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Regular icosahedron

In geometry, the regular icosahedron (or simply icosahedron) is a convex polyhedron that can be constructed from pentagonal antiprism by attaching two pentagonal pyramids with regular faces to each of its pentagonal faces, or by putting points onto the cube. The resulting polyhedron has 20 equilateral triangles as its faces, 30 edges, and 12 vertices. It is an example of a Platonic solid and of a deltahedron. The icosahedral graph represents the skeleton of a regular icosahedron.

Many polyhedrons are constructed from the regular icosahedron. For example, most of the Kepler–Poinsot polyhedron is constructed by faceting. Some of the Johnson solids can be constructed by removing the pentagonal pyramids. The regular icosahedron has many relations with other Platonic solids, one of them is the regular dodecahedron as its dual polyhedron and has the historical background on the comparison mensuration. It also has many relations with other polytopes.

The appearance of regular icosahedron can be found in nature, such as the virus with icosahedral-shaped shells and radiolarians. Other applications of the regular icosahedron are the usage of its net in cartography, twenty-sided dice that may have been found in ancient times and role-playing games.

Construction
The regular icosahedron can be constructed like other gyroelongated bipyramids, started from a pentagonal antiprism by attaching two pentagonal pyramids with regular faces to each of its faces. These pyramids cover the pentagonal faces, replacing them with five equilateral triangles, such that the resulting polyhedron has 20 equilateral triangles as its faces. This process construction is known as the gyroelongation, so the resulting polyhedron is also called gyroelongated pentagonal bipyramid..

Another way to construct it is by putting two points on each surface of a cube. In each face, draw a segment line between the midpoints of two opposite edges and locate two points with the golden ratio distance from each midpoint. These twelve vertices describe the three mutually perpendicular planes, with edges drawn between each of them. Because of the constructions above, the regular icosahedron is Platonic solid, a family of polyhedra with regular faces. A polyhedron with only equilateral triangles as faces is called a deltahedron. There are only eight different convex deltahedra, one of which is the regular icosahedron.

One possible system of Cartesian coordinate for the vertices of a regular icosahedron, giving the edge length 2, is: $$ \left(0, \pm 1, \pm \varphi \right), \left(\pm 1, \pm \varphi, 0 \right), \left(\pm \varphi, 0, \pm 1 \right), $$ where $$\varphi = (1 + \sqrt{5})/2 $$ denotes the golden ratio.

Mensuration
The insphere of a convex polyhedron is a sphere inside the polyhedron, touching every face. The circumsphere of a convex polyhedron is a sphere that contains the polyhedron and touches every vertex. The midsphere of a convex polyhedron is a sphere tangent to every edge. Therefore, given that the edge length $$ a $$ of a regular icosahedron, the radius of insphere (inradius) $$ r_I $$, the radius of circumsphere (circumradius) $$ r_C $$, and the radius of midsphere (midradius) $$ r_M $$ are, respectively: $$ r_I = \frac{\varphi^2 a}{2 \sqrt{3}} \approx 0.756a, \qquad r_C = \frac{\sqrt{\varphi^2 + 1}}{2}a \approx 0.951a, \qquad r_M = \frac{\varphi}{2}a \approx 0.809a. $$

The surface area of polyhedra is the sum of its every face. Therefore, the surface area of regular icosahedra $$ A $$ equals the area of 20 equilateral triangles. The volume of a regular icosahedron $$ V $$ is obtained by calculating the volume of all pyramids with the base of triangular faces and the height with the distance from a triangular face's centroid to the center inside the regular icosahedron, the circumradius of a regular icosahedron. $$ A = 5\sqrt{3}a^2 \approx 8.660a^2, \qquad V = \frac{5 \varphi^2}{6}a^3 \approx 2.182a^3. $$ A problem dating back to the ancient Greeks is determining which of two shapes has a larger volume, an icosahedron inscribed in a sphere, or a dodecahedron inscribed in the same sphere. The problem was solved by Hero, Pappus, and Fibonacci, among others. Apollonius of Perga discovered the curious result that the ratio of volumes of these two shapes is the same as the ratio of their surface areas. Both volumes have formulas involving the golden ratio, but taken to different powers. As it turns out, the icosahedron occupies less of the sphere's volume (60.54%) than the dodecahedron (66.49%).

The dihedral angle of a regular icosahedron can be calculated by adding the angle of pentagonal pyramids with regular faces and a pentagonal antiprism. The dihedral angle of a pentagonal antiprism and pentagonal pyramid between two adjacent triangular faces are approximately $$ 138.2^\circ $$. The dihedral angle of a pentagonal antiprism between pentagon-to-triangle is $$ 100.8^\circ $$, and the dihedral angle of a pentagonal pyramid between the same faces is $$ 37.4^\circ $$. Therefore, for the regular icosahedron, the dihedral angle between two adjacent triangles, on the edge where the pentagonal pyramid and pentagonal antiprism are attached is $$ 37.4^\circ + 100.8^\circ = 138.2^\circ $$.

Symmetry
The rotational symmetry group of the regular icosahedron is isomorphic to the alternating group on five letters. This non-abelian simple group is the only non-trivial normal subgroup of the symmetric group on five letters. Since the Galois group of the general quintic equation is isomorphic to the symmetric group on five letters, and this normal subgroup is simple and non-abelian, the general quintic equation does not have a solution in radicals. The proof of the Abel–Ruffini theorem uses this simple fact, and Felix Klein wrote a book that made use of the theory of icosahedral symmetries to derive an analytical solution to the general quintic equation.

The full symmetry group of the icosahedron (including reflections) is known as the full icosahedral group. It is isomorphic to the product of the rotational symmetry group and the group $$C_2$$ of size two, which is generated by the reflection through the center of the icosahedron.

Icosahedral graph
Every Platonic graph, including the icosahedral graph, is a polyhedral graph. This means that they are planar graphs, graphs that can be drawn in the plane without crossing its edges; and they are 3-vertex-connected, meaning that the removal of any two of its vertices leaves a connected subgraph. According to Steinitz theorem, the icosahedral graph endowed with these heretofore properties represents the skeleton of a regular icosahedron.

The icosahedral graph is Hamiltonian, meaning that it contains a Hamiltonian cycle, or a cycle that visits each vertex exactly once.

In other Platonic solids
Aside from comparing the mensuration between the regular icosahedron and regular dodecahedron, they are dual to each other. An icosahedron can be inscribed in a dodecahedron by placing its vertices at the face centers of the dodecahedron, and vice versa.

An icosahedron can be inscribed in an octahedron by placing its 12 vertices on the 12 edges of the octahedron such that they divide each edge into its two golden sections. Because the golden sections are unequal, there are five different ways to do this consistently, so five disjoint icosahedra can be inscribed in each octahedron.

An icosahedron of edge length $\frac{1}{\varphi} \approx 0.618$ can be inscribed in a unit-edge-length cube by placing six of its edges (3 orthogonal opposite pairs) on the square faces of the cube, centered on the face centers and parallel or perpendicular to the square's edges. Because there are five times as many icosahedron edges as cube faces, there are five ways to do this consistently, so five disjoint icosahedra can be inscribed in each cube. The edge lengths of the cube and the inscribed icosahedron are in the golden ratio.

Stellation
The icosahedron has a large number of stellations. stated 59 stellations were identified for the regular icosahedron. The first form is the icosahedron itself. One is a regular Kepler–Poinsot polyhedron. Three are regular compound polyhedra.

Facetings
The small stellated dodecahedron, great dodecahedron, and great icosahedron are three facetings of the regular icosahedron. They share the same vertex arrangement. They all have 30 edges. The regular icosahedron and great dodecahedron share the same edge arrangement but differ in faces (triangles vs pentagons), as do the small stellated dodecahedron and great icosahedron (pentagrams vs triangles).

Diminishment
The Johnson solids are the polyhedra whose faces are all regular, but not uniform. This means they do not include the Archimedean solids, Catalan solids, prisms, and antiprisms. Some of them are constructed involving the removal of the part of a regular icosahedron, a process known as diminishment. They are gyroelongated pentagonal pyramid, metabidiminished icosahedron, and tridiminished icosahedron, which remove one, two, and three pentagonal pyramids from the icosahedron, respectively. The similar dissected regular icosahedron has 2 adjacent vertices diminished, leaving two trapezoidal faces, and a bifastigium has 2 opposite sets of vertices removed and 4 trapezoidal faces.

Relations to the 600-cell and other 4-polytopes
The icosahedron is the dimensional analogue of the 600-cell, a regular 4-dimensional polytope. The 600-cell has icosahedral cross sections of two sizes, and each of its 120 vertices is an icosahedral pyramid; the icosahedron is the vertex figure of the 600-cell.

The unit-radius 600-cell has tetrahedral cells of edge length $\frac{1}{\varphi}$, 20 of which meet at each vertex to form an icosahedral pyramid (a 4-pyramid with an icosahedron as its base). Thus the 600-cell contains 120 icosahedra of edge length $\frac{1}{\varphi}$. The 600-cell also contains unit-edge-length cubes and unit-edge-length octahedra as interior features formed by its unit-length chords. In the unit-radius 120-cell (another regular 4-polytope which is both the dual of the 600-cell and a compound of 5 600-cells) we find all three kinds of inscribed icosahedra (in a dodecahedron, in an octahedron, and in a cube).

A semiregular 4-polytope, the snub 24-cell, has icosahedral cells.

Relations to other uniform polytopes
As has been mentioned above, the regular icosahedron is unique among the Platonic solids in possessing a dihedral angle is approximately $ 138.19^\circ $. Thus, just as hexagons have angles not less than 120° and cannot be used as the faces of a convex regular polyhedron because such a construction would not meet the requirement that at least three faces meet at a vertex and leave a positive defect for folding in three dimensions, icosahedra cannot be used as the cells of a convex regular polychoron because, similarly, at least three cells must meet at an edge and leave a positive defect for folding in four dimensions (in general for a convex polytope in n dimensions, at least three facets must meet at a peak and leave a positive defect for folding in n-space). However, when combined with suitable cells having smaller dihedral angles, icosahedra can be used as cells in semi-regular polychora (for example the snub 24-cell), just as hexagons can be used as faces in semi-regular polyhedra (for example the truncated icosahedron). Finally, non-convex polytopes do not carry the same strict requirements as convex polytopes, and icosahedra are indeed the cells of the icosahedral 120-cell, one of the ten non-convex regular polychora.

There are distortions of the icosahedron that, while no longer regular, are nevertheless vertex-uniform. These are invariant under the same rotations as the tetrahedron, and are somewhat analogous to the snub cube and snub dodecahedron, including some forms which are chiral and some with $ T_h $-symmetry, i.e. have different planes of symmetry from the tetrahedron.

Appearances
Dice are the common objects with the different polyhedron, one of them is the regular icosahedron. The twenty-sided dice was found in many ancient times. One example is the dice from the Ptolemaic of Egypt, which was later the Greek letters inscribed on the faces in the period of Greece and Roman. Another example was found in the treasure of Tipu Sultan, which was made out of golden and with numbers written on each face. In several roleplaying games, such as Dungeons & Dragons, the twenty-sided die (labeled as d20) is commonly used in determining success or failure of an action. It may be numbered from "0" to "9" twice, in which form it usually serves as a ten-sided die (d10); most modern versions are labeled from "1" to "20". Scattergories is another board game, where the player names the categories in the card with given the set time. The naming of such categories is initially with the letters contained in every twenty-sided dice.

The regular icosahedron may also appear in many fields of science. In virology, herpes virus have icosahedral shells. The outer protein shell of HIV is enclosed in a regular icosahedron, as is the head of a typical myovirus. Several species of radiolarians discovered by Ernst Haeckel, described its shells as the like-shaped various regular polyhedra; one of which is Circogonia icosahedra, whose skeleton is shaped like a regular icosahedron. In chemistry, the closo-carboranes are compounds with a shape resembling the regular icosahedron. Icosahedral twinning also occurs in crystals, especially nanoparticles. Many borides and allotropes of boron such as α- and β-rhombohedral contain boron B12 icosahedron as a basic structure unit. In cartography, R. Buckminster Fuller used the net of a regular icosahedron to create a map known as Dymaxion map, by subdividing the net into triangles, followed by calculating the grid on the Earth's surface, and transferring the results from the sphere to the polyhedron. This projection was created during the time that Fuller realized that the Greenland is smaller than South America. In the Thomson problem, concerning the minimum-energy configuration of $$n$$ charged particles on a sphere, and for the Tammes problem of constructing a spherical code maximizing the smallest distance among the points, the minimum solution known for $$n = 12$$ places the points at the vertices of a regular icosahedron, inscribed in a sphere. This configuration is proven optimal for the Tammes problem, but a rigorous solution to this instance of the Thomson problem is unknown.

title: Regular icosahedron


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Industrial archaeology of Dartmoor

The industrial archaeology of Dartmoor covers a number of the industries which have, over the ages, taken place on Dartmoor, and the remaining evidence surrounding them. Currently only three industries are economically significant, yet all three will inevitably leave their own traces on the moor: china clay mining, farming and tourism.

A good general guide to the commercial activities on Dartmoor at the end of the 19th century is William Crossing's The Dartmoor Worker.

Mining
In former times, lead, silver, tin and copper were mined extensively on Dartmoor. The most obvious evidence of mining to the casual visitor to Dartmoor are the remains of the old engine-house at Wheal Betsy which is alongside the A386 road between Tavistock and Okehampton. The word Wheal has a particular meaning in Devon and Cornwall being either a tin or a copper mine, however in the case of Wheal Betsy it was principally lead and silver which were mined.

Once widely practised by many miners across the moor, by the early 1900s only a few tinners remained, and mining had almost completely ceased twenty years later. Some of the more significant mines were Eylesbarrow, Knock Mine, Vitifer Mine and Hexworthy Mine. The last active mine in the Dartmoor area was Great Rock Mine, which shut down in 1969.

Quarrying
Dartmoor granite has been used in many Devon and Cornish buildings. The prison at Princetown was built from granite taken from Walkhampton Common. When the horse tramroad from Plymouth to Princetown was completed in 1823, large quantities of granite were more easily transported.

There were three major granite quarries on the moor: Haytor, Foggintor and Merrivale. The granite quarries around Haytor were the source of the stone used in several famous structures, including the New London Bridge, completed in 1831. This granite was transported from the moor via the Haytor Granite Tramway, stretches of which are still visible.

The extensive quarries at Foggintor provided granite for the construction of London's Nelson's Column in the early 1840s, and New Scotland Yard was faced with granite from the quarry at Merrivale. Merrivale Quarry continued excavating and working its own granite until the 1970s, producing gravestones and agricultural rollers. Work at Merrivale continued until the 1990s, for the last 20 years imported stone such as gabbro from Norway and Italian marble was dressed and polished. The unusual pink granite at Great Trowlesworthy Tor was also quarried, and there were many other small granite quarries dotted around the moor. Various metamorphic rocks were also quarried in the metamorphic aureole around the edge of the moor, most notably at Meldon.

Gunpowder factory
In 1844 a factory for making gunpowder was built on the open moor, not far from Postbridge. Gunpowder was needed for the tin mines and granite quarries then in operation on the moor. The buildings were widely spaced from one another for safety and the mechanical power for grinding ("incorporating") the powder was derived from waterwheels driven by a leat.

Now known as "Powdermills" or "Powder Mills", there are extensive remains of this factory still visible. Two chimneys still stand and the walls of the two sturdily-built incorporating mills with central waterwheels survive well: they were built with substantial walls but flimsy roofs so that in the event of an explosion, the force of the blast would be directed safely upwards. The ruins of a number of ancillary buildings also survive. A proving mortar—a type of small cannon used to gauge the strength of the gunpowder—used by the factory still lies by the side of the road to the nearby pottery.

Peat-cutting
Peat-cutting for fuel occurred at some locations on Dartmoor until certainly the 1970s, usually for personal use. The right of Dartmoor commoners to cut peat for fuel is known as turbary. These rights were conferred a long time ago, pre-dating most written records. The area once known as the Turbary of Alberysheved between the River Teign and the headwaters of the River Bovey is mentioned in the Perambulation of the Forest of Dartmoor of 1240 (by 1609 the name of the area had changed to Turf Hill).

An attempt was made to commercialise the cutting of peat in 1901 at Rattle Brook Head, however this quickly failed.

Warrens
From at least the 13th century until early in the 20th, rabbits were kept on a commercial scale, both for their flesh and their fur. Documentary evidence for this exists in place names such as Trowlesworthy Warren (mentioned in a document dated 1272) and Warren House Inn. The physical evidence, in the form of pillow mounds is also plentiful, for example there are 50 pillow mounds at Legis Tor Warren. The sophistication of the warreners is shown by the existence of vermin traps that were placed near the warrens to capture weasels and stoats attempting to get at the rabbits.

The significance of the term warren nowadays is not what it once was. In the Middle Ages it was a privileged place, and the creatures of the warren were protected by the king 'for his princely delight and pleasure'.

The subject of warrening on Dartmoor was addressed in Eden Phillpotts' story The River.

Farming
Farming has been practised on Dartmoor since time immemorial. The dry-stone walls which separate fields and mark boundaries give an idea of the extent to which the landscape has been shaped by farming. There is little or no arable farming within the moor, mostly being given over to livestock farming on account of the thin and rocky soil. Some Dartmoor farms are remote in the extreme.

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

title: Industrial archaeology of Dartmoor


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Idempotence

Idempotence is the property of certain operations in mathematics and computer science whereby they can be applied multiple times without changing the result beyond the initial application. The concept of idempotence arises in a number of places in abstract algebra (in particular, in the theory of projectors and closure operators) and functional programming (in which it is connected to the property of referential transparency).

The term was introduced by American mathematician Benjamin Peirce in 1870 in the context of elements of algebras that remain invariant when raised to a positive integer power, and literally means "(the quality of having) the same power", from  + potence (same + power).

Definition
An element $$x$$ of a set $$S$$ equipped with a binary operator $$\cdot$$ is said to be idempotent under $$\cdot$$ if
 * $x\cdot x=x$.

The binary operation $$\cdot$$ is said to be idempotent if
 * $x\cdot x=x$ for all $x\in S$.

Examples

 * In the monoid $$(\mathbb{N}, \times)$$ of the natural numbers with multiplication, only $$0$$ and $$1$$ are idempotent. Indeed, $0\times 0 = 0$ and $1\times 1=1$.
 * In the monoid $$(\mathbb{N}, +)$$ of the natural numbers with addition, only $$0$$ is idempotent. Indeed, 0 + 0 = 0.
 * In a magma $$(M, \cdot)$$, an identity element $$e$$ or an absorbing element $$a$$, if it exists, is idempotent. Indeed, $e\cdot e=e$ and $a\cdot a=a$.
 * In a group $$(G, \cdot)$$, the identity element $$e$$ is the only idempotent element. Indeed, if $$x$$ is an element of $$G$$ such that $x\cdot x=x$, then $x\cdot x=x\cdot e$ and finally $$x=e$$ by multiplying on the left by the inverse element of $$x$$.
 * In the monoids $$(\mathcal{P}(E), \cup)$$ and $$(\mathcal{P}(E), \cap)$$ of the power set $$\mathcal{P}(E)$$ of the set $$E$$ with set union $$\cup$$ and set intersection $$\cap$$ respectively, $$\cup$$ and $$\cap$$ are idempotent. Indeed, $x\cup x=x$ for all $x\in \mathcal{P}(E)$, and $x\cap x=x$ for all $x\in \mathcal{P}(E)$.
 * In the monoids $$(\{0, 1\}, \vee)$$ and $$(\{0, 1\}, \wedge)$$ of the Boolean domain with logical disjunction $$\vee$$ and logical conjunction $$\wedge$$ respectively, $$\vee$$ and $$\wedge$$ are idempotent. Indeed, $x\vee x=x$ for all $x\in \{0, 1\}$, and $x\wedge x=x$ for all $x\in \{0, 1\}$.
 * In a GCD domain (for instance in $$\mathbb{Z}$$), the operations of GCD and LCM are idempotent.
 * In a Boolean ring, multiplication is idempotent.
 * In a Tropical semiring, addition is idempotent.
 * In a ring of quadratic matrices, the determinant of an idempotent matrix is either 0 or 1. If the determinant is 1, the matrix necessarily is the identity matrix.

Idempotent functions
In the monoid $$(E^E, \circ)$$ of the functions from a set $$E$$ to itself (see set exponentiation) with function composition $$\circ$$, idempotent elements are the functions $f\colon E\to E$ such that $f\circ f = f$, that is such that $f(f(x))=f(x)$ for all $x\in E$ (in other words, the image $$f(x)$$ of each element $$x\in E$$ is a fixed point of $$f$$). For example:
 * the absolute value is idempotent. Indeed, $\operatorname{abs}\circ \operatorname{abs}=\operatorname{abs}$, that is $\operatorname{abs}(\operatorname{abs}(x))=\operatorname{abs}(x)$ for all $x$;
 * constant functions are idempotent;
 * the identity function is idempotent;
 * the floor, ceiling and fractional part functions are idempotent;
 * the real part function $$\mathrm{Re}(z)$$ of a complex number, is idempotent.
 * the subgroup generated function from the power set of a group to itself is idempotent;
 * the convex hull function from the power set of an affine space over the reals to itself is idempotent;
 * the closure and interior functions of the power set of a topological space to itself are idempotent;
 * the Kleene star and Kleene plus functions of the power set of a monoid to itself are idempotent;
 * the idempotent endomorphisms of a vector space are its projections.

If the set $$E$$ has $$n$$ elements, we can partition it into $$k$$ chosen fixed points and $n-k$ non-fixed points under $$f$$, and then $$k^{n-k}$$ is the number of different idempotent functions. Hence, taking into account all possible partitions,
 * $$\sum_{k=0}^n {n \choose k} k^{n-k}$$

is the total number of possible idempotent functions on the set. The integer sequence of the number of idempotent functions as given by the sum above for n = 0, 1, 2, 3, 4, 5, 6, 7, 8, ... starts with 1, 1, 3, 10, 41, 196, 1057, 6322, 41393, ... .

Neither the property of being idempotent nor that of being not is preserved under function composition. As an example for the former, $f(x)=x$ mod 3 and $$g(x)=\max(x, 5)$$ are both idempotent, but $f\circ g$ is not, although $g\circ f$ happens to be. As an example for the latter, the negation function $$\neg$$ on the Boolean domain is not idempotent, but $\neg\circ\neg$ is. Similarly, unary negation $-(\cdot)$ of real numbers is not idempotent, but $-(\cdot)\circ -(\cdot)$ is. In both cases, the composition is simply the identity function, which is idempotent.

Computer science meaning
In computer science, the term idempotence may have a different meaning depending on the context in which it is applied:
 * in imperative programming, a subroutine with side effects is idempotent if multiple calls to the subroutine have the same effect on the system state as a single call, in other words if the function from the system state space to itself associated with the subroutine is idempotent in the mathematical sense given in the definition;
 * in functional programming, a pure function is idempotent if it is idempotent in the mathematical sense given in the definition.

This is a very useful property in many situations, as it means that an operation can be repeated or retried as often as necessary without causing unintended effects. With non-idempotent operations, the algorithm may have to keep track of whether the operation was already performed or not.

Computer science examples
A function looking up a customer's name and address in a database is typically idempotent, since this will not cause the database to change. Similarly, a request for changing a customer's address to XYZ is typically idempotent, because the final address will be the same no matter how many times the request is submitted. However, a customer request for placing an order is typically not idempotent since multiple requests will lead to multiple orders being placed. A request for canceling a particular order is idempotent because no matter how many requests are made the order remains canceled.

A sequence of idempotent subroutines where at least one subroutine is different from the others, however, is not necessarily idempotent if a later subroutine in the sequence changes a value that an earlier subroutine depends on—idempotence is not closed under sequential composition. For example, suppose the initial value of a variable is 3 and there is a subroutine sequence that reads the variable, then changes it to 5, and then reads it again. Each step in the sequence is idempotent: both steps reading the variable have no side effects and the step changing the variable to 5 will always have the same effect no matter how many times it is executed. Nonetheless, executing the entire sequence once produces the output (3, 5), but executing it a second time produces the output (5, 5), so the sequence is not idempotent.

In the Hypertext Transfer Protocol (HTTP), idempotence and safety are the major attributes that separate HTTP methods. Of the major HTTP methods, GET, PUT, and DELETE should be implemented in an idempotent manner according to the standard, but POST doesn't need to be. GET retrieves the state of a resource; PUT updates the state of a resource; and DELETE deletes a resource. As in the example above, reading data usually has no side effects, so it is idempotent (in fact nullipotent). Updating and deleting a given data are each usually idempotent as long as the request uniquely identifies the resource and only that resource again in the future. PUT and DELETE with unique identifiers reduce to the simple case of assignment to a variable of either a value or the null-value, respectively, and are idempotent for the same reason; the end result is always the same as the result of the initial execution, even if the response differs.

Violation of the unique identification requirement in storage or deletion typically causes violation of idempotence. For example, storing or deleting a given set of content without specifying a unique identifier: POST requests, which do not need to be idempotent, often do not contain unique identifiers, so the creation of the identifier is delegated to the receiving system which then creates a corresponding new record. Similarly, PUT and DELETE requests with nonspecific criteria may result in different outcomes depending on the state of the system - for example, a request to delete the most recent record. In each case, subsequent executions will further modify the state of the system, so they are not idempotent.

In event stream processing, idempotence refers to the ability of a system to produce the same outcome, even if the same file, event or message is received more than once.

In a load–store architecture, instructions that might possibly cause a page fault are idempotent. So if a page fault occurs, the operating system can load the page from disk and then simply re-execute the faulted instruction. In a processor where such instructions are not idempotent, dealing with page faults is much more complex.

When reformatting output, pretty-printing is expected to be idempotent. In other words, if the output is already "pretty", there should be nothing to do for the pretty-printer.

In service-oriented architecture (SOA), a multiple-step orchestration process composed entirely of idempotent steps can be replayed without side-effects if any part of that process fails.

Many operations that are idempotent often have ways to "resume" a process if it is interrupted – ways that finish much faster than starting all over from the beginning. For example, resuming a file transfer, synchronizing files, creating a software build, installing an application and all of its dependencies with a package manager, etc.

Applied examples
Applied examples that many people could encounter in their day-to-day lives include elevator call buttons and crosswalk buttons. The initial activation of the button moves the system into a requesting state, until the request is satisfied. Subsequent activations of the button between the initial activation and the request being satisfied have no effect, unless the system is designed to adjust the time for satisfying the request based on the number of activations.

title: Idempotence


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Ithaca, New York

Ithaca is a city in and the county seat of Tompkins County, New York, United States. Situated on the southern shore of Cayuga Lake in the Finger Lakes region of New York, Ithaca is the largest community in the Ithaca metropolitan statistical area. It is named after the Greek island of Ithaca. As of 2020, the city's population was 32,108.

A college town, Ithaca is home to Cornell University, an Ivy League university, and Ithaca College. Nearby is Tompkins Cortland Community College (TC3), located in Dryden.

17th century
Native Americans lived in this area for thousands of years. When reached by Europeans, this area was controlled by the Cayuga tribe of Indians, one of the Five Civilized Tribes or Iroquois League. Jesuit missionaries from New France in present-day Quebec had a mission to convert the Cayuga as early as 1657.

18th century
Saponi and Tutelo peoples, Siouan-speaking tribes, later occupied lands at the south end of Cayuga Lake. Dependent tributaries of the Cayuga, they had been permitted to settle on the tribe's hunting lands at the south end of Cayuga Lake, and in Pony (originally Sapony) Hollow of present-day Newfield, New York. Remnants of these tribes had been forced from Virginia and North Carolina by tribal conflicts and European colonial settlement. Similarly, the Tuscarora people, an Iroquoian-speaking tribe from the Carolinas, migrated after defeat in the Yamasee War; they settled with the Oneida people and became the sixth nation of the Haudenosaunee, with chiefs stating the migration was complete in 1722.

During the American Revolutionary War, four of the then six Iroquois nations helped the British attempt to crush the revolution, although bands made decisions on fighting in a highly decentralized way. Conflict with the rebel colonists was fierce throughout the Mohawk Valley and Western New York. In retaliation for conflicts to the east and resentment at the way in which the Iroquois made war, the 1779 Sullivan Expedition was conducted against the Iroquois in the west of the state, destroying more than 40 villages and stored winter crops and forcing their retreat from the area. It destroyed the Tutelo village of Coregonal, located near what is now the junction of state routes 13 and 13A just south of Ithaca. Most Iroquois were forced from the state after the Revolutionary War, but some remnants remained. The state sold off the former Iroquois lands to stimulate development and settlement by non-indigenous Americans; lands were also granted as payment to veterans of the war.

Within the current boundaries of Ithaca, Native Americans maintained a temporary hunting camp at the base of Cascadilla Gorge. In 1788, eleven men from Kingston, New York, came to the area with two Lenape guides, to explore what they considered wilderness. The following year Jacob Yaple, Isaac Dumond, and Peter Hinepaw returned with their families and constructed log cabins. That same year Abraham Bloodgood of Albany obtained a patent from the state for 1,400 acres, which included all of the present downtown west of Tioga Street.

In 1790, the federal government and state began an official program to grant land in the area, known as the Central New York Military Tract, as payment for service to Continental Army soldiers of the Revolutionary War, when the newly established federal government was cash poor. Most local land titles trace back to these Revolutionary war grants. However, the Bloodgood tract was not part of the state bounties to veterans. It was originally granted to a member of the state militia, Martinus Zielie, as a bounty under a different law for recruiting men to enlist in the Continental Army.

As part of this process, the Central New York Military Tract, which included northern Tompkins County, was surveyed under the direction of Simeon De Witt, Bloodgood's son-in-law and the Surveyor General of New York. Simeon commissioned his first cousin, Moses De Witt, after whom DeWitt, New York, is named, to survey the area around the south end of Cayuga Lake. Both Simeon and Moses were first cousins of DeWitt Clinton through his mother, Mary De Witt, who married James Clinton, brother of Governor George Clinton. The Commissioners of Lands of New York State (chairman Gov. George Clinton) met in 1790. The Military Tract township in which Ithaca is located was named the Town of Ulysses. A few years later De Witt moved to Ithaca, then called variously "The Flats," "The City," or "Sodom"; he renamed it for the Greek island home of Ulysses in the spirit of the multitude of settlement names in the region derived from classical literature, such as Aurelius, Ovid, and especially of Ulysses, New York, the town that contained Ithaca at the time.

Around 1791, De Witt surveyed what is now the downtown area into lots and sold them at modest prices. That same year John Yaple built a grist mill on Cascadilla Creek. The first frame house was erected in 1800 by Abram Markle. In 1804, the village had a postmaster and, in 1805, a tavern.

19th century
Ithaca became a transshipping point for salt from curing beds near Salina, New York, to buyers south and east. This prompted construction in 1810 of the Owego Turnpike. When the War of 1812 cut off access to gypsum in Nova Scotia, which was used for fertilizer, Ithaca became the center of trade in Cayuga gypsum. The Cayuga Steamboat Company was organized in 1819 and, in 1820, launched the first steamboat on Cayuga Lake, the Enterprise. In 1821, the village was incorporated at the same time the Town of Ithaca was organized and separated from the parent Town of Ulysses. In 1834, the Ithaca and Owego Railroad's first horse drawn train began service, connecting traffic on the east–west Erie Canal, which was completed in 1825, with the Susquehanna River to the south to expand the trade network.

With the Long Depression of 1837, the Ithaca and Owego Railroad was re-organized as the Cayuga and Susquehanna Railroad. It was re-engineered with switchbacks downhill into Ithaca in the late 1840s. In the late 20th century, a short section of its abandoned right-of-way in the City and Town of Ithaca was used for the South Hill Recreation Way.

However, easier early railroad routes were constructed that bypassed Ithaca, such as that of the Syracuse, Binghamton & New York, built in 1854. In the decade following the American Civil War, railroads were built from Ithaca to Auburn, Geneva, Cayuga, Cortland, Elmira, and Athens, Pennsylvania, mainly with financing from Ezra Cornell. These were all branch-lines, since the city, located on a steep hill by the lake, prevented it from being directly connected to a major transportation artery.

In 1892, when the Bethlehem, Pennsylvania-based Lehigh Valley Railroad built its main, double-track freight line from Van Etten Junction to Geneva and on to Buffalo, New York, it bypassed Ithaca and Auburn to the west, running via Burdett and eastern Schuyler County on easier grades, just as the Delaware, Lackawanna and Western Railroad had done a decade earlier, in 1882, with its own, new Binghamton-Buffalo mainline extension to the south and west, via Owego, Waverly, Bath, and Dansville. Two of three daily New York City-Buffalo roundtrip passenger trains served Ithaca on the older, original Lehigh Valley Ithaca Branch between Van Etten Junction and Geneva, until discontinuance of the Black Diamond daylight train, on May 11, 1959. On May 25, 1959, the overnight "Maple Leaf" train was shifted back to the Ithaca Branch from the main line via Burdett, and operated on this route until the Lehigh Valley Railroad discontinued this last passenger service on February 4, 1961.

In the late 19th century, more industry developed in Ithaca. In 1883, William Henry Baker and his partners founded the Ithaca Gun Company, which manufactured shotguns. The original factory was located in the Fall Creek neighborhood of the city, on a slope later known as Gun Hill, where the nearby waterfall supplied the main source of energy for the plant. The company became an icon in the hunting and shooting world, and its shotguns were known for their fine decorative work. Wooden gunstocks with knots or other imperfections were donated to the high school woodworking shop to be made into lamps. John Philip Sousa and trick-shooter Annie Oakley favored Ithaca Gun Company guns. In 1937, the company began producing the Ithaca 37, based on a 1915 patent by noted firearms designer John Browning. Its 12-gauge shotguns were the standard used for decades by the New York City Police Department and Los Angeles Police Department.

In 1885, Ithaca Children's Home was established on West Seneca Street. The orphanage had two programs at the time: a residential home for both orphaned and destitute children, and a day nursery. The village established its first trolley in 1887. Ithaca developed as a small manufacturing and retail center and was incorporated as a city in 1888. The largest industrial company in the area was Morse Chain, elements of which were absorbed into Emerson Power Transmission on South Hill and Borg Warner Automotive in Lansing, New York.

Ithaca claims to be the birthplace of the ice cream sundae, created in 1892 when fountain shop owner Chester Platt "served his local priest vanilla ice cream covered in cherry syrup with a dark candied cherry on top. The priest suggested the dessert be named after the day, Sunday, although the spelling was later changed out of fear some would find it offensive." The local Unitarian church, where the priest, Rev. John Scott, preached, has an annual "Sundae Sunday" every September in commemoration. Ithaca's claim has long been disputed by Two Rivers, Wisconsin. Also in 1892, the Ithaca Kitty became one of the first mass-produced stuffed animal toys in the United States.

20th century
In 1900, Cornell University anatomy professor G. S. Moler made an early movie using frame-by-frame technology. For The Skeleton Dance, he took single-frame photos of a human skeleton in varying positions, giving the illusion of a dancing skeleton. During the early 20th century, Ithaca was an important center in the silent film industry. These films often featured the local natural scenery. Many of these films were the work of Leopold Wharton and his brother Theodore; The Wharton Studio was on the site of what is now Stewart Park.

In 1903, a typhoid epidemic resulting from poor sanitation infrastructure devastated the city. Not having access to unpolluted water was one suspicion to the cause of the outbreak because "[r]efuse and the contents of the early sewer system dumped directly into the inlet". One out of ten citizens fell ill or died. Local residents lost fifty-one people to the illness that year, but there was “an average of thirty-nine cases each year” for the consecutive ten years following.

The Star Theatre on East Seneca Street was built in 1911 and became the most popular vaudeville venue in the region. Wharton movies were also filmed and shown there. After the film industry centralized in Hollywood, production in Ithaca effectively ceased. Few of the silent films made in Ithaca have been preserved.

After World War II, the Langmuir Research Labs of General Electric developed as a major employer; the defense industry continued to expand. GE's headquarters were in Schenectady, New York, to the northeast in the Mohawk Valley.

Although Ithaca has a history of Ku Klux Klan activity, including a cross-burning in 1923 and 1924, "the peak years of Klan activity in Ithaca were 1923-1925" and it represented only a fraction of the population. Ithaca is known for its political activism regarding civil rights and environmental issues. “Martin Luther King Jr. came to speak twice in Ithaca, in 1960 and 1961”. The annual Ithaca Festival, which often takes place on the Ithaca Commons or Stewart Park, frequently centers around themes promoting "a political statement into a cultural and festive event”

21st century
The Ithaca Gun Company tested their shotguns behind the plant on Lake Street; the shot fell into the Fall Creek gorge at the base of Ithaca Falls. Lead accumulated in the soil in and around the factory and gorge. A major lead clean-up effort sponsored by the United States Superfund took place from 2002 to 2004, managed through the Environmental Protection Agency. The old Ithaca Gun building has been dismantled. It was scheduled to be replaced by the development of an apartment complex on the cleaned land.

The former Morse Chain company factory on South Hill, now owned by Emerson Power Transmission, was the site of extensive groundwater and soil contamination from its industrial operations. Emerson Power Transmission has been working with the state and South Hill residents to determine the extent and danger of the contamination and aid in cleanup.

In 2004, Gayraud Townsend, a 20-year-old senior in Cornell's School of Industrial and Labor Relations, was sworn in as alderman of the city council: the first black male to be elected to the council and the youngest African American to be elected to office in the United States. He served his full term and has mentored other student politicians. In 2011, Svante Myrick, a 2009 Cornell University graduate, was elected as the youngest mayor of the city of Ithaca.

Geography
The valley in which Cayuga Lake is located is long and narrow with a north–south orientation. Ithaca is located at the southern end (the "head") of the lake, but the valley continues to the southwest behind the city. Originally a river valley, it was deepened and widened by the action of Pleistocene ice sheets over the last several hundred thousand years. These ice sheets gouged the land crosswise to preexisting streams, producing hanging valleys. Once the last ice sheets receded — around twenty or thirty thousand years ago — these streams cut deep into the steep hillsides, forming the many distinctive gorges, rapids, and waterfalls seen in the region; examples include Fall and Cascadilla Creeks in Ithaca, and nearby Buttermilk Falls, Enfield Gorge, and Taughannock Falls. Cayuga Lake is the most recent lake in a long series of lakes which developed as the ice retreated northward. The lake drains to the north, and was formed behind a dam of glacial debris called a moraine.

Rock in the region is predominantly Devonian shale and sandstone. North of Ithaca, it is relatively fossil rich. The world-renowned fossils found in this area can be examined at the Museum of the Earth. Glacial erratics can also be found in the area.

Ithaca was founded on flat land just south of the lake — land that formed in fairly recent geological times when silt filled the southern end of the lake. The city ultimately spread to the adjacent hillsides, which rise several hundred feet above the central flats: East Hill, West Hill, and South Hill. The Cornell campus is loosely bounded to the north and south by Fall and Cascadilla Creeks, respectively.

The natural vegetation of the Ithaca area is northern temperate broadleaf forest. It is dominated by deciduous trees, including maple, sycamore, black walnut, birch, and oak; coniferous trees include white pine, Norway spruce, and eastern hemlock. The city of Ithaca has a rich diversity of tree plantings, with over 190 species, including cherry, southern magnolia, and ginkgo. In addition to visual beauty, this species diversification helps reduce the impact of arboreal epidemics, such as that caused by the emerald ash borer.

Climate
According to the Köppen climate classification method, Ithaca experiences a warm-summer humid continental climate, also known as a hemiboreal climate (Dfb). Summers are warm but brief, and it is cool-to-cold the rest of the year, with long, snowy winters; an average of 67 in of snow falls per year. In addition, frost may occur any time of year except mid-summer.

Winter is typically characterized by freezing temperatures, cloudy skies and light-to-moderate snows, with some heavier falls; the largest snowfall in one day was 26.0 in on February 14, 1914. But the season is also variable; there can be short mild periods with some rain, but also outbreaks of frigid air with night temperatures down to -10 °F or lower. Summers usually bring sunshine, along with moderate heat and humidity, but also frequent afternoon thunderstorms. Nights are pleasant and sometimes cool. Occasionally, there can be heatwaves, with temperatures rising into the 90 °F to 95 °F range, but they tend to be brief.

The average date of the first freeze is October 5, and the average date of the last freeze is May 15, giving Ithaca a growing season of 141 days. The average date of the first and last snowfalls are November 12 and April 7, respectively. The hardiness zone is between 5b and 6a. Extreme temperatures range from −25 °F as recently as February 2, 1961, up to 103 °F on July 9, 1936.

The valley flatland has slightly cooler weather in winter, and occasionally Ithaca residents experience simultaneous snow on the hills and rain in the valley. The phenomenon of mixed precipitation (rain, wind, and snow), common in the late fall and early spring, is known tongue-in-cheek as ithacation to many of the local residents.

Due to the microclimates created by the impact of the lakes, the region surrounding Ithaca (Finger Lakes American Viticultural Area) experiences a short but adequate growing season for winemaking similar to the Rhine Valley wine district of Germany. As such, the region is home to many wineries.

Demographics
Ithaca is the principal city of the Ithaca-Cortland Combined Statistical Area, which includes the Ithaca Metropolitan Statistical Area (Tompkins County) and the Cortland Micropolitan Statistical Area (Cortland County),  which had a combined population of 145,100 at the 2000 census.

As of the census of 2000, there were 29,287 people, 10,287 households, and 2,962 families residing in the city. The population density was 5,360.9 /mi2. There were 10,736 housing units at an average density of 1,965.2 /mi2. The racial makeup of the city was 73.97% White, 13.65% Asian, 6.71% Black or African American, 0.39% Native American, 0.05% Pacific Islander, 1.86% from other races, and 3.36% from two or more races. Hispanic or Latino of any race were 5.31% of the population.

There were 10,287 households, out of which 14.2% had children under the age of 18 living with them, 19.0% were married couples living together, 7.8% had a female householder with no husband present, and 71.2% were non-families. 43.3% of all households were made up of individuals, and 7.4% had someone living alone who was 65 years of age or older. The average household size was 2.13 and the average family size was 2.81.

In the city, the population was spread out, with 9.2% under the age of 18, 53.8% from 18 to 24, 20.1% from 25 to 44, 10.6% from 45 to 64, and 6.3% who were 65 years of age or older. The median age was 22 years. For every 100 females, there were 102.6 males. For every 100 females age 18 and over, there were 102.2 males.

The median income for a household in the city was $21,441, and the median income for a family was $42,304. Males had a median income of $29,562 versus $27,828 for females. The per capita income for the city was $13,408. About 13.2% of individuals and 4.2% of families were below the poverty line.

Greater Ithaca
The term "Greater Ithaca" encompasses both the City and Town of Ithaca, as well as several smaller settled places within or adjacent to the Town:

Municipalities

 * Village of Groton
 * Village of Lansing
 * the southern part of the Town of Lansing
 * Village of Cayuga Heights
 * Hamlet of Forest Home
 * Hamlet of South Hill

Census-designated places

 * East Ithaca
 * Northeast Ithaca
 * Northwest Ithaca

Local government
There are two governmental entities in the area: the Town of Ithaca and the City of Ithaca. The Town of Ithaca is one of the nine towns comprising Tompkins County. The City of Ithaca is surrounded by, but legally independent of, the Town.

The City of Ithaca has a mayor–council government. The charter of the City of Ithaca provides for a full-time mayor and city judge, each independent and elected at-large. Since 1995, the mayor has been elected to a four-year term, and since 1989, the city judge has been elected to a six-year term.

Since 1983, the city has been divided into five wards. Each elects two representatives to the city council, known as the Common Council, for staggered four-year terms. In March 2015, the Common Council unanimously adopted a resolution recognizing freedom from domestic violence as a fundamental human right. In September 2023, the Common Council unanimously passed an extensive local ordinance to "protect, defend and shield transgender individuals".

Since students won the right to vote where they attend colleges, some have become more active in local politics. In 2004, Gayraud Townsend, a 20-year-old senior in Cornell's School of Industrial and Labor Relations, was sworn in as alderman of the city council, representing the fourth Ward. He was the first black male to be elected to the council and was then the youngest African American to be elected to office in the United States. In 2011, Cornell graduate Svante Myrick was elected Mayor of the City of Ithaca, becoming the youngest mayor in the city's history.

In December, 2005, the City and Town governments began discussing opportunities for increased government consolidation, including the possibility of joining the two into a single entity. This topic had been previously discussed in 1963 and 1969. Cayuga Heights, a village adjacent to the city on its northeast, voted against annexation into the city of Ithaca in 1954.

Politics
Politically, the majority of the city's voters (many of them students) have supported liberalism and the Democratic Party. A November 2004 study by ePodunk lists it as New York's most liberal city. This contrasts with the more conservative leanings of the generally rural Upstate New York region; the city's voters are also more liberal than those in the rest of Tompkins County. In 2008, Barack Obama, running against New York State's US Senator Hillary Clinton, won Tompkins County in the Democratic Presidential Primary, the only county that he won in New York State. Obama won Tompkins County (including Ithaca) by a wide margin of 41% over his opponent John McCain in the November 2008 election.

Sister city
Ithaca is a sister city of:
 * Eldoret, Kenya

Colleges
Ithaca is a major educational center in Central New York. The two major post-secondary educational institutions located in Ithaca were each founded in the late 19th century. In 1865, Ezra Cornell founded Cornell University, which overlooks the town from East Hill. It was opened as a coeducational institution. Women first enrolled in 1870. Ezra Cornell also established a public library for the city. Ithaca College was founded as the Ithaca Conservatory of Music in 1892. Ithaca College was originally located in the downtown area but relocated to South Hill in the 1960s. In 2018, there were 23,600 students enrolled at Cornell and 6,700 at Ithaca College. Tompkins Cortland Community College is located in the neighboring town of Dryden, and has an extension center in downtown Ithaca. Empire State College offers non-traditional college courses to adults in downtown Ithaca.

Public schools
The Ithaca City School District, based in Ithaca, encompasses the city and its surrounding area and enrolls about 5,500 K-12 students in eight elementary schools (roughly one for every neighborhood), two middle schools (Boynton and Dewitt), Ithaca High School and the Lehman Alternative Community School, a combined middle and high school. Several private elementary and secondary schools are located in the Ithaca area, including the Roman Catholic Immaculate Conception School, the Cascadilla School, the New Roots Charter School, the Elizabeth Ann Clune Montessori School, the Namaste Montessori School (in the Trumansburg area) and the Ithaca Waldorf School. Ithaca has two networks for supporting its home-schooling families: Loving Education At Home (LEAH) and the Northern Light Learning Center (NLLC). TST BOCES is located in Tompkins County.

Library
The Tompkins County Public Library, located at 101 East Green Street, serves as the public library for Tompkins County and is the Central Library for the Finger Lakes Library System. The library serves over 38,000 registered borrowers and contains nearly 260,000 items in its circulating collection, and circulates about 800,000 items annually.

Economy
The economy of Ithaca is based on education and further supported by agriculture, technology and tourism. As of 2006, Ithaca has continued to have one of the few expanding economies in New York State outside New York City. It draws commuters for work from the neighboring rural counties of Cortland, Tioga, and Schuyler, as well as from the more urbanized Chemung County.

Ithaca has tried to maintain its traditional downtown shopping area with its pedestrian orientation; this includes the Ithaca Commons pedestrian mall and Center Ithaca, a small mixed-use complex built at the end of the urban renewal era. Another commercial center, Collegetown, is located next to the Cornell campus. It features a number of restaurants, shops and bars, and an increasing number of high-rise apartments. It is primarily frequented by Cornell University students.

Ithaca has many of the businesses characteristic of small American university towns: bookstores, art-house cinemas, craft stores and vegetarian-friendly restaurants. The collective Moosewood Restaurant, founded in 1973, published a number of vegetarian cookbooks. Bon Appetit magazine ranked it among the thirteen most influential restaurants of the 20th century. Ithaca has many local restaurants and chains, both in the city and town, with a range of ethnic foods.

The Ithaca Farmers Market, a cooperative, first opened for business on Saturdays in 1973. It is located at Steamboat Landing, where steamboats from Cayuga Lake used to dock.

The South Hills Business Campus originally opened in 1957 as the regional headquarters of the National Cash Register Company. Running three full factory shifts, NCR was a major employer. Although it was sold in 1991 to American Telephone and Telegraph and later acquired by Cognitive TPG, it remains a major tenant of the South Hill Business Campus, which is now owned by a group of private investors.

Agriculture
Ithaca, home to the Cornell University College of Agriculture and Life Sciences, has a deep connection to Central New York's farming and dairy industries. About 60 small farms are located in the greater Ithaca/Trumansburg area, including a number of research farms managed by the Cornell University Agricultural Experiment Station. Cornell's Dairy Research Facility is a center of research and support for New York's large and growing milk and yogurt industries.

Media
The Ithaca Journal, founded in 1815, is a morning daily newspaper that has been owned by Gannett since 1912. The Ithaca Voice is a nonprofit digital news site with a mission to improve civic and political understanding in Ithaca and Tompkins County. The Ithaca Times is a free alternative weekly newspaper that's published every Wednesday. The Cornell Daily Sun is also published in Ithaca, operating since 1880. Other media outlets include the online magazine 14850.com.

Ithaca is home to several radio stations:

 * WICB 91.7 FM is a non-commercial, student-run station owned by Ithaca College.
 * WPIE 1160 AM/107.1 FM "ESPN Ithaca" is a sports talk station locally owned by Taughannock Media.
 * WQNY "Q-Country" 103.7 FM, owned by The Cayuga Radio Group, a subsidiary of Saga Communications, Inc.
 * WINO 88.1 FM, Ithaca Community Radio, has a studio and offices in the Clinton House, and also broadcasts at 91.9 FM in Watkins Glen.
 * WVBR-FM 93.5 FM/105.5 FM, affiliated with Cornell University, is a student-owned and operated commercial station with music, sports including Cornell hockey, and community members hosting specialty programming.
 * WYXL "Lite Rock" 97.3 FM
 * News/talk WHCU 870 AM
 * Progressive talk WNYY 1470 AM
 * Classic rock "I-100" WIII 99.9 FM

Public radio:
 * WSQG 90.9 FM, WSKG-FM's Ithaca frequency, provides NPR and classical music programming.
 * WITH 90.1 FM is the local translator for public radio and AAA station WRUR-FM in Rochester.

Other FM stations include: Saga's "98.7 The Vine", a low-powered translator station; WFIZ "Z95.5", airing a top-40 (CHR) format; contemporary Christian music station WCII 88.9; and classic rock "The Wall" WLLW 99.3 and 96.3, based in Seneca Falls with a transmitter in Ithaca.

Culture
Founded in 1983, the Sciencenter is a non-profit hands-on science museum, accredited by the American Alliance of Museums (AAM). It is a member of the Association of Science-Technology Centers (ASTC) and Association of Children's Museums (ACM).

The Museum of the Earth is a natural history museum created in 2003 by the Paleontological Research Institution (PRI). The PRI was founded in Ithaca in 1932 and is the publisher of the oldest journal of paleontology in the western hemisphere. Exhibits cover the 4.5-billion-year history of the earth in an accessible manner, including interactive displays. As of 2004, the PRI is now formally affiliated with Cornell.

The Cayuga Nature Center occupies the site of the 1914 Cayuga Preventorium, a facility for children with tuberculosis; treatment of what was then considered an incurable disease was based on rest and good nutrition. In 1981, the Cayuga Nature Center was incorporated as an independent, private, non-profit educational organization, offering environmental education to local school districts. In 2011, the PRI merged with the Cayuga Nature Center, making it a sister organization to the Museum of the Earth.

The Cornell Lab of Ornithology is located in the Imogene Powers Johnson Center for Birds and Biodiversity. The Lab's Visitors' Center and observation areas are open to the public. Displays include a surround-sound theater, object-theater presentation, sound studio and informational kiosks featuring bird sounds and information.

The Herbert F. Johnson Museum of Art houses one of the finest collections of art in upstate New York. Special exhibitions are mounted each year, plus selections from a global permanent collection, which is displayed on six public floors. The collection includes art from throughout Asia, Africa, Europe, the Americas, graphic arts, medallic art and Tiffany glass, ranging from the ancient to the contemporary.

The Center for the Arts at Ithaca, Inc., operates the "Hangar Theatre". Opened in 1975 in a renovated municipal airport hangar, the Hangar hosts a summer season and brings a range of theatre to regional audiences including students, producing a school tour and Artists-in-the-Schools programs. Ithaca is also the home to Kitchen Theatre Company, a non-profit professional company with a theatre on West State Street, and Civic Ensemble, a creative collaborative ensemble staging emerging playwrights' work and community-based original productions.

Ithaca is noted for its annual community celebration, The Ithaca Festival. Ithaca also hosts one of the largest used-book sales in the United States.

The Constance Saltonstall Foundation for the Arts supports New York State artists and writers through two key programs: free stipend-supported, juried residencies and a self-directed, non-juried, low-cost retreats. Saltonstall was founded in 1995 and is located eight miles outside Ithaca. Between 1996 and 2008, the Saltonstall Foundation provided grants to individual artists and writers from central and western New York counties. Saltonstall hosts Open House events for the public to meet the current artists and writers at the residency and to learn about the foundation.

Founded in 1992, the Namgyal Monastery in Ithaca is the North American seat of the Dalai Lama's Namgyal Monastery.

The city and town also sponsor The Apple Festival in the fall, the Chili Fest in February, the Finger Lakes International Dragon Boat Festival in July, Porchfest in late September and the Ithaca Brew Fest in Stewart Park in September.

Ithaca has also pioneered the Ithaca Health Fund, a popular cooperative health insurance. Ithaca is home to Ithaca Hours, one of the first local currency systems in the United States. It was developed by Paul Glover.

Music
Ithaca is the home of the Cayuga Chamber Orchestra.

The Cornell Concert Series has been hosting musicians and ensembles of international stature since 1903. For its initial 84 years, the series featured Western classical artists exclusively. In 1987, however, the series broke with tradition to present Ravi Shankar and has since grown to encompass a broader spectrum of the world's great music. Now, it balances a mix of Western classical music, traditions from around the world, jazz, and new music in these genres. In a single season, Cornell Concert Series presents performers ranging from the Leipzig Tomanerchor and Danish Quartet to Simon Shaheen, Vida Guitar Quartet, and Eighth Blackbird.

The School of Music at Ithaca College was founded in 1892 by William Egbert as a music conservatory on Buffalo Street. Among the degree programs offered are those in Performance, Theory, Music Education and Composition. Since 1941, the School of Music has been accredited by the National Association of Schools of Music.

Ithaca's Suzuki school, Ithaca Talent Education, provides musical training for children of all ages and also teacher training for undergraduate and graduate-level students. The Community School of Music and Art uses an extensive scholarship system to offer classes and lessons to any student, regardless of age, background, economic status or artistic ability.

A number of musicians call Ithaca home, most notably Samite of Uganda, The Burns Sisters, The Horse Flies, Johnny Dowd, Mary Lorson, cellist Hank Roberts, Anna Coogan, John Brown's Body, Kurt Riley, X Ambassadors, and Alex Kresovich. Old-time music is a staple, and folk music is featured weekly on WVBR-FM's Bound for Glory, North America's longest-running live folk concert broadcast. The Finger Lakes GrassRoots Festival of Music and Dance, hosted by local band Donna the Buffalo, is held annually during the third week in July in the nearby village of Trumansburg, with more than 60 local, national and international acts.

Ithaca is the center of a thriving live music scene, featuring more than 200 groups playing most genres of American popular and world music, the predominant genres being folk, rock, blues, jazz, country, lo-fi and reggae. There are more than 80 live music venues within a 40-mile radius of the city, including cafes, pubs, clubs and concert halls.

Transportation
In 2009, the Ithaca metropolitan statistical area (MSA) ranked as the highest in the United States for the percentage of commuters who walked to work (15.1 percent). In 2013, the Ithaca MSA ranked as the second-lowest in the United States for percentage of commuters who traveled by private vehicle (68.7 percent). During the same year, 17.5 percent of commuters in the Ithaca MSA walked to work.

Roads
Ithaca is in the rural Finger Lakes region about 225 mi northwest of New York City; the nearest larger cities, Binghamton and Syracuse, are an hour's drive away by car, Rochester and Scranton are two hours, Buffalo and Albany are three hours. New York City, Philadelphia, Toronto, and Ottawa are approximately four hours away.

Ithaca lies at over a half-hour's drive from any interstate highway, and all car trips to Ithaca involve some driving on two-lane state rural highways. The city is at the convergence of many regional two-lane state highways: Routes 13, 13A, 34, 79, 89, 96, 96B and 366. These are usually not congested except in Ithaca proper. However, Route 79 between the I-81 access at Whitney Point and Ithaca receives a significant amount of Ithaca-bound congestion right before Ithaca's colleges reopen after breaks.

In July 2008, a non-profit called Ithaca Carshare began a carsharing service in Ithaca. Ithaca Carshare has a fleet of vehicles shared by over 1500 members as of July, 2015 and has become a popular service among both city residents and the college communities. Vehicles are located throughout Ithaca downtown and at the two major institutions. With Ithaca Carshare as the first locally-run carsharing organization in New York State, others have since launched in Buffalo, Albany, and Syracuse.

Rideshare services to promote carpooling and vanpooling are operated by ZIMRIDE and VRIDE. A community mobility education program, Way2Go, is operated by Cornell Cooperative Extension of Tompkins County. Way2Go's website provides consumer information and videos. Way2Go works collaboratively to help people save money, stress less, go green and improve mobility options. The 2-1-1 Tompkins/Cortland Help line connects people with services, including transportation, in the community, by telephone and web on a 24/7 basis. The information and referral service is operated by the Human Services Coalition of Tompkins County, Inc. Together, 2-1-1 Information and Referral and Way2Go are a one-call, one-click resource designed to mobility services information for Ithaca and throughout Tompkins County.

Bus
There is frequent intercity bus service by Greyhound Lines, New York Trailways, OurBus, FlixBus, and Shortline (Coach USA), particularly to Binghamton and New York City, with limited service to Rochester, Buffalo and Syracuse, and via connections in Binghamton to Utica and Albany. OurBus provides limited holiday services to Allentown, Pennsylvania, Philadelphia, and Washington, D.C.. Cornell University runs a premium campus-to-campus bus between its Ithaca campus and its medical school in Manhattan, New York City, which is open to the public. Starting in September 2019, intercity buses began serving Ithaca from the downtown bus stop at 131 East Green Street after the former Greyhound bus station on West State Street closed due to staff retirement and building maintenance issues. OurBus now picks up and drops off on Seneca Street, near the downtown Starbucks and Hilton Garden Inn.

Ithaca is the center of an extensive bus public transportation network. Tompkins Consolidated Area Transit, Inc. (TCAT, Inc.) is a not-for-profit corporation that provides public transportation for Tompkins County, New York. TCAT was reorganized as a non-profit corporation in 2004 and is primarily supported locally by Cornell University, the City of Ithaca and Tompkins County. TCAT's ridership increased from 2.7 million in 2004 to 4.4 million in 2013. TCAT operates 34 routes, many running seven days a week. It has frequent service to downtown, Cornell University, Ithaca College, and The Shops at Ithaca Mall in the Lansing, New York, but less frequent service to residential and rural areas, including Trumansburg and Newfield. Chemung County Transit (C-TRAN) runs weekday commuter service from Chemung County to Ithaca. Cortland Transit runs commuter service to Cornell University. Tioga County Public Transit operated three routes to Ithaca and Cornell, but ceased operations on November 30, 2014.

GADABOUT Transportation Services, Inc. provides demand-response paratransit service for seniors over 60 and people with disabilities. Ithaca Dispatch provides local and regional taxi service. In addition, Ithaca Airline Limousine and IthaCar Service connect to the local airports.

Airports
Ithaca is served by Ithaca Tompkins International Airport, located about three miles to the northeast of the city center. In late 2019, the airport completed a major $34.8 million renovation which included a larger terminal with additional passenger gates and jet bridges, expanded passenger amenities and a 5000 sqft customs facility that enables it to receive international charter and private flights.

American Airlines pulled out of Ithaca on September 7, 2022, citing pilot shortages. Delta Connection provides service to and from John F. Kennedy International Airport, operated by its commuter partner Endeavor Air, using the Bombardier CRJ200 commuter-jet. United Express offers daily flights to its hub at Newark Liberty Airport, operated by its commuter partner GoJet Airlines, using the two-class Bombardier CRJ550 commuter-jet.

Railways
Into the mid-20th century, it was possible to reach Ithaca by passenger rail. At least two trains per day serviced Ithaca along the Delaware, Lackawanna and Western Railroad until 1942, or the Lehigh Valley Railroad. The trip took about seven hours from New York City, about eight hours from Philadelphia, and about three hours from Buffalo, New York. There has been no passenger rail service since February 4, 1961.

Beginning in the 1870s, there were trains to Buffalo via Geneva, New York, to New York City via Wilkes-Barre, Pennsylvania on the Lehigh Valley Railroad, to Hoboken, New Jersey with a train change in Owego via Binghampton and Scranton, Pennsylvania on the Delaware, Lackawanna and Western Railroad, and to the U.S. Northeast via Cortland, New York on the Lehigh Valley Railroad. The Lehigh Valley's top New York City-Ithaca-Buffalo passenger train, the daylight Black Diamond, was publicized as "The Handsomest Train in the World," but it took a roundabout route to New York City, traveling south to Waverly, New York, to Wilkes-Barre and Easton, and then across New Jersey. It was named after the railroad's largest commodity, anthracite coal, and made its last run on May 11, 1959.

Until March 1942, the Lackawanna Railroad operated two shuttle trains a day between Ithaca and Owego, where passengers could transfer to westbound trains to Buffalo and Chicago or eastbound to Binghamton, Scranton, Pennsylvania, and Hoboken, New Jersey, across the Hudson River from New York City. Until September 15, 1958, the Lackawanna maintained Syracuse-Binghamton service through nearby Cortland, to the east. Until May 11, 1959, two Lehigh Valley trains a day made both westbound and eastbound stops in Ithaca. The last passenger train making stops in Ithaca was the Lehigh Valley's overnight Maple Leaf, which discontinued in February 1961.

Within Ithaca, electric railways ran along Stewart Avenue and Eddy Street. Ithaca was the fourth community in New York state with a street railway; streetcars ran from 1887 until the summer of 1935.

In December 2018, the Ithaca Central Railroad, a Watco subsidiary, took over operation via lease of the 48.8 mi Norfolk Southern Ithaca Secondary line from Sayre, Pennsylvania to the Cargill Salt mine site on the eastern shore of Cayuga Lake, near Myers Point. Unit coal trains carrying bituminous coal were delivered to the Ithaca Central at Sayre by Norfolk Southern for less than eight months afterward, traveling to the Ridge site of the Cayuga Operating Company: a coal-burning power plant known as Milliken Station during NYSEG ownership. The power plant closed on August 29, 2019. As of 2022, there are ambitious, proposed plans to convert its brownfield site into a major data center. The main rail freight traffic is now salt from the Cargill salt mine farther north. Norfolk Southern's tracks, headed north on the former Lehigh Valley Auburn and Ithaca Branch, include a distinctive section in Ithaca that runs along the side of Fulton St. (NY13 southbound), although not in the street itself.

Points of interest

 * Buttermilk Falls State Park
 * Carl Sagan's Grave
 * Cayuga Nature Center
 * Cornell Botanic Gardens
 * Cornell University
 * Finger Lakes Trail
 * Ithaca College
 * Ithaca Commons
 * Ithaca Dog Park
 * Ithaca Falls
 * Paleontological Research Institution's Museum of the Earth
 * Robert H. Treman State Park
 * Sagan Planet Walk
 * Sapsucker Woods Sanctuary
 * Sciencenter
 * Stewart Park
 * Taughannock Falls State Park

Reputation
In addition to its liberal politics, Ithaca is commonly listed among the most culturally liberal of American small cities. In 1997, Utne Reader named Ithaca "America's most enlightened town". As of 2007, according to ePodunk's Gay Index, Ithaca has a score of 231, versus a national average score of 100. Like many small college towns, Ithaca has also received accolades for having a high overall quality of life.

In its earliest years, during the frontier days, what is now Ithaca was briefly known by the names "The Flats" and "Sodom," the name of the Biblical city of sin, due to its reputation as a town of "notorious immorality", a place of horse racing, gambling, profanity, Sabbath-breaking and readily-available liquor. Simeon De Witt renamed the town Ithaca for Odysseus' home island in the early 19th century, though nearby Robert H. Treman State Park still contains Lucifer Falls. Ithaca is primarily known for its growing wineries and microbreweries, live music, colleges and small dairy farms.

title: Ithaca, New York


text:
Talk:Ithaca, New York

Someone blocked me for no good reason. Was trying to correct two mistakes in several of my own prior edits. Please info this unjust block of 2/10/22 now. — Preceding unsigned comment added by 2600:1004:B114:5E9B:7104:C5E4:76C8:664E (talk) 23:47, 10 February 2022 (UTC)

Wiki Education Foundation-supported course assignment
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Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 00:56, 17 January 2022 (UTC)

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The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for deletion: Participate in the deletion discussion at the. —Community Tech bot (talk) 18:52, 20 February 2022 (UTC)
 * Ithaca yogurt.jpg

"Cayuga Radio Group" listed at Redirects for discussion
The redirect [//en.wikipedia.org/w/index.php?title=Cayuga_Radio_Group&redirect=no Cayuga Radio Group] has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at until a consensus is reached.  WC  Quidditch  ☎   ✎  00:34, 4 March 2023 (UTC)

Semi-protected edit request on 23 January 2024
Within the Ithaca information box at the start of this article, it should be noted that Robert G. Cantelmo is the current mayor of the city. As of 2024, the position is no longer held by Laura Lewis. Mppennekamp (talk) 15:29, 23 January 2024 (UTC)
 * Red information icon with gradient background.svg Not done: please provide reliable sources that support the change you want to be made. Shadow311 (talk) 15:55, 23 January 2024 (UTC)
 * I've updated it; source is city government council page, which I've added. OhNo itsJamie Talk 15:56, 23 January 2024 (UTC)

Semi-protected edit request on 31 May 2024
Change "In 2011, Svante Myrick, a 2009 Cornell University graduated, was elected as the youngest mayor of the city of Ithaca." to "In 2011, Svante Myrick, a 2009 Cornell University graduate, was elected as the youngest mayor of the city of Ithaca."

"graduated" should become "graduate". 142.126.47.14 (talk) 14:08, 31 May 2024 (UTC)

 * ✅ - Thanks for pointing that out - Arjayay (talk) 14:27, 31 May 2024 (UTC)

title: Talk:Ithaca, New York