hours' sailing time from the Gulf of Mexico. Located in the fourth-largest city in the United States, it is the busiest port in the U.S. in terms of foreign tonnage and the busiest in the U.S. in terms of overall tonnage. Though originally the port's terminals were primarily within the Houston city limits, the port has expanded to such a degree that today it has facilities in multiple communities in the surrounding area. In particular the port's busiest terminal, the Barbours Cut Terminal, is located in Morgan's Point.

The Port of Houston is a cooperative entity consisting of both the port authority, which operates the major terminals along the Houston Ship Channel, and more than 150 private companies situated along Buffalo Bayou and Galveston Bay. Many petroleum corporations have built refineries along the channel where they are partially protected from the threat of major storms in the Gulf of Mexico. The petrochemical complex associated with the Port of Houston is one of the largest in the world.

History
The original Port of Houston was located at the confluence of Buffalo Bayou and White Oak Bayou in downtown Houston by the University of Houston–Downtown. This area is called "Allen's Landing" and is now a park. It is the birthplace of the City of Houston.

Shipping points grew at multiple locations on Buffalo Bayou including the port of Harrisburg (now part of Houston) and the docks on the Allen Ranch. By the end of the 19th century Buffalo Bayou had become a major shipping channel with traffic beginning to rival Galveston.

The citizens of Harris County approved creation of the modern port in 1909, believing that an inland port would better serve the region after the destructive Galveston Hurricane of 1900. President Woodrow Wilson officially opened the port to traffic as the World Port of Houston and Buffalo Bayou on November 10, 1914. In the 1930s the Port became the focus of labor conflict, with sometimes intense battles between strikers and authorities, during the 1935 Gulf Coast longshoremen's strike and the 1936 Gulf Coast maritime workers' strike among other incidents.

In 1911, there was a campaign persuading voters to approve a $1.25 million bond to raise money for dredging the waterway. The campaign was successful and voters approved the bond issuance and creation of the Harris County Houston Ship Channel Navigation District that is called Port of Houston Authority (POHA) today.

Early supporters would prove to be correct; the port has grown to be one of the world's largest. By 1961, it was already among the busiest ports in the US. In 1977 the Port of Houston opened the Barbours Cut Terminal, Texas' first cargo container terminal, at Morgan's Point. This new terminal, in the Bay Area, quickly became the port's most important terminal. The opening of the Bayport Terminal in 2006 further extended the port authority's reach outside the city of Houston.

The port today
Approximately 215 e6ST of cargo moved through the Port in 2005, most of which is petroleum related. The Port has two separate terminals dedicated to the handling of cargo containers: Barbours Cut (at Morgan's Point), and Bayport (in Pasadena, opened in October 2006). The Barbours Cut terminal was, in fact, the port's first terminal specifically designed for these shipments. Additional general cargo terminals include Turning Basin, Jacintoport, Woodhouse, and Care.

The Port Authority offers a 90-minute free cruise aboard the M/V Sam Houston, details of which can be found on its website. Since the Houston Ship Channel is closed to recreational traffic, this is the only means by which the general public can view port operations, and thus the tours are highly popular.

Most Volkswagen (and Audi) automobiles sold in North America pass through the port of Houston.

The Port is operated by the Port of Houston Authority, an independent political subdivision of the State of Texas governed by a seven-member commission. The City of Houston and the Harris County Commissioners Court each appoint two commissioners; these two governmental entities also jointly appoint the chairman of the Port Commission. The Harris County Mayors and Councils Association and the City of Pasadena each appoint one commissioner. Daily operations are overseen by an Executive Director who serves at the will of the Commission.

A renovation project for the Port's Turning Basin Terminal began in 2010 and is expected to take 10 years. The Turning Basin Terminal is a multipurpose complex with open wharves and 37 docks that are used for direct discharge and loading of breakbulk, containerized, project or heavy-lift cargoes. The goal of the renovation is to accommodate the increase in the transportation of steel, which increased more than 3.1 e6ST in the first nine months of 2011, up from 1.9 e6ST over the same period in the previous year.

Trade data

The Port of Houston is a major point of international trade for the United States. The following is the trade volume by world region reported by the Greater Houston Partnership as of 2006.
 * Europe 31%
 * Latin America 22%
 * Asia/Pacific Rim 15%
 * North America 13%
 * Middle East 7%
 * Africa 12%

Foreign Trade Zone
The Port of Houston Authority manages Foreign Trade Zone (FTZ) No. 84, which includes many privately owned and port-owned sites located throughout Houston and Harris County, Texas. The Houston Zone offers users special benefits. For example, customs duties on imported goods entering the FTZ can be delayed until the cargo is removed from the zone. No duty is paid if the merchandise is exported directly from the zone.

The following Sub Zones are a part of The Port of Houston FTZ No. 84:
 * 84E Gulf Coast Maritime
 * 84F Valero Refining Co.
 * 84H Shaffer, Inc.
 * 84I Tuboscope Vetco Int'l
 * 84J Shell Oil Co.
 * 84K Dril-Quip
 * 84L Tadiran Microwave Networks
 * 84M Hydril USA Manufacturing LLC
 * 84N Pasadena Refining System, Inc.
 * 84O ExxonMobil
 * 84P Houston Refining LP
 * 84Q Equistar Chemicals
 * 84R Michelin North America, Inc.

List of firsts
Despite being one of the youngest major ports in the world (the port reached its 100th birthday in 2014) it has already racked up an impressive list of firsts.

Notable firsts include:
 * First port to be built with federal funds and local matching funds, thus guaranteeing local support (every port since 1930 has had a local match requirement)
 * First direct shipment of cotton to Europe (November 1919 via the M/V Merry Mount)
 * First double-stack container train (1981)
 * When the Baytown Tunnel was removed in 1997 to allow deepening and widening of the Houston Ship Channel (it was replaced by the Fred Hartman Bridge), it was the largest tunnel so removed (35 ft diameter by 1,041 ft length) without closing the channel, losing time due to accidents, or impacting the navigational safety of the port.
 * First port to conduct air emissions testing of its off-road equipment (2000)
 * First port to meet ISO 14001 standards for environmental excellence (2002), and the first port to be recertified to ISO 14001 standards (2004)

In 1968 Texas historian Marilyn McAdams Sibley published The Port of Houston: A History.

title: Port of Houston


text:
Wikipedia:WikiProject United States regions/Hierarchy Discussion

This is part of a WikiProject. For optional guidelines on contributing see WikiProject U.S. Regions


text:
Niagara County Community College

Niagara County Community College (NCCC) is a public community college in Sanborn, New York. Founded in 1962, NCCC is sponsored by Niagara County and offers associate degrees as part of the State University of New York system. Dual admissions programs facilitate transfer to four-year colleges upon completion of the two-year degree programs. NCCC operates the Niagara Falls Culinary Institute as a remote campus within the former Rainbow Centre Factory Outlet in downtown Niagara Falls, New York.

History
The college's first campus opened on September 30, 1963 within a former Nabisco factory at 430 Buffalo Avenue in downtown Niagara Falls, New York.

The current campus opened on February 5, 1973 at the corner of New York State Route 31 and New York State Route 429 in the suburban community of Sanborn, New York. It was built on 287 acre of semi-wooded land, with eight interconnected buildings:

 * Ernest Notar Administration (Building A)
 * Business (Building B)
 * Science (Building C)
 * Henrietta G. Lewis Library (Building D)
 * Humanities & Social Sciences (Building E)
 * Arts & Media (Building F)
 * Student Center (Building G)
 * Athletics (Building H)

The school's library was named in honor of philanthropist Henrietta Grigg-Lewis on November 15, 2005 after her foundation donated $1 million for modernizing the facility.

On August 29, 2008, the college opened its first student housing complex featuring suite style units for 308 students.

The school's Niagara Falls Culinary Institute opened on September 28, 2012 within the former Rainbow Centre Factory Outlet in downtown Niagara Falls, New York.

Presidents

 * Ernest Notar, 1963–1975
 * Jack C. Watson, 1975–1979
 * Donald J. Donato, 1979–1989
 * Gerald L. Miller, 1989–1999
 * Antonette Cleveland, 1999–2002
 * James P. Klyczek, 2002–2017
 * William J. Murabito, 2017–2024
 * Lloyd A. Holmes, 2024–present

Athletics
NCCC athletic teams were first known as the Frontiersmen from 1962–1984, and then the Trailblazers from 1984–2010. They became the Thunderwolves in 2010, along with the introduction of mascot Tripp the Thunderwolf.

Eric Knuutila has coached wrestling at the college since 1973, producing four national champions including Rashad Evans.

The 1977–78 men's basketball team fell one game shy of a perfect season after losing the 1978 NJCAA Men's Division I Basketball Championship.

Alumni

 * Mark Bridges, costume designer
 * Rashad Evans, mixed martial artist
 * Eric Gansworth, novelist and poet
 * Rick Hockenos, former basketball player and coach
 * Richard Jacob, basketball coach
 * Sean Jamieson, former baseball player
 * Nancy J. King, member of the Maryland State Senate
 * George Maziarz, former member of the New York State Senate
 * Joe Micon, former member of the Indiana House of Representatives

Faculty

 * Ray Hall, basketball coach
 * Rich Kilgour, lacrosse coach
 * Yu Liu, professor
 * Don Luce, professor

title: Niagara County Community College


text:
Fence lizard

A Fence lizard can be any of several species of spiny lizard (genus Sceloporus), especially:

 * The eastern fence lizard or northern fence lizard, Sceloporus undulatus
 * The western fence lizard, Sceloporus occidentalis

Note that there are many other species in the Spiny Lizard genus, Sceloporus.

title: Fence lizard


text:
Bortom det blå

Bortom det blå is an album by Swedish singer Lisa Ekdahl. It is entirely in the Swedish language.

Track listing

 * 1) Bortom det blå
 * 2) Gå dit ifall du minns
 * 3) Två lyckliga dårar
 * 4) Jag behöver inget mer
 * 5) Vi tillhör varann
 * 6) Sakta sakta
 * 7) Jag vill bara vara
 * 8) Du var inte där för mig
 * 9) Hyenorna skrattade gamarna
 * 10) Genom dig ser jag ljuset
 * 11) Cirklar
 * 12) Vill ha dig kvar
 * 13) Tänk inte mera
 * 14) Natten skyddar de älskande

title: Bortom det blå


text:
Gaines Township

Gaines Township may refer to the following places in the United States:

 * Gaines Township, Genesee County, Michigan
 * Gaines Township, Kent County, Michigan
 * Gaines Township, Pennsylvania

title: Gaines Township


text:
Powerball

Powerball is an American lottery game offered by 45 states, the District of Columbia, Puerto Rico and the U.S. Virgin Islands, and overseen by the Multi-State Lottery Association (MUSL), which also manages other large jackpot games such as the Mega Millions. Drawings are held three times weekly on Mondays, Wednesdays, and Saturdays at 10:59 p.m. Eastern Time, at the Florida Lottery's headquarters in Tallahassee.

The winning numbers are made up of five "white balls" from a matrix of 69 and one "Powerball" from a matrix of 26, resulting in jackpot odds of 1 in 292,201,338 per play. Each play costs two dollars, but players in some states can add Power Play, which allows players to increase the payout of their winning numbers, or Double Play, which allows players to use their numbers in a second, concurrent drawing with a different prize pool, each for an additional dollar. The official cutoff for ticket sales is 10:00 p.m. Eastern Time; some lotteries cut off sales earlier. Powerball's minimum jackpot starts at $20 million annuity. Powerball jackpot winners have the choice of taking the annuity or lump sum cash prize. The annuity is paid in 30 graduated installments over 29 years with each annuity payment increasing 5% annually, whereas the lump sum payment, with a cash value of about half of the advertised jackpot, is paid all at once.

Powerball is known for producing some of the largest lottery jackpots in history, including the record-breaking $2.1 billion jackpot won by a ticket purchased in Altadena, California, in 2022.

Mega Millions and Powerball
Alabama, Alaska, Hawaii, Nevada, and Utah do not have state lotteries.

1988 precursor: Lotto America
Powerball's predecessor began in 1988; the multi-state game was known as Lotto America. The game, and name, were changed to Powerball on April 19, 1992; its first drawing was held April 22.

Dr. Edward J. Stanek was president of the Iowa Lottery, and along with Steve Caputo, invented the Powerball game.

1992: Powerball begins
When it was launched in 1992 Powerball became the first game to use two drums. Using two drums to draw numbers from, offers more manipulation by simultaneously allowing low jackpot odds, numerous prize levels and high overall odds of winning (as explained later, a ticket can win by matching only one number). The two-drum concept was suggested by Steve Caputo of the Oregon Lottery. The two-drum concept has since been used by The Big Game (now Mega Millions) in the US, Australia's Powerball, Thunderball in the UK, Eurojackpot and EuroMillions.

Through 2008, Powerball drawings usually were held at Screenscape Studios in West Des Moines, Iowa. The drawings' host was longtime Iowa radio personality Mike Pace, who had hosted MUSL drawings since Lotto America began in 1988. In 1996, Powerball went "on the road" for the first time, holding five remote drawings at the Summer Olympics in Atlanta. A few weeks later, Georgia became the only jurisdiction to leave Powerball (Maine, which joined MUSL in 1990, left when Powerball began). In August 1996, Georgia joined the then-new The Big Game, then the other major U.S. lottery group. It planned to sell tickets for both games for the rest of 1996; but within days Georgia was removed from MUSL, not to return until the 2010 cross-sell expansion.

On November 2, 1997, the annuity was changed from 20 to 25 yearly payments; the cash option was added.

In 1998, Florida was given permission by its government to participate in a multi-state game. It was set to offer Powerball; but in early 1999, new governor Jeb Bush prevented Florida from joining since he believed Powerball would hurt the existing Florida Lottery games. In 2008, Governor Charlie Crist allowed Florida to join MUSL on January 4, 2009.

2001: Introduction of Power Play
On March 7, 2001, an optional multiplier (called Power Play) was added, allowing players to multiply non-jackpot winnings by up to five by paying an extra $1 per game. A wheel was introduced to select the Power Play multiplier for each drawing (the next year, the 1x was removed from the Power Play wheel).

2009: Move to Florida
With the start of Powerball sales in Florida on January 4, 2009 (with its first drawing on January 7), the matrices changed to 5/59 + 1/39 (adding four white ball numbers and dropping three red balls). This changed the jackpot probability from 1:146 million to 1:195 million; the overall probability became 1:35.

Based on statistical projections, the average jackpot win increased from $95 million to $141 million. Over 3.5 million additional prizes were expected to be won yearly due to the change in probability. The starting jackpot increased to $20 million, with minimum rollovers of $5 million. The jackpot contribution increased from 30.3% to 32.5% of total sales. The Power Play option was modified; second prize, usually $200,000, was given an automatic 5x multiplier, making the 5+0 prize $1 million cash. The bonus second prize if the jackpot exceeded its previous record by $25 million, triggered only twice, was eliminated with the 2012 format change.

The conditions for Florida joining Powerball included a move of the live drawings from Iowa to Universal Studios in Orlando. The three hosts rotating announcing duties from Universal Studios were Tracy Wiu, Elizabeth Hart and Scott Adams (MUSL headquarters remained in Iowa, where its other draws are held). The wheel that was used to determine the Power Play multiplier was retired when the drawings moved to Florida; a random number generator (RNG) was used until the 2012 format change.

Arkansas became the 33rd MUSL member on October 31, 2009, the last to join before the 2010 cross-sell expansion. The Ohio Lottery added Powerball on April 16, 2010, it joined Mega Millions (along with New York) years earlier, when The Big Game added Mega Millions to its name.

2010: Cross-sell expansion
In March 2009, it was reported that New Jersey, already a Mega Millions member, sought permission to join Powerball. Shortly after, discussions were revealed about allowing each US lottery to offer both games. On October 13, the Mega Millions consortium and MUSL reached an agreement in principle to cross-sell Mega Millions and Powerball. In November, MUSL signed an agreement to start streaming Powerball drawings online.

On January 31, 2010, the date of the cross-sell expansion, Mega Millions and MUSL each added lotteries; eight Powerball members added Mega Millions by May. The Montana Lottery joined Mega Millions on March 1, 2010. Nebraska added Mega Millions on March 20, 2010, Oregon followed on March 28, 2010, Arizona joined Mega Millions on April 18, 2010, Maine added Mega Millions on May 9, 2010, Colorado and South Dakota joined Mega Millions on May 16, 2010. The U.S. Virgin Islands joined Mega Millions in October 2010.

Before the agreement, the only places that sold both Mega Millions and Powerball tickets were retailers straddling a border; one retailer on the Sharon, Pennsylvania/Masury, Ohio, border sold both Mega Millions (via the Ohio Lottery) and Powerball (Pennsylvania) before the agreement and continued to be the only retailer to sell tickets for both lotteries.

Illinois joining Powerball on the expansion date, it became the second multi-jurisdictional lottery game (after Mega Millions, which Illinois already participated in) whose drawings were carried nationally. Both games' drawings were simulcast via Chicago cable superstation WGN-TV through its national WGN America feed. WGN-TV aired Illinois Lottery drawings nationally from 1992 to 2015 after acquiring broadcast rights from Chicago's Fox owned-and-operated station WFLD in 1988, which took the rights from WGN-TV in 1987. Powerball drawings were aired on WGN-TV and WGN America on Wednesday and Saturday immediately following the station's 9:00 p.m. (Central Time) newscast, with the Mega Millions drawings being aired Tue and Fri evenings after the newscast. WGN served as a default carrier of Mega Millions or Powerball where no local television station carries either multi-jurisdictional lottery's drawings.

On March 13, 2010, New Jersey became the first previous Mega Millions-only member (just before the cross-selling expansion) to produce a jackpot-winning Powerball ticket. It was worth over $211 million in annuity payments; it was sold in Morris Plains. On May 28, 2010, North Carolina became the first previous MUSL member (just before the cross-selling expansion) to produce a jackpot-winning Mega Millions ticket; that jackpot was $12 million (annuity).

On June 2, 2010, Ohio won a Powerball jackpot; it became the first lottery selling either Mega Millions or Powerball (when 2010 began) to provide a jackpot-winning ticket for its newer game. The ticket was worth a $261 million annuity; it was sold in Sunbury. Ohio's second Powerball jackpot-winning ticket, sold for the June 23, 2010, drawing, was part of another first; since Montana also provided a jackpot winner for that drawing, it was the first time a jackpot was shared through lotteries which sold competing games before the cross-selling expansion, as Montana sold only Powerball before the expansion date.

2012 format change
On January 15, 2012, the price of each basic Powerball play doubled to $2, while PowerPlay games became $3; the minimum jackpot doubled to $40 million. A non-jackpot play matching the five white balls won $1 million. The red balls decreased from 39 to 35. The drawings were moved from Universal Studios Orlando to the Florida Lottery's studios in Tallahassee. Sam Arlen began his tenure as host in 2012, with Laura W. Johnson served as Arlen’s co-host.

These changes were made to increase the frequency of nine-figure jackpots; a Powerball spokesperson believed a $500 million jackpot was feasible (it became a reality within the year, ) and that the first $1 billion jackpot in US history would occur by 2012 (though it didn't occur until 4 years later.) Less than three months after the Powerball changes, Mega Millions' jackpot reached $656,000,000 despite remaining a $1-per-play game. The random Power Play multiplier was retired for a set, fixed dollar amount payout. The $25 million rollover "cap" (creating larger 5+0 prizes) was eliminated.

California joined on April 8, 2013; it has never offered the Power Play option, as all payouts in California Lottery drawing games, by law, are parimutuel. Mega Millions, which became available in California in 2005, offers its Megaplier in its other 45 jurisdictions.

On January 22, 2014, the variable Power Play option returned (2x-5x) for multiplying non-jackpot prizes.

In October 2014, Puerto Rico joined Powerball; the first mainly Spanish-speaking jurisdiction offering the game; as of 2016 it had not joined Mega Millions.

2015 format change
On October 4, 2015, the Powerball format changed again; the white-ball pool increased from 59 to 69 while the Powerball pool decreased from 35 to 26. While this improved the chance of winning any prize to 1 in 24, it also lengthened the jackpot odds to 1 in 292,201,338. The 4+1 prize became $50,000; the 10x PowerPlay became available in drawings with a jackpot of under $150 million. Three months later, the format produced a $1.5 billion jackpot, double the previous record, after 20 consecutive rollovers.

2020 COVID-19 adjustments and 2021 provisional removal by Idaho
On April 2, 2020, the Powerball starting jackpot amount was temporarily reset from $40 million to $20 million with the annuity option, with at least a $2 million rollover for each drawing without a jackpot winner, due to the COVID-19 pandemic in the United States. This was done to enforce social distancing and discourage crowding of selling venues for large jackpots, and to account for lower interest rates.

On March 10, 2021, following Powerball's move to expand its operations in Australia later that year and in the United Kingdom in 2022, the Idaho Legislature voted overwhelmingly to end the state's participation in the lottery after more than 30 years. State lawmakers cited fears of outside revenue being generated from the foreign involvement as reasons behind the vote. The removal would have taken place when non-US jurisdictions were allowed to join in August 2021, but was rendered moot when the expansion was put on hold.

2021 addition of Monday drawings and introduction of Double Play
On May 23, 2021, Powerball announced that starting on August 23, 2021, draws would occur on Monday, in addition to Wednesday and Saturday. Along with the new Monday drawings, a new Double Play option was added for 12 states (including host state Florida) and Puerto Rico, allowing players to reuse their Powerball numbers in a second drawing (held 30 minutes after the main drawing) for a chance to win a $10 million top prize by paying an extra $1 per game.

Due to technical difficulties that occurred before the start of the new draw schedule, the first ever Monday draw did not occur on its usual time meaning that the first Monday draw did not happen as planned for the group that operates the game. Michele Lyles became the third regular hostess of the Powerball drawings serving alongside Arlen and Johnson. Randy Trainor originally served as a substitute host if neither Arlen, Johnson or Lyles are available. In 2024, Trainor was promoted to regular host while Arlen was demoted to substitute host.

2022 delay
The scheduled November 7, 2022, drawing of the record-breaking $2.04B jackpot was delayed due to incomplete security protocols regarding ticket sales at an unnamed lottery until the next day  at 8:59 a.m. EST. Prior to the November 7 delay, there had been delays on April 9 and October 19th and on March 16, 2022. Days after the drawing was completed for the $2.04 Billion Powerball Jackpot, the Minnesota Lottery announced later that week that it had been responsible for the delay. Lottery officials there said there was a technical problem with the communication system that prevented the drawing from happening.

Basic game
The minimum Powerball bet is $2. In each game, players select five numbers from a set of 69 white balls and one number from 26 red Powerballs; the red ball number can be the same as one of the white balls. The drawing order of the five white balls is irrelevant; all tickets show the white ball numbers in ascending order. Players cannot use the drawn Powerball to match one of their white numbers, or vice versa. Players can select their own numbers, or have the terminal pseudorandomly select the numbers (the name for this varies by state, but most are called some variation of "quick pick", "easy pick", etc.).

In each drawing, winning numbers are selected using two ball machines: one containing the white balls and the other containing the red Powerballs. Five white balls are drawn from the first machine and the red ball from the second machine. Games matching at least three white balls or the red Powerball win.

Two identical machines are used for each drawing, randomly selected from four sets. The model of machine used is the Halogen, manufactured by Smartplay International of Edgewater Park, New Jersey. There are eight ball sets (four of each color); one set of each color is randomly selected before a drawing. The balls are mixed by a turntable at the bottom of the machine that propels the balls around the chamber. When the machine selects a ball, the turntable slows to catch it, sends it up the shaft, and then down the rail to the display. (The Florida Lottery was considering switching to a random number generator in 2019 for its in-state drawings; it is unknown whether Powerball was affected.) If the onsite location is unavailable, as was the case during Hurricane Michael, a backup machine is located at MUSL headquarters in Iowa. The drawings are supervised by Carroll & Company, CPA’s.

The double matrices and probabilities in the game's history:

†Power Play was introduced in 2001.

‡10× available if jackpot is under $150 million.

While Mega Millions and Powerball each have similar jackpot odds despite having a different double matrix (Mega Millions is 5/70 + 1/25), since Powerball is $2 per play, it now takes $584,402,676 (not counting Power Play side bets) on average to produce a jackpot-winning ticket.

Power Play
For an additional $1 per game, a player may activate the Power Play option. Activating it multiplies lower-tier winnings (base prize $50,000 or less) by up to 5, or 10 when the jackpot is under $150 million. Power Play is drawn separately from the 6 numbers. The 5+0 prize is automatically doubled to $2 million if Power Play is activated.

The dilemma for players is whether to maximize the chance at the jackpot or increase lower-tier winnings. If a player selects a fixed amount of money to spend on tickets at a certain time, the player will give up one guess of the winning set of numbers every two times this player activates Power Play in respect of one of the purchased tickets.

Power Play, when it began in 2001, was drawn with a special wheel. In 2006 and 2007, MUSL replaced one of the 5× spaces on the Power Play wheel with a 10×. During each month-long promotion, MUSL guaranteed that there would be at least one drawing with a 10× multiplier. The promotion returned in 2008; the ball landed in the 10× space twice. After being absent in 2009, the 10× multiplier returned in May 2010 (after the Power Play drawing was changed to RNG.) The promotion was extended for the only time, as the 10× multiplier was not drawn until June 12, 2010. The second prize 5× guarantee continued; the 10× applied to all non-jackpot prizes, as in previous promotions.

Power Play's success has led to similar multipliers in other games, most notably Megaplier, available through all Mega Millions members except California. The 2012 Powerball changes resulted in all eight lower-tier levels having "fixed" Power Play prizes.

On January 19, 2014, PowerPlay was modified; it used 30 balls with the following distribution:
 * 2× (15)
 * 3× (9)
 * 4×/5×: 3 each

On October 4, 2015, PowerPlay changed again, using 42 or 43† balls as follows:
 * 2× (24)
 * 3× (13)
 * 4× (3)
 * 5× (2)
 * 10× (1)†

† 10× available when jackpot is under $150 million.

Double Play
A Double Play option is available in 14 states and Puerto Rico. For an additional $1, players may reuse their Powerball numbers in a second drawing with a different prize structure held approximately 30 minutes after the main drawing. The Double Play top prize is worth $10 million, which stays as a fixed amount in every drawing, even if there's no winner. Unlike the main drawing's increasing jackpots, the $10 million top prize in Double Play is a not annuitized. Thus, a player is able to receive a cash lump sum worth $10 million, subject to state and federal taxes. A Powerball ticket with the Double Play option costs $3. If both the Power Play and Double Play options are chosen, then the total cost is $4.

Prizes and odds
Payouts as of October 7, 2015:

Overall odds of winning a prize are 1 in 24.87.

Former prizes/odds (January 19, 2014 – October 3, 2015):

Payouts and odds for Double Play:

Overall odds of winning were 1 in 31.85.

All non-jackpot prizes are fixed amounts (except in California); they may be reduced and paid on a parimutuel basis, with each member paying differing amounts for the same prize tier, if the liability exceeds the funds in the prize pool for any game member.

Jackpot accumulation and payment options
Jackpot winners have the option of receiving their prize in cash (in two installments; one from the winning jurisdiction, then the combined funds from the other members) or as a graduated annuity paid in 30 yearly installments. The pre-tax amount of the first annuity payment is approximately 1.505% of the jackpot amount. Each annuity payment is 5% higher than in the previous year to adjust for inflation.

The advertised estimated jackpot represents the total payments that would be paid to jackpot winner(s) should they accept the annuity option. This estimate is based on the funds accumulated in the jackpot pool rolled over from prior drawings, expected sales for the next drawing, and market interest rates for the securities that would be used to fund the annuity. The estimated jackpot usually is 32.5% of the (non–Power Play) revenue of each base ($1) play, submitted by game members to accumulate into a prize pool to fund the jackpot. If the jackpot is not won in a particular drawing, the prize pool carries over to the next drawing, accumulating until there is a jackpot winner. This prize pool is the cash that is paid to a jackpot winner if they choose cash. If the winner chooses the annuity, current market rates are used to calculate the graduated payment schedule and the initial installment is paid. The remaining funds in the prize pool are invested to generate the income required to fund the remaining installments. If there are multiple jackpot winners for a drawing, the jackpot prize pool is divided equally for all such plays.

MUSL and its members accept all investment risk and are contractually obligated and liable to the winner to make all scheduled payments to annuity winners. If a jackpot ticket is not claimed, the funds in the prize pool are returned to members in proportion to the amount they contributed to the prize pool. The members have different rules regulating how unclaimed funds are used.

When the Powerball jackpot is won, the next jackpot is guaranteed to be $20 million (annuity). If a jackpot is not won, the minimum rollover is $10 million. The cash in the jackpot pool is guaranteed to be the current value of the annuity. If revenue from ticket sales falls below expectations, game members must contribute additional funds to the jackpot pool to cover the shortage; the most likely scenario where this can occur is if the jackpot is won in consecutive drawings.

Because of the COVID-19 pandemic in the United States and resulting drop in ticket sales plus the falling interest rates on which annuity prizes were based, Powerball administrators reduced the minimum starting jackpot to $20 million, and the minimum increase to $2 million when the previous jackpot is not won.

Claiming prizes
A winning ticket must be claimed in the jurisdiction in which it was purchased, regardless of residence. The minimum age to play Powerball is 18, except in Nebraska (19), and Arizona, Iowa, Louisiana and Mississippi (21).

Generally, Powerball players do not have to choose cash or annuity unless they win a jackpot (then they usually have 60 days to choose). Exceptions include Florida and Missouri; the 60-day "clock" starts with the drawing, so a jackpot winner who wishes to take the cash option needs to make immediate plans to claim their prize. New Jersey and Texas require the cash/annuity choice to be made when playing; in New Jersey, an annuity ticket can be changed to cash after winning, while in Texas, the choice is binding. (When the cash option was introduced in 1997, all Powerball players had to make the choice when playing. This regulation was phased out by 1999.) All Powerball prizes must be claimed within a period ranging from 90 days to a year, depending on where the ticket was bought.

Powerball winnings in California are subject to federal income tax only. Conversely, Powerball winnings in Puerto Rico are not subject to federal income tax, only local tax. There is no state income tax in Florida, South Dakota, Texas, Washington and Wyoming, and only on interest and dividends in New Hampshire and Tennessee. In all other states, winnings are subject to both federal income tax and that state's income tax, provided the winning ticket was purchased in the winner's home state. Winnings from tickets purchased outside of one's home state may be subject to the income tax laws of both states (with possible credit based on the two jurisdictions), though this depends on the states in question.

Secondary prizes
Unlike the jackpot pool, other prizes are the responsibility and liability of each participating lottery. All revenue for Powerball ticket sales not used for jackpots is retained by each member; none of this revenue is shared with other lotteries. Members are liable only for the payment of secondary prizes sold there.

Since the secondary prizes are defined in fixed amounts (except in California), if the liability for a given prize level exceed the funds in the prize pool for that level the amount of the prize may be reduced and the prize pool be distributed on a parimutuel basis and result in a prize lower than the fixed amounts given in the prize tables. Because the secondary prize pools are calculated independently, it is possible lower-tier prizes will differ among the game members.

Notable wins
Over time, the size of jackpots has increased because of the higher ticket price, the larger number of states participating, and the reduced odds of winning.

Because the quoted jackpot amount is an annuity of 30 graduated annual payments, its cash value relative to the annuity fluctuates. The actual ratio depends on projected interest rates and other factors. MUSL starts with the cash value, built from a percentage of sales, and then calculates the advertised jackpot amount from that value, based on the average costs of the three best securities bids.

On December 25, 2002, the president of a construction firm in Putnam County, West Virginia, won $314.9 million ($ million today), then a new record for a single ticket in an American lottery. The winner chose the cash option of $170 million, receiving approximately $83 million after West Virginia and Federal withholdings.

On October 19, 2005, a family from Jacksonville, Oregon, won $340 million ($ million today). The winners chose the cash payout of $164.4 million (before withholdings), smaller than a previous winners cash payout in 2002 due to a then-recent change in the annuity structure.

A jackpot of $365 million ($ million today) was won on February 18, 2006, by one ticket in Nebraska. It was shared by eight people who worked at a meatpacking plant. The group chose the cash option of approximately $177.3 million, before withholdings.

On August 25, 2007, a jackpot worth $314 million ($ million today) was won by a retired auto worker from Ohio; that ticket was bought in Richmond, Indiana, a community that had previously sold a jackpot-winning ticket of over $200 million.

In November 2011, three Greenwich, Connecticut, financial executives shared a jackpot of $254.2 million ($ million today), the largest prize on a Connecticut-bought ticket. Choosing the cash option, the men split nearly $104 million after withholdings. The jackpot, at the time, was the 12th largest in Powerball history.

On May 18, 2013, the world's largest one-ticket jackpot at the time, an annuity of approximately $590.5 million ($ million today), was won by a Powerball ticket sold in Zephyrhills, Florida. On June 5, Florida Lottery officials announced the winner who purchased the "quick pick" ticket at a Publix supermarket. The winner chose the cash option of approximately $370.8 million, before Federal withholding; Florida does not have a state income tax.

On January 13, 2016, the world's largest lottery jackpot at the time, an annuity of approximately $1.586 billion was split among three Powerball tickets in Chino Hills, California, Melbourne Beach, Florida, and Munford, Tennessee, each worth $528.8 million. Since there is no income tax in Florida or Tennessee (and California does not tax lottery winnings), the cash option after Federal withholdings is $187.2 million each.

On August 23, 2017, the owner of a Powerball ticket sold in Chicopee, Massachusetts, won more than $750 million, one of the largest prizes in the lottery's history. A mother of two from Massachusetts was the lucky winner.

On March 27, 2019, a single ticket purchased in Wisconsin was the only winner of a $768.4 million ($477 million cash) Powerball jackpot, the third largest in U.S. lottery history. The winner of the enormous prize was identified as a 24-year-old Wisconsin man.

On November 8, 2022, a single ticket purchased in Altadena, California, was the only winner of a $2.04 billion Powerball jackpot, the largest in U.S. lottery history. The prize was claimed on February 14, 2023. The winner was revealed as Edwin Castro. He opted to collect his prize as a lump sum payment of $997.6 million. He purchased his ticket at Joe's Service Center in Altadena, which received a $1 million reward from the Powerball operator for selling the winning ticket.

On July 19, 2023, a single ticket purchased in Los Angeles, California, was the only winner of a $1.08 billion ($558.1 million cash) Powerball jackpot.

On October 11, 2023, a single ticket purchased in Frazier Park, California, was the only winner of a $1.76 billion ($774.1 million cash) Powerball jackpot, the second-largest in U.S lottery history.

Fortune cookie payout
The Powerball drawing on March 30, 2005, produced 110 second-prize winners. The total payout to these winners was $19.4 million, with 89 winners receiving $100,000 each, while the other 21 winners received $500,000 each as they were Power Play selections.

MUSL officials initially suspected fraud or a reporting error. However, all 110 winners had played numbers from fortune cookies made by Wonton Food Inc. of Long Island City, New York. The factory had printed the numbers "22, 28, 32, 33, 39, 40" on thousands of fortunes. The "40" in the fortune did not match the Powerball number, 42. No employees of Wonton Food played those numbers. At the time, the closest game member was Connecticut. Because the ticket holders had won as result of a coincidence rather than foul play, the payouts were made.

Had the fortune cookie given 42 as the Powerball number, these winners would have shared the $25 million jackpot: each $227,272 annuity or $122,727 cash (before withholdings). The fortune on the cookie read: "All the preparation you've done will finally be paying off."

Computers and slot machines
In 2006, WMS Gaming released a range of slot machines under the Powerball brand name. In 2007, the Oregon Lottery released a Windows Sidebar gadget that displays the winning numbers for Powerball in real-time. The gadget also provides large jackpot announcements.

The New York Lottery introduced a Powerball scratchcard in 2010. Five winning numbers plus a Powerball were printed across the top of the card, with 12 opportunities to match. Matching the winning numbers or the Powerball won. The top prize was $1 million (annuity); unlike actual Powerball, there was no cash option for the top prize.

title: Powerball


text:
Frank O'Hara

Francis Russell "Frank" O'Hara (March 27, 1926 – July 25, 1966) was an American writer, poet, and art critic. A curator at the Museum of Modern Art, O'Hara became prominent in New York City's art world. O'Hara is regarded as a leading figure in the New York School, an informal group of artists, writers, and musicians who drew inspiration from jazz, surrealism, abstract expressionism, action painting, and contemporary avant-garde art movements.

O'Hara's poetry is personal in tone and content, and has been described as sounding "like entries in a diary". Poet and critic Mark Doty has said O'Hara's poetry is "urbane, ironic, sometimes genuinely celebratory and often wildly funny" containing "material and associations alien to academic verse" such as "the camp icons of movie stars of the twenties and thirties, the daily landscape of social activity in Manhattan, jazz music, telephone calls from friends". O'Hara's writing sought to capture in his poetry the immediacy of life, feeling that poetry should be "between two persons instead of two pages."

The Collected Poems of Frank O'Hara edited by Donald Allen (Knopf, 1971), the first of several posthumous collections, shared the 1972 National Book Award for Poetry. Brad Gooch's City Poet is the first substantial biography on O'Hara.

Early life and education
Frank O'Hara, the son of Russell Joseph O'Hara and Katherine (née Broderick), was born on March 27, 1926, at Maryland General Hospital, Baltimore and grew up in Grafton, Massachusetts. He attended St. John's High School. He grew up believing his birthday was in June, when, in fact, he had been born in March—as his parents disguised his true date of birth because he had been conceived out of wedlock. He studied piano at the New England Conservatory in Boston from 1941 to 1944 and served in the U.S. Navy in the South Pacific and Japan as a sonarman on the destroyer USS Nicholas during World War II.

With the funding made available to veterans he attended Harvard University, where artist and writer Edward Gorey was his roommate. O'Hara was heavily influenced by visual art and by contemporary music, which was his first love (he remained a fine piano player all his life and would shock new partners by suddenly playing music by Sergei Rachmaninoff when visiting them). His favorite poets were Pierre Reverdy, Arthur Rimbaud, Stéphane Mallarmé, Boris Pasternak, and Vladimir Mayakovsky. While at Harvard, O'Hara met John Ashbery and began publishing poems in the Harvard Advocate. Despite his love of music, O'Hara changed his major and graduated from Harvard in 1950 with a degree in English.

He then attended the University of Michigan in Ann Arbor, where he won a Hopwood Award and, in 1951, received a master's degree in English.

Early career
In the autumn of 1951, O'Hara moved into an apartment in New York City with Joe LeSueur, who was his roommate and sometime lover for the next 11 years. It was during this time that he began teaching at The New School. O'Hara was active in the art world, working as a reviewer for ARTnews, and in 1960 was assistant curator of painting and sculpture exhibitions for the Museum of Modern Art. He was a friend of the artists Norman Bluhm, Mike Goldberg, Grace Hartigan, Alex Katz, Willem de Kooning, Joan Mitchell, and Larry Rivers.

Poetry
While O'Hara's poetry is generally autobiographical, it tends to make observations about his life in New York, rather than exploring his past. In his introduction to The Collected Poems of Frank O'Hara, Donald Allen says, "that Frank O'Hara tended to think of his poems as a record of his life is apparent in much of his work." O'Hara discussed this aspect of his poetry in a statement for Donald Allen's The New American Poetry:

"What is happening to me, allowing for lies and exaggerations which I try to avoid, goes into my poems. I don't think my experiences are clarified or made beautiful for myself or anyone else, they are just there in whatever form I can find them. . .My formal 'stance' is found at the crossroads where what I know and can't get meets what is left of that I know and can bear without hatred. . .It may be that poetry makes life's nebulous events tangible to me and restores their detail; or conversely that poetry brings forth the intangible quality of incidents which are all too concrete and circumstantial. Or each on specific occasions, or both all the time."

His initial time in the Navy, during his basic training at Sampson Naval Training Center, in upstate New York, along with earlier years at St. John's High School, began to shape a distinguished style of solitary observation that would later inform his poems. Immersion in regimented daily routine, first at Catholic school, then in the Navy, enabled him to separate himself from situations and make witty, often singularly perceptive commentary. Sometimes he cataloged it for use in later writing, or, perhaps more often, put it into letters. This skill at scrutinizing and recording amid the bustle and churn of daily life would later be one of the important aspects that shaped O'Hara as an urban poet, writing off the cuff.

Among his friends, O'Hara was known to treat poetry dismissively, as something to be done only in the moment. John Ashbery says he witnessed O'Hara "Dashing poems off at odd moments—in his office at the Museum of Modern Art, in the street at lunchtime, or even in a room full of people—he would then put them away in drawers and cartons and half forget them."

In the summer of 1951, O'Hara read a manifesto in The Kenyon Review written by the poet, novelist and anarchistic social critic Paul Goodman. In the essay, Goodman argues that the postwar American "advanced guard" writers must articulate the deep-seated, personal disquiet felt across the culture but left unvoiced. The essay encouraged O'Hara to write poetry that was embarrassing in its directness, and even seen as hostile to literary standards then in place. O'Hara's poetry began to erase poetry's cautious border between what is public and what is private.

In 1959, he wrote a mock manifesto (originally published in the magazine Yūgen in 1961) called Personism: A Manifesto, in which he explains his position on formal structure: "I don't ... like rhythm, assonance, all that stuff. You just go on your nerve. If someone's chasing you down the street with a knife you just run, you don't turn around and shout, 'Give it up! I was a track star for Mineola Prep.'" He says, in response to academic overemphasis on form, "As for measure and other technical apparatus, that's just common sense: if you're going to buy a pair of pants you want them to be tight enough so everyone will want to go to bed with you. There's nothing metaphysical about it." He claims that on August 27, 1959, while talking to LeRoi Jones, he founded a movement called Personism which may be "the death of literature as we know it."

He says,

"It does not have to do with personality or intimacy, far from it! But to give you a vague idea, one of its minimal aspects is to address itself to one person (other than the poet himself), thus evoking overtones of love without destroying love's life-giving vulgarity, and sustaining the poet's feelings toward the poem while preventing love from distracting him into feeling about the person."

His poetry shows the influence of abstract expressionism, surrealism, Russian poetry, and poets associated with French symbolism. Ashbery says, "The poetry that meant the most to him when he began writing was either French – Rimbaud, Mallarmé, the Surrealists: poets who speak the language of every day into the reader's dream – or Russian – Pasternak and especially Mayakovsky, for whom he picked up what James Schuyler has called the 'intimate yell.'" As part of the New York School of poetry, O'Hara to some degree encapsulated the compositional philosophy of New York School painters.

Ashbery says, "Frank O'Hara's concept of the poem as the chronicle of the creative act that produces it was strengthened by his intimate experience of Pollock's, Kline's, and de Kooning's great paintings of the late '40s and early '50s and of the imaginative realism of painters like Jane Freilicher and Larry Rivers."

O'Hara was also influenced by William Carlos Williams, so much so that he lists Williams (along with Hart Crane and Walt Whitman) as one of three poets who were "better than the movies." According to Marjorie Perloff in her book Frank O'Hara, Poet among Painters, he and Williams both use everyday language and simple statements split at irregular intervals. Perloff points out the similarities between O'Hara's "Autobiographia Literaria" and Williams's "Invocation and Conclusion". At the end of "Autobiographia Literaria", the speaker says, "And here I am, the/center of all beauty!/writing these poems!/Imagine!" Similarly, Williams at the end of "Invocation and Conclusion" says, "Now look at me!" These lines show a shared interest in the self as an individual who can only be himself in isolation. A similar idea is expressed in a line from Williams's "Danse Russe": "Who shall say I am not/ the happy genius of my household?"

Personal life
Frank O'Hara, who was gay, met Joe LeSueur in 1951, and the two maintained a relationship until 1965, living together on and off from 1955 to 1965.

From 1959 to 1963, the two lived at 441 East 9th Street in the East Village. Known throughout his life for his extreme sociability, passion, and warmth, O'Hara had hundreds of friends and lovers throughout his life, many from the New York art and poetry worlds. Soon after arriving in New York, he was employed at the Museum of Modern Art, selling postcards at the admissions desk, and began to write seriously.

O'Hara met longtime partner Vincent Warren in the summer of 1959. Warren, a Canadian ballet dancer, was the inspiration for several of O'Hara's poems, including "Poem (A la Recherche d'Gertrude Stein)", "Les Luths", "Poem (So many echoes in my head)", and "Having a Coke With You". Warren died on October 25, 2017, 51 years after O'Hara's death.

Death
In the early morning hours of July 24, 1966, O'Hara was struck by a jeep on the Fire Island beach, after the beach taxi in which he had been riding with a group of friends broke down in the dark. He died the next day at age 40 of a ruptured liver at Bayview Hospital in Mastic Beach, Long Island. Attempts to bring negligent homicide charges against the jeep's driver, 23-year-old Kenneth L. Ruzicka, were unsuccessful; many of O'Hara's friends felt the local police had conducted a lax investigation to protect one of their own locals. O'Hara was buried in Green River Cemetery on Long Island. The painter Larry Rivers, a longtime friend and lover, delivered one of the eulogies, along with Bill Berkson, Edwin Denby, and René d'Harnoncourt.

In music
In First Aid Kit's song "To A Poet", there is the lyric, "But Frank put it best when he said 'you can't plan on the heart'", a reference to O'Hara's poem, "My Heart".

In Martha's song "1967, I Miss You, I'm Lonely", the lyric, "I look at you and I am confident that I'd rather look at you than all the portraits in existence in the world, except possibly O'Hara by Grace Hartigan, " references both O'Hara's poem, "Having a Coke With You", and Grace Hartigan's portrait of O'Hara.

Rilo Kiley's 2004 album More Adventurous is titled after a line in O'Hara's poem "Meditations in an Emergency": "Each time my heart is broken it makes me feel more adventurous..." The title track references the same line: "I read with every broken heart, we should become more adventurous"

Frankie Cosmos's music is influenced by O'Hara's works, visible in two of her albums, Zentropy and Next Thing. Greta Kline has stated that her stage name derived from the poet.

The song Frank O'Hara by the band Sea Wolf (band) describes a relationship with the Poet.

In film
In the 2011 film Beastly, the lovestruck main characters read O'Hara's poem "Having a Coke with You" aloud to each other.

In literature
O'Hara is a minor character in William Boyd's 2002 novel Any Human Heart.

O'Hara's Lunch Poems is the basis of Paul Legault's Lunch Poems 2.

In television
In the season 1 episode of the HBO series Bored to Death, "The Case of the Missing Screenplay", the main character loses a screenplay written by Jim Jarmusch about the life of Frank O'Hara.

In the last episode of the series Normal People, based on Sally Rooney's novel of the same name, Connell's gift for Marianne's birthday is said to be a Frank O'Hara's collection of poetry.

Several episodes of Mad Men (season 2) reference O'Hara's collection of poetry, Meditations in an Emergency. The first episode shows a character reading from it over lunch in a bar (recalling O'Hara's 1964 collection Lunch Poems) as does the last episode, which uses the book's title as its episode title. In the twelfth episode, Don Draper finds his copy of Meditations in an Emergency in Anna Draper's home in California.

In plays
The poetry of Frank O'Hara features prominently in Rachel Bonds's 2017 play At the Old Place.

Landmarks
On June 10, 2014, a plaque was unveiled outside one of O'Hara's New York City residences, at 441 East Ninth Street. Poets Tony Towle, who inherited the apartment from O'Hara, and Edmund Berrigan read his works at the event.

Books published during his lifetime

 * A City Winter and Other Poems. Two Drawings by Larry Rivers. (New York: Tibor de Nagy Gallery Editions, 1951 [sic, i.e. 1952])
 * Oranges: 12 pastorals. (New York: Tibor de Nagy Gallery Editions, 1953; New York: Angel Hair Books, 1969)
 * Meditations in an Emergency. (New York: Grove Press, 1957; 1967)
 * Second Avenue. Cover drawing by Larry Rivers. (New York: Totem Press in Association with Corinth Books, 1960)
 * Odes. Prints by Michael Goldberg. (New York: Tiber Press, 1960)
 * Lunch Poems. (San Francisco, CA: City Lights Books, The Pocket Poets Series (No. 19), 1964)
 * Love Poems (Tentative Title). (New York: Tibor de Nagy Gallery Editions, 1965)

Posthumous works

 * In Memory of My Feelings, commemorative volume illustrated by 30 U.S. artists and edited by Bill Berkson (New York: The Museum of Modern Art, 1967)
 * The Collected Poems of Frank O'Hara. Edited by Donald Allen with an introduction by John Ashbery (1st ed. New York: Knopf, 1971; Berkeley: University of California Press, 1995) —shared the National Book Award with Howard Moss, Selected Poems
 * The Selected Poems of Frank O'Hara. Edited by Donald Allen (New York: Knopf, 1974; Vintage Books, 1974)
 * Standing Still and Walking in New York. Edited by Donald Allen (Bolinas, Calif: Grey Fox Press; Berkeley, Calif: distributed by Bookpeople, 1975)
 * Early Writing. Edited by Donald Allen (Bolinas, Calif: Grey Fox; Berkeley: distributed by Bookpeople, 1977)
 * Poems Retrieved. Edited by Donald Allen (Bolinas, Calif: Grey Fox Press; Berkeley, Calif: distributed by Bookpeople, 1977)
 * Selected Plays. Edited by Ron Padgett, Joan Simon, and Anne Waldman (1st ed. New York: Full Court Press, 1978)
 * Amorous Nightmares of Delay: Selected Plays. (Baltimore, MD: Johns Hopkins University Press, 1997)
 * Selected Poems. Edited by Mark Ford (New York: Knopf, 2008)
 * Poems Retrieved (City Lights, 2013)
 * Lunch Poems. 50th Anniversary Edition (City Lights, 2014)

Exhibitions

 * Jackson Pollock. (New York: George Braziller, Inc. 1959)
 * New Spanish painting and sculpture. (New York: The Museum of Modern Art, 1960)
 * Robert Motherwell: with selections from the artist's writings. by Frank O'Hara (New York: The Museum of Modern Art, 1965)
 * Nakian. (New York: The Museum of Modern Art, 1966)
 * Art Chronicles, 1954–1966. (New York: G. Braziller, 1975)

On O'Hara

 * Frank O'Hara: Poet Among Painters by Marjorie Perloff (New York: G. Braziller, 1977; 1st paperback ed. Austin: University of Texas Press, 1979; Chicago, IL: University of Chicago Press, with a new introduction, 1998)
 * Frank O'Hara by Alan Feldman (Boston: Twayne Publishers, 1979 ... frontispiece photo of Frank O'Hara c. by Richard Moore)
 * Frank O'Hara: A Comprehensive Bibliography by Alexander Smith, Jr. (New York: Garland, 1979; 2nd print. corrected, 1980)
 * Homage to Frank O'Hara. edited by Bill Berkson and Joe LeSueur, cover by Jane Freilicher (originally published as Big Sky 11/12 in April, 1978; rev. ed. Berkeley: Creative Arts Book Company, 1980)
 * Art with the touch of a poet: Frank O'Hara. exhibit companion compiled by Hildegard Cummings (Storrs, Conn. : The William Benton Museum of Art, University of Connecticut, 1983 ... January 24-March 13, 1983)
 * Frank O'Hara: To Be True To A City edited by Jim Elledge (Ann Arbor: University of Michigan Press, 1990)
 * City Poet: The Life and Times of Frank O'Hara by Brad Gooch (1st ed. New York: Knopf, 1993; New York: HarperPerennial, 1994)
 * In Memory of My Feelings: Frank O'Hara and American Art by Russell Ferguson (Los Angeles: The Museum of Contemporary Art, Los Angeles / University of California Press, 1999)
 * Hyperscapes in the Poetry of Frank O'Hara: Difference, Homosexuality, Topography by Hazel Smith (Liverpool University Press, Liverpool, 2000)
 * Digressions on Some Poems by Frank O'Hara by Joe LeSueur (New York: Farrar, Straus and Giroux, 2003).
 * Frank O'Hara: The Poetics of Coterie by Lytle Shaw (Iowa City: University of Iowa Press, 2006)
 * Also a Poet: Frank O'Hara, My Father, and Me by Ada Calhoun (New York: Grove Press, 2022)

Painting

 * Alice Neel, Frank O'Hara, (1960), 85.7 x 40.6 x 2.5 cm, National Portrait Gallery, Smithsonian Institution
 * Larry Rivers, O'Hara Nude with Boots (1954), 97" x 53", Larry Rivers Foundation
 * Jasper Johns, In Memory of My Feelings - Frank O'Hara (1961), 40 1/4" x 60", MCA, Chicago
 * Wynn Chamberlain, Poets (Clothed), Poets (Naked), (1964), Earl McGrath collection.
 * Alfred Leslie, a link to The Death Cycle, (1966), - The Death of Frank O'Hara Alfred Leslie’s The Killing Cycle
 * Grace Hartigan, Frank O'Hara, 1926-1966, (1966), 80 1/8 x 80 in. (203.4 x 203.2 cm), Smithsonian American Art Museum, Gift of Grace Hartigan.

title: Frank O'Hara