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Coin flipping

Coin flipping, coin tossing, or heads or tails is the practice of throwing a coin in the air and checking which side is showing when it lands, in order to randomly choose between two alternatives, heads or tails, sometimes used to resolve a dispute between two parties. It is a form of sortition which inherently has two possible outcomes. The party who calls the side that is facing up when the coin lands wins.

History

Coin flipping was known to the Romans as navia aut caput ("ship or head"), as some coins had a ship on one side and the head of the emperor on the other. In England, this was referred to as cross and pile.

Process
During a coin toss, the coin is thrown into the air such that it rotates edge-over-edge an unpredictable number of times. Either beforehand or when the coin is in the air, an interested party declares "heads" or "tails", indicating which side of the coin that party is choosing. The other party is assigned the opposite side. Depending on custom, the coin may be caught; caught and inverted; or allowed to land on the ground. When the coin comes to rest, the toss is complete and the party who called correctly or was assigned the upper side is declared the winner.

It is possible for a coin to land on its side, usually by landing up against an object (such as a shoe) or by getting stuck in the ground. However, even on a flat surface it is possible for a coin to land on its edge. A computational model suggests that the chance of a coin landing on its edge and staying there is about 1 in 6000 for an American nickel.

The coin may be any type as long as it has two distinct sides; it need not be a circulating coin as such. Larger coins tend to be more popular than smaller ones. Some high-profile coin tosses, such as the Cricket World Cup and the Super Bowl, use custom-made ceremonial medallions.

Three-way
Three-way coin flips are also possible, by a different process – this can be done either to choose one or two out of three. To choose two out of three, three coins are flipped, and if two coins come up the same and one different, the different one loses (is out), leaving two players. To choose one out of three, the previous is either reversed (the odd coin out is the winner) or a regular two-way coin flip between the two remaining players can decide. The three-way flip is 75% likely to work each time it is tried (if all coins are heads or all are tails, each of which occur 1/8 of the time due to the chances being 0.5 by 0.5 by 0.5, the flip is repeated until the results differ), and does not require that "heads" or "tails" be called. A well-known example of such a three-way coin flip (choose two out of three) is dramatized in Friday Night Lights (originally a book, subsequently film and TV series), wherein three Texas high school football teams use a three-way coin flip. A legacy of that particular 1988 coin flip was to reduce the use of coin flips to break ties in Texas sports, instead using point systems to reduce the frequency of ties.

Use in dispute resolution

Coin tossing is a simple and unbiased way of settling a dispute or deciding between two or more arbitrary options. In a game theoretic analysis it provides even odds to both sides involved, requiring little effort and preventing the dispute from escalating into a struggle. It is used widely in sports and other games to decide arbitrary factors such as which side of the field a team will play from, or which side will attack or defend initially; these decisions may tend to favor one side, or may be neutral. Factors such as wind direction, the position of the sun, and other conditions may affect the decision. In team sports it is often the captain who makes the call, while the umpire or referee usually oversees such proceedings. A competitive method may be used instead of a toss in some situations, for example in basketball the jump ball is employed, while the face-off plays a similar role in ice hockey.

Coin flipping is used to decide which end of the field the teams will play to and/or which team gets first use of the ball, or similar questions in football matches, American football games, Australian rules football, volleyball, and other sports requiring such decisions. In the U.S. a specially minted coin is flipped in National Football League games; the coin is then sent to the Pro Football Hall of Fame, and other coins of the special series minted at the same time are sold to collectors. The original XFL, a short-lived American football league, attempted to avoid coin tosses by implementing a face-off style "opening scramble," in which one player from each team tried to recover a loose football; the team whose player recovered the ball got first choice. Because of the high rate of injury in these events, it has not achieved mainstream popularity in any football league (a modified version was adopted by X-League Indoor Football, in which each player pursued his own ball), and coin tossing remains the method of choice in American football. (The revived XFL, which launched in 2020, removed the coin toss altogether and allowed that decision to be made as part of a team's home field advantage.)

In an association football match, the team winning the coin toss chooses which goal to attack in the first half; the opposing team kicks off for the first half. For the second half, the teams switch ends, and the team that won the coin toss kicks off. Coin tosses are also used to decide which team has the pick of going first or second in a penalty shoot-out. Before the early-1970s introduction of the penalty shootout, coin tosses were occasionally needed to decide the outcome of drawn matches where a replay was not possible. The most famous instance of this was the semifinal game of the 1968 European Championship between Italy and the Soviet Union, which finished 0–0 after extra time. Italy won, and went on to become European champions.

In cricket the toss is often significant, as the decision whether to bat or bowl first can influence the outcome of the game. The coin toss in cricket is very important than other games because in many situations it can lead to win or loose the game. Factors such as pitch conditions, weather and day or night time are considered by the team captain who wins the toss. Now there are websites such as flip a coin online which domestic sports team use to toss the coin.

Similarly, in tennis a coin toss is used in professional matches to determine which player serves first. The player who wins the toss decides whether to serve first or return, while the loser of the toss decides which end of the court each player plays on first.

In duels a coin toss was sometimes used to determine which combatant had the sun at his back. In some other sports, the result of the toss is less crucial and merely a way to fairly choose between two more or less equal options.

The National Football League also has a coin toss for tie-breaking among teams for playoff berths and seeding, but the rules make the need for coin toss, which is random rather than competitive, very unlikely. A similar procedure breaks ties for the purposes of seeding in the NFL Draft; these coin tosses are more common, since the tie-breaking procedure for the draft is much less elaborate than the one used for playoff seeding.

Major League Baseball once conducted a series of coin flips as a contingency on the last month of its regular season to determine home teams for any potential one-game playoff games that might need to be added to the regular season. Most of these cases did not occur. From the 2009 season, the method to determine home-field advantage was changed.

Fédération Internationale d'Escrime rules use a coin toss to determine the winner of some fencing matches that remain tied at the end of a "sudden death" extra minute of competition. Although in most international matches this is now done electronically by the scoring apparatus.

In the United States Asa Lovejoy and Francis W. Pettygrove, who each owned the claim to the land that would later become Portland, Oregon, wanted to name the new town after their respective hometowns of Boston, Massachusetts and Portland, Maine; Pettygrove won the coin flip.

Scientists sometimes use coin flipping to determine the order in which they appear on the list of authors of scholarly papers.

In addition to its practical applications in sports, coin tossing is symbolic of the democratic principle of equal opportunity. When two parties face an impasse, the act of flipping a coin signifies a commitment to impartiality and a willingness to accept the outcome, no matter how arbitrary it may seem. This shared acceptance of chance as the ultimate arbiter can foster cooperation and conflict resolution in various aspects of life beyond sports, including business negotiations and interpersonal conflicts.

Australia
In December 2006, Australian television networks Seven and Ten, which shared the broadcasting of the 2007 AFL Season, decided who would broadcast the Grand Final with the toss of a coin. Network Ten won.

Canada
In some jurisdictions, a coin is flipped to decide between two candidates who poll equal number of votes in an election, or two companies tendering equal prices for a project. For example, a coin toss decided a City of Toronto tender in 2003 for painting lines on 1,605 km of city streets: the bids were $161,110.00 ($100.3800623 per km), $146,584.65 ($91.33 per km, exactly), and two equal bids of $111,242.55 ($69.31 per km, exactly).

Philippines
"Drawing of lots" is one of the methods to break ties to determine a winner in an election; the coin flip is considered an acceptable variant. Each candidate will be given five chances to flip a coin; the candidate with the most "heads" wins. The 2013 mayoral election in San Teodoro, Oriental Mindoro was decided on a coin flip, with a winner being proclaimed after the second round when both candidates remained tied in the first round.

United Kingdom
In the United Kingdom, if a local or national election has resulted in a tie where candidates receive exactly the same number of votes, then the winner can be decided either by drawing straws/lots, coin flip, or drawing a high card in pack of cards.

United States
In the United States, when a new state is added to the Union, a coin toss determines the class of the senators (i.e., the election cycle in which the term each of the new state's senators will expire) in the US Senate. Also, a number of states provide for "drawing lots" in the event an election ends in a tie, and this is usually resolved by a coin toss or picking names from a hat. A 2017 election to the 94th District of the Virginia House of Delegates resulted in a tie between Republican incumbent David Yancey and Democratic challenger Shelly Simmonds, with exactly 11,608 votes each. Under state law, the election was to be decided by drawing a name from a bowl, although a coin toss would also have been an acceptable option. The chair of the Board of Elections drew the film canister with Yancey's name, and he was declared the winner. Additionally, the outcome of the draw determined control of the entire House, as Republicans won 50 of the other 99 seats and Democrats 49. A Yancey win extended the Republican advantage to 51–49, whereas a Simmonds win would have resulted in a 50–50 tie. As there is no provision for breaking ties in the House as a whole, this would have forced a power sharing agreement between the two parties.

Physics
The outcome of coin flipping has been studied by the mathematician and former magician Persi Diaconis and his collaborators. They have demonstrated that a mechanical coin flipper which imparts the same initial conditions for every toss has a highly predictable outcome – the phase space is fairly regular. Further, in actual flipping, people exhibit slight bias – "coin tossing is fair to two decimals but not to three. That is, typical flips show biases such as 0.495 or 0.503."

In studying coin flipping, to observe the rotation speed of coin flips, Diaconis first used a strobe light and a coin with one side painted black, the other white, so that when the speed of the strobe flash equaled the rotation rate of the coin, it would appear to always show the same side. This proved difficult to use, and rotation rate was more accurately computed by attaching floss to a coin, such that it would wind around the coin – after a flip, one could count rotations by unwinding the floss, and then compute rotation rate as flips over air time.

Moreover, their theoretical analysis of the physics of coin tosses predicts a slight bias for a caught coin to be caught the same way up as it was thrown, with a probability of around 0.51, though a subsequent attempt to verify this experimentally gave ambiguous results. Stage magicians and gamblers, with practice, are able to greatly increase this bias, whilst still making throws which are visually indistinguishable from normal throws.

Since the images on the two sides of actual coins are made of raised metal, the toss is likely to slightly favor one face or the other if the coin is allowed to roll on one edge upon landing. Coin spinning is much more likely to be biased than flipping, and conjurers trim the edges of coins so that when spun they usually land on a particular face.

Counterintuitive properties
Human intuition about conditional probability is often very poor and can give rise to some seemingly surprising observations. For example, if the successive tosses of a coin are recorded as a string of "H" and "T", then for any trial of tosses, it is twice as likely that the triplet TTH will occur before THT than after it. It is three times as likely that "THH will precede HHT" than that "THH will follow HHT"; see also Penney's game.

Mathematics
The mathematical abstraction of the statistics of coin flipping is described by means of the Bernoulli process; a single flip of a coin is a Bernoulli trial. In the study of statistics, coin-flipping plays the role of being an introductory example of the complexities of statistics. A commonly treated textbook topic is that of checking if a coin is fair.

Telecommunications
There is no reliable way to use a true coin flip to settle a dispute between two parties if they cannot both see the coin—for example, over the phone. The flipping party could easily lie about the outcome of the toss. In telecommunications and cryptography, the following algorithm can be used:

 * 1) Alice and Bob each privately choose a random word, e.g.   and   respectively.
 * 2) Alice privately decides to call "tails" on the coin flip.
 * 3) Bob sends Alice his chosen word.
 * 4) Alice computes a cryptographic hash of a string that includes the two chosen words and the call (e.g.  ), and sends that hash (e.g.  ) to Bob.
 * 5) Bob performs the physical coin flip, and announces the result, heads or tails, to Alice.
 * 6) Alice reveals that the string she hashed was , including both of their words and a call of
 * 7) Bob confirms for himself that   is the hash of
 * 8) Both parties can now determine whether Alice's call of "tails" matched Bob's coin.

Bob, by providing his own random word, guarantees that Alice is not able to precompute an image pair of "tail/random string" or "head/random string", for two different random words. Bob is also unable to reverse Alice's hash to see what her chosen outcome was before flipping the coin, and to lie effectively about its outcome, because he does not know Alice's random word at that point in the process.

Lotteries
The New Zealand lottery game Big Wednesday uses a coin toss. If a player matches all 6 of their numbers, the coin toss will decide whether they win a cash jackpot (minimum of NZ$25,000) or a bigger jackpot with luxury prizes (minimum of NZ$2 million cash, plus value of luxury prizes.) The coin toss is also used in determining the Second Chance winner's prize.

Clarifying feelings
A technique attributed to Sigmund Freud to help in making difficult decisions is to toss a coin not actually to determine the decision, but to clarify the decision-maker's feelings. He explained: "I did not say you should follow blindly what the coin tells you. What I want you to do is to note what the coin indicates. Then look into your own reactions. Ask yourself: Am I pleased? Am I disappointed? That will help you to recognize how you really feel about the matter, deep down inside. With that as a basis, you'll then be ready to make up your mind and come to the right decision."

Danish poet Piet Hein's 1966 book Grooks includes a poem, "A Psychological Tip", on a similar theme:

Whenever you're called on to make up your mind, And you're hampered by not having any, The best way to solve the dilemma, you'll find, Is simply by spinning a penny. No—not so that chance shall decide the affair While you're passively standing there moping; But the moment the penny is up in the air, You suddenly know what you're hoping.

title: Coin flipping


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Shirokawa, Ehime

Shirokawa (城川町) was a town located in Higashiuwa District, Ehime Prefecture, Japan.

As of 2003, the town had an estimated population of 4,583 and a density of 36.00 persons per km2. The total area was 127.31 km2.

On April 1, 2004, Shirokawa, along with the towns of Akehama, Nomura and Uwa (all from Higashiuwa District), and the town of Mikame (from Nishiuwa District), was merged to create the city of Seiyo.

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

title: Shirokawa, Ehime


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Higashiuwa District, Ehime

Higashiuwa (東宇和郡) was a district located in Ehime Prefecture, Japan.

History

 * 1878 — Uwa District was split up by Meiji era land reforms. Higashiuwa District was thus born. (1 town, 21 villages)
 * January 1, 1914 — Parts of the village of Tanisuji was merged into the village of No.
 * January 1, 1922 — The village of No was elevated to town status to become the town of Nomura. (2 towns, 20 villages)
 * February 11, 1922 — The village of Kamiuwa was merged into the town of Uwa. (2 towns, 19 villages)
 * December 1, 1929 — The villages of Kasagi and Yamada were merged to create the village of Iwaki. (2 towns, 18 villages)
 * April 1, 1943, parts of the village of Ukena (from Kamiukena District) was merged into the village of Sōkawa.
 * March 31, 1954 — The villages of Yusukawa, Doi, Takagawa and Uonashi were merged to create the village of Kurosegawa. (2 towns, 15 villages)
 * March 31, 1954 — The villages of Tada, Nakagawa, Iwaki, Shimouwa and Tanosuji were merged into the town of Uwa. (2 towns, 10 villages)
 * February 11, 1955 — The villages of Nakasuji, Tanisuji, Sōkawa, and parts of Kaibuki and Yokobayashi were merged into the town of Nomura. (2 towns, 7 villages)
 * February 11, 1955 — Parts of the villages of Kaibuki and Yokobayashi merged into the village of Hijikawa in Kita District (now the city of Ōzu). (2 towns, 5 villages)
 * March 31, 1955 — The villages of Tawarazu and Karie were merged to create the village of Toyoumi. (2 towns, 4 villages)
 * March 31, 1955 — The village of Tamatsu was merged into the town of Yoshida (from Kitauwa District) (now the city of Uwajima). (2 towns, 3 villages)
 * January 1, 1958 — The villages of Toyoumi and Takayama were merged to create the town of Akehama. (3 towns, 1 village)
 * August 1, 1958 — parts of the city of Ōzu was merged into the town of Uwa.
 * April 1, 1959 — The village of Kurosegawa was renamed and elevated to town status to become the town of Shirokawa. (4 towns)
 * April 1, 2004 — The towns of Akehama, Nomura, Shirokawa and Uwa, along with the town of Mikame (from Nishiuwa District) were to create the city of Seiyo. Therefore, Higashiuwa District was dissolved as a result of this merger.

title: Higashiuwa District, Ehime


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Yoshida, Ehime

Yoshida (吉田町) was a town located in Kitauwa District, Ehime Prefecture, Japan.

As of 2003, the town had an estimated population of 12,418 and a density of 257.85 persons per km2. The total area was 48.16 km2.

On August 1, 2005, Yoshida, along with the towns of Mima and Tsushima (all from Kitauwa District), was merged into the expanded city of Uwajima.

title: Yoshida, Ehime


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Mima, Ehime

Mima (三間町) was a town located in Kitauwa District, Ehime Prefecture, Japan.

As of 2003, the town had an estimated population of 6,562 and a density of 115.30 persons per km2. The total area was 56.91 km2.

On August 1, 2005, Mima, along with the towns of Tsushima and Yoshida (all from Kitauwa District), was merged into the expanded city of Uwajima.

title: Mima, Ehime


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Proper time

In relativity, proper time (from Latin, meaning own time) along a timelike world line is defined as the time as measured by a clock following that line. The proper time interval between two events on a world line is the change in proper time, which is independent of coordinates, and is a Lorentz scalar. The interval is the quantity of interest, since proper time itself is fixed only up to an arbitrary additive constant, namely the setting of the clock at some event along the world line.

The proper time interval between two events depends not only on the events, but also the world line connecting them, and hence on the motion of the clock between the events. It is expressed as an integral over the world line (analogous to arc length in Euclidean space). An accelerated clock will measure a smaller elapsed time between two events than that measured by a non-accelerated (inertial) clock between the same two events. The twin paradox is an example of this effect.

By convention, proper time is usually represented by the Greek letter τ (tau) to distinguish it from coordinate time represented by t. Coordinate time is the time between two events as measured by an observer using that observer's own method of assigning a time to an event. In the special case of an inertial observer in special relativity, the time is measured using the observer's clock and the observer's definition of simultaneity.

The concept of proper time was introduced by Hermann Minkowski in 1908, and is an important feature of Minkowski diagrams.

Mathematical formalism
The formal definition of proper time involves describing the path through spacetime that represents a clock, observer, or test particle, and the metric structure of that spacetime. Proper time is the pseudo-Riemannian arc length of world lines in four-dimensional spacetime. From the mathematical point of view, coordinate time is assumed to be predefined and an expression for proper time as a function of coordinate time is required. On the other hand, proper time is measured experimentally and coordinate time is calculated from the proper time of inertial clocks.

Proper time can only be defined for timelike paths through spacetime which allow for the construction of an accompanying set of physical rulers and clocks. The same formalism for spacelike paths leads to a measurement of proper distance rather than proper time. For lightlike paths, there exists no concept of proper time and it is undefined as the spacetime interval is zero. Instead, an arbitrary and physically irrelevant affine parameter unrelated to time must be introduced.

In special relativity
With the timelike convention for the metric signature, the Minkowski metric is defined by $$\eta_{\mu\nu} = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix} ,$$ and the coordinates by $$(x^0, x^1, x^2, x^3) = (ct, x, y, z)$$ for arbitrary Lorentz frames.

In any such frame an infinitesimal interval, here assumed timelike, between two events is expressed as

and separates points on a trajectory of a particle (think clock). The same interval can be expressed in coordinates such that at each moment, the particle is at rest. Such a frame is called an instantaneous rest frame, denoted here by the coordinates $$(c\tau,x_\tau,y_\tau,z_\tau)$$ for each instant. Due to the invariance of the interval (instantaneous rest frames taken at different times are related by Lorentz transformations) one may write $$ds^2 = c^2 d\tau^2 - dx_\tau^2 - dy_\tau^2 - dz_\tau^2 = c^2 d\tau^2,$$ since in the instantaneous rest frame, the particle or the frame itself is at rest, i.e., $$dx_\tau = dy_\tau = dz_\tau = 0$$. Since the interval is assumed timelike (ie. $$ds^2 > 0$$), taking the square root of the above yields $$ds = cd\tau,$$ or $$d\tau = \frac{ds}{c}.$$ Given this differential expression for $$, the proper time interval is defined as

Here $τ$ is the worldline from some initial event to some final event with the ordering of the events fixed by the requirement that the final event occurs later according to the clock than the initial event.

Using $$ and again the invariance of the interval, one may write

where $$ (x^0, x^1, x^2, x^3 ) : [ a, b ] \rightarrow P $$ is an arbitrary bijective parametrization of the worldline $P$ such that $$(x^0(a), x^1(a), x^2(a), x^3(a))\quad\text{and}\quad (x^0(b), x^1(b), x^2(b), x^3(b))$$ give the endpoints of $$ and a < b; $v(t)$ is the coordinate speed at coordinate time $$; and $x(t)$, $y(t)$, and $z(t)$ are space coordinates. The first expression is manifestly Lorentz invariant. They are all Lorentz invariant, since proper time and proper time intervals are coordinate-independent by definition.

If $t, x, y, z$, are parameterised by a parameter $P$, this can be written as $$ \Delta\tau = \int \sqrt {\left (\frac{dt}{d\lambda}\right)^2 - \frac{1}{c^2} \left [ \left (\frac{dx}{d\lambda}\right)^2 + \left (\frac{dy}{d\lambda}\right)^2 + \left ( \frac{dz}{d\lambda}\right)^2 \right] } \,d\lambda.$$

If the motion of the particle is constant, the expression simplifies to $$ \Delta \tau = \sqrt{\left(\Delta t\right)^2 - \frac{\left(\Delta x\right)^2}{c^2} - \frac{\left(\Delta y\right)^2}{c^2} - \frac{\left(\Delta z\right)^2}{c^2}},$$ where Δ means the change in coordinates between the initial and final events. The definition in special relativity generalizes straightforwardly to general relativity as follows below.

In general relativity
Proper time is defined in general relativity as follows: Given a pseudo-Riemannian manifold with a local coordinates $x^{μ}$ and equipped with a metric tensor $g_{μν}$, the proper time interval $Δτ$ between two events along a timelike path $P$ is given by the line integral

This expression is, as it should be, invariant under coordinate changes. It reduces (in appropriate coordinates) to the expression of special relativity in flat spacetime.

In the same way that coordinates can be chosen such that $x^{1}, x^{2}, x^{3} = const$ in special relativity, this can be done in general relativity too. Then, in these coordinates, $$\Delta\tau = \int_P d\tau = \int_P \frac{1}{c}\sqrt{g_{00}} dx^0.$$

This expression generalizes definition $t$ and can be taken as the definition. Then using invariance of the interval, equation $λ$ follows from it in the same way $P$ follows from $$, except that here arbitrary coordinate changes are allowed.

Example 1: The twin "paradox"
For a twin paradox scenario, let there be an observer A who moves between the A-coordinates (0,0,0,0) and (10 years, 0, 0, 0) inertially. This means that A stays at $$x = y = z = 0$$ for 10 years of A-coordinate time. The proper time interval for A between the two events is then $$\Delta \tau_A = \sqrt{(10\text{ years})^2} = 10\text{ years}.$$

So being "at rest" in a special relativity coordinate system means that proper time and coordinate time are the same.

Let there now be another observer B who travels in the x direction from (0,0,0,0) for 5 years of A-coordinate time at 0.866c to (5 years, 4.33 light-years, 0, 0). Once there, B accelerates, and travels in the other spatial direction for another 5 years of A-coordinate time to (10 years, 0, 0, 0). For each leg of the trip, the proper time interval can be calculated using A-coordinates, and is given by $$\Delta \tau_{leg} = \sqrt{(\text{5 years})^2 - (\text{4.33 years})^2} = \sqrt{6.25\;\mathrm{years}^2} = \text{2.5 years}.$$

So the total proper time for observer B to go from (0,0,0,0) to (5 years, 4.33 light-years, 0, 0) and then to (10 years, 0, 0, 0) is $$\Delta \tau_B = 2 \Delta \tau_{leg} = \text{5 years}.$$

Thus it is shown that the proper time equation incorporates the time dilation effect. In fact, for an object in a SR (special relativity) spacetime traveling with velocity $$v$$ for a time $$\Delta T$$, the proper time interval experienced is $$\Delta \tau = \sqrt{\Delta T^2 - \left(\frac{v_x \Delta T}{c}\right)^2 - \left(\frac{v_y \Delta T}{c}\right)^2 - \left(\frac{v_z \Delta T}{c}\right)^2 } = \Delta T \sqrt{1 - \frac{v^2}{c^2}}, $$ which is the SR time dilation formula.

Example 2: The rotating disk
An observer rotating around another inertial observer is in an accelerated frame of reference. For such an observer, the incremental ($$d\tau$$) form of the proper time equation is needed, along with a parameterized description of the path being taken, as shown below.

Let there be an observer C on a disk rotating in the xy plane at a coordinate angular rate of $$\omega$$ and who is at a distance of r from the center of the disk with the center of the disk at $x = y = z = 0$. The path of observer C is given by $$(T, \, r\cos(\omega T), \, r\sin(\omega T), \, 0)$$, where $$T $$ is the current coordinate time. When r and $$\omega$$ are constant, $$dx = -r \omega \sin(\omega T) \, dT$$ and $$dy = r \omega \cos(\omega T) \, dT$$. The incremental proper time formula then becomes $$d\tau = \sqrt{dT^2 - \left(\frac{r \omega}{c}\right)^2 \sin^2(\omega T)\; dT^2 - \left(\frac{r \omega}{c}\right)^2 \cos^2(\omega T) \; dT^2} = dT\sqrt{1 - \left ( \frac{r\omega}{c} \right )^2}.$$

So for an observer rotating at a constant distance of r from a given point in spacetime at a constant angular rate of ω between coordinate times $$T_1$$ and $$T_2$$, the proper time experienced will be $$\int_{T_1}^{T_2} d\tau = (T_2 - T_1) \sqrt{ 1 - \left ( \frac{r\omega}{c} \right )^2} = \Delta T \sqrt{1 - v^2/c^2},$$ as $v = rω$ for a rotating observer. This result is the same as for the linear motion example, and shows the general application of the integral form of the proper time formula.

Examples in general relativity
The difference between SR and general relativity (GR) is that in GR one can use any metric which is a solution of the Einstein field equations, not just the Minkowski metric. Because inertial motion in curved spacetimes lacks the simple expression it has in SR, the line integral form of the proper time equation must always be used.

Example 3: The rotating disk (again)
An appropriate coordinate conversion done against the Minkowski metric creates coordinates where an object on a rotating disk stays in the same spatial coordinate position. The new coordinates are $$r= \sqrt{x^2 + y^2}$$ and $$\theta = \arctan\left(\frac{y}{x}\right) - \omega t.$$

The t and z coordinates remain unchanged. In this new coordinate system, the incremental proper time equation is $$d\tau = \sqrt{\left [1 - \left (\frac{r \omega}{c} \right )^2 \right] dt^2 - \frac{dr^2}{c^2} - \frac{r^2\, d\theta^2}{c^2} - \frac{dz^2}{c^2} - 2 \frac{r^2 \omega \, dt \, d\theta}{c^2}}.$$

With r, θ, and z being constant over time, this simplifies to $$d\tau = dt \sqrt{ 1 - \left (\frac{r \omega}{c} \right )^2 },$$ which is the same as in Example 2.

Now let there be an object off of the rotating disk and at inertial rest with respect to the center of the disk and at a distance of R from it. This object has a coordinate motion described by $dθ = −ω dt$, which describes the inertially at-rest object of counter-rotating in the view of the rotating observer. Now the proper time equation becomes $$d\tau = \sqrt{\left [1 - \left (\frac{R \omega}{c} \right )^2 \right] dt^2 - \left (\frac{R\omega}{c} \right ) ^2 \,dt^2 + 2 \left ( \frac{R \omega}{c} \right ) ^2 \,dt^2} = dt. $$

So for the inertial at-rest observer, coordinate time and proper time are once again found to pass at the same rate, as expected and required for the internal self-consistency of relativity theory.

Example 4: The Schwarzschild solution – time on the Earth
The Schwarzschild solution has an incremental proper time equation of $$ d\tau = \sqrt{ \left( 1 - \frac{2m}{r} \right) dt^2 - \frac{1}{c^2} \left( 1 - \frac{2m}{r} \right)^{-1} dr^2 - \frac{r^2}{c^2} d\phi^2 - \frac{r^2}{c^2} \sin^2(\phi ) \, d\theta^2 }, $$ where
 * t is time as calibrated with a clock distant from and at inertial rest with respect to the Earth,
 * r is a radial coordinate (which is effectively the distance from the Earth's center),
 * ɸ is a co-latitudinal coordinate, the angular separation from the north pole in radians.
 * θ is a longitudinal coordinate, analogous to the longitude on the Earth's surface but independent of the Earth's rotation. This is also given in radians.
 * m is the geometrized mass of the Earth, m = GM/c2,
 * M is the mass of the Earth,
 * G is the gravitational constant.

To demonstrate the use of the proper time relationship, several sub-examples involving the Earth will be used here.

For the Earth, $M = 5,974,200,000,000,000,000,000,000 kg$, meaning that $m = 0.004 m$. When standing on the north pole, we can assume $$dr = d\theta = d\phi = 0 $$ (meaning that we are neither moving up or down or along the surface of the Earth). In this case, the Schwarzschild solution proper time equation becomes $d\tau = dt \,\sqrt{1 - 2m/r}$. Then using the polar radius of the Earth as the radial coordinate (or $$r = \text{6,356,752 metres}$$), we find that $$d\tau = \sqrt{\left ( 1 - 1.3908 \times 10^{-9} \right ) \;dt^2} = \left (1 - 6.9540 \times 10^{-10} \right ) \,dt.$$

At the equator, the radius of the Earth is $r = 6,378,137 metres$. In addition, the rotation of the Earth needs to be taken into account. This imparts on an observer an angular velocity of $$ d\theta / dt$$ of 2π divided by the sidereal period of the Earth's rotation, 86162.4 seconds. So $$d\theta = 7.2923 \times 10^{-5} \, dt$$. The proper time equation then produces $$d\tau = \sqrt{\left ( 1 - 1.3908 \times 10^{-9} \right ) dt^2 - 2.4069 \times 10^{-12}\, dt^2} = \left( 1 - 6.9660 \times 10^{-10}\right ) \, dt.$$

From a non-relativistic point of view this should have been the same as the previous result. This example demonstrates how the proper time equation is used, even though the Earth rotates and hence is not spherically symmetric as assumed by the Schwarzschild solution. To describe the effects of rotation more accurately the Kerr metric may be used.

title: Proper time


text:
User talk:Johnasher

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title: User talk:Johnasher


text:
Public holidays in Samoa

Public holidays in Samoa are defined in the Public Holidays Act 2008:

In addition to holidays with fixed dates, polling day and the day before polling day is a public holiday in any year when an election is held. In addition, the O le Ao o le Malo can declare public holidays in accordance with the Act.

title: Public holidays in Samoa


text:
Matsuno, Ehime

Matsuno (松野町) is a town located in Kitauwa District, Ehime Prefecture, Japan. , the town had an estimated population of 3,693 in 1978 households, and a population density of 38 persons per km². The total area of the town is 98.45 sqkm.

Geography
Matsuno is located in mountainous southwestern Ehime Prefecture, on the middle reaches of the Hiromi River, one of the tributaries of the Shimanto River. Forests occupy 84% of the total area. Although located due east of Uwajima across Mount Onigajo, due to lack of roads, it is not possible to go directly to Uwajima from Matsuno without going through Kihoku. A small portion of the town is within the borders of the Ashizuri-Uwakai National Park.

Surrounding municipalities
Ehime Prefecture Kōchi Prefecture
 * Uwajima
 * Kihoku
 * Shimanto (city)
 * Shimanto (town)

Climate
Matsuno has a Humid subtropical climate (Köppen Cfa) characterized by warm summers and cool winters with light snowfall. The average annual temperature in Matsuno is 14.5 °C. The average annual rainfall is 2010 mm with September as the wettest month. The temperatures are highest on average in January, at around 25.0 °C, and lowest in January, at around 3.9 °C.

Demographics
Per Japanese census data, the population of Matsuno has been decreased steadily since the 1950s.

History
The area of Matsuno was part of ancient Iyo Province. During the Edo period, the area was part of the holdings of Uwajima Domain ruled by the Date clan from their seat at Uwajima Castle. The villages of Meiji (明治村) and Yoshinobu (吉野生村) within Kitauwa District were established with the creation of the modern municipalities system on October 1, 1889. Meiji was elevated to town status on November 10, 1940 and renamed Matsumaru (松丸町). Matsumaru merged with Yoshinobu on March 31, 1955 to form the town of Matsuno. Proposals to merge with neighboring Kihoku and/or Uwajima were shelved in 2010 after a highly contentious referendum, leaving Matsuno is as the least populous town in Ehime.

Government
Matsuo has a mayor-council form of government with a directly elected mayor and a unicameral town council of seven members. Matsuno, together with Uwajima and Kihoku, contributes four members to the Ehime Prefectural Assembly. In terms of national politics, the town is part of Ehime 4th district of the lower house of the Diet of Japan.

Economy
Matsuno's economy is centered on forestry and to a lesser extent, horticulture. Matsuno is known for its peach production, but not on a large scale. There are many river terraces formed by undulating rivers, and there is little flat land.

Education
Matsuo has two public elementary schools and one public middle school operated by the town government. The town does not have a high school.

Railways
Shikoku Railway Company - Yodo Line
 * Matsuchi - Yoshinobu - Matsumaru

Local attractions
The town is known for its annual half-marathon. The total area is 98.50 km2.

title: Matsuno, Ehime


text:
Kārlis Ulmanis

Kārlis Augusts Vilhelms Ulmanis (4 September 1877 – 20 September 1942) was a Latvian politician and a dictator. He was one of the most prominent Latvian politicians of pre-World War II Latvia during the Interwar period of independence from November 1918 to June 1940 and served as the country's first prime minister.

He served four times as prime minister, the last time as the head of an authoritarian regime, during which he subsequently also adopted the title of President of Latvia. The legacy of his dictatorship continues to divide public opinion in Latvia today.

Early life
Born in a prosperous farming family, Ulmanis studied agriculture at the Swiss Federal Institute of Technology Zurich and at Leipzig University. He then worked in Latvia as a writer, lecturer, and manager in agricultural positions. He was politically active during the 1905 Revolution, was briefly imprisoned in Pskov, and subsequently fled Latvia to avoid incarceration by the Russian authorities. During this period of exile, he studied at the University of Nebraska–Lincoln in the United States as Karl August Ulmann, earning a Bachelor of Science degree in agriculture. After working briefly at that university as a lecturer, Ulmanis moved to Houston, Texas. The dairy business he had bought there ran into financial difficulties.

Ulmanis returned to Latvia from American exile in 1913, after being informed that it was now safe for political exiles to return due to the declaration of a general amnesty by Nicholas II of Russia. This safety was short-lived as World War I broke out one year later and Courland Governorate was partially occupied by Germany in 1915.

Political career in independent Latvia
In the last stages of World War I, he founded the Latvian Farmers' Union, one of the two most prominent political parties in Latvia at that time. Ulmanis was one of the principal founders of the People's Council, which proclaimed Latvia's independence on 18 November 1918, with Ulmanis as the Prime Minister of the first Provisional government of Latvia. After the Latvian War of Independence of 1919–1920, a constitutional convention established Latvia as a parliamentary democracy in 1920. Ulmanis served as Prime Minister in several subsequent Latvian government administrations from 1918 to 1934.

Coup of 15 May 1934
On the night of 15–16 May 1934, Ulmanis, with the support of Minister of War Jānis Balodis, proclaimed a state of war and dissolved all political parties and the Saeima (parliament). The bloodless coup was carried out by army and units of the national guard Aizsargi loyal to Ulmanis. They moved against key government offices, communications and transportation facilities. Many elected officials and politicians (almost exclusively Social Democrats, as well as figures from the extreme right and left) were detained, as were any military officers who resisted the coup d'etat. Some 2,000 Social Democrats were initially detained by the authorities, including most of the Social Democratic members of the disbanded Saeima, as were members of various right-wing radical organisations, such as Pērkonkrusts.

In all, 369 Social Democrats, 95 members of Pērkonkrusts, pro-Nazi activists from the Baltic German community, and a handful of politicians from other parties were interned in a prison camp established in the Karosta district of Liepāja. After several Social Democrats, such as Bruno Kalniņš, had been cleared of weapons charges by the courts, most of those imprisoned began to be released over time. Those convicted by the courts of treasonous acts, such as the leader of Pērkonkrusts Gustavs Celmiņš, remained behind bars for the duration of their sentences, three years in the case of Celmiņš.

For the next four years, Ulmanis ruled by decree, without a parliament. A decree vested the Saeima's functions in the cabinet until a new constitution could be drafted. Although the incumbent State President Alberts Kviesis did not support the coup, he remained in office and collaborated with Ulmanis.

On 19 March 1936 Ulmanis' cabinet drafted a law that provided for Ulmanis to become State President as well as Prime Minister upon the expiration of Kviesis' term. This clearly violated the Constitution, which stipulated that the chairman of the Saeima would become acting president pending new elections. However, no one dared object. When Kviesis left office on 11 April 1936, Ulmanis combined the offices of president and prime minister.

Authoritarian regime
The Ulmanis regime was unique among other European dictatorships of the interwar period. Ulmanis did not create a ruling party, rubber-stamp parliament or a new ideology. It was a personal, paternalistic dictatorship in which Ulmanis—who called himself "the leader of the people"—claimed to do what he thought was best for Latvians. All political life was proscribed, culture and economy was eventually organized into a type of corporate statism made popular during those years by Mussolini. Chambers of Professions were created, similar to Chambers of Corporations in other dictatorships.

All political parties, including Ulmanis' own Farmers' Union, were outlawed. Part of the constitution of the Latvian Republic and civil liberties were suspended. All newspapers owned by political parties or organisations were closed and all publications were subjected to censorship and government oversight by the Ministry of Public Affairs led by Alfrēds Bērziņš. The army and the Aizsargi paramilitary were lavished with privileges.

Ulmanis is often believed to have been a popular leader especially among farmers and ethnic Latvians. This is debatable. His party had never won more than 17 percent of the vote in any election and had seen its support steadily decline in the years since the 1922 constitutional convention. In the 1931 election, the Farmers' Union only won 12.2 percent of the vote, an all-time low. Some historians believe that one of the chief motives for the coup was his fear of losing even more votes in the upcoming elections. From the time of his coup until his demise, for obvious reasons, no reliable voting or popularity statistics were available.

Ideology
Ulmanis was a Latvian nationalist, who espoused the slogan "Latvia for Latvians" which meant that Latvia was to be a Latvian nation state, not a multinational state with traditional Baltic German elites and Jewish entrepreneurial class. At the same time, the slogan "Latvia's sun shines equally over everyone" was used and no ethnic group was actively targeted. A limited number of German, Jewish and other minority press and organizations continued to exist as far as the limitations of authoritarian dictatorship permitted. Yiddish newspapers were hit particularly hard. In practice only the religious party Agudat Israel's newspaper Haint was not forbidden, while popular publications Dos Folk, Frimorgn, Riger Tog, and Naier Fraitik were closed. The official 1936 chamber of commerce list of newspapers and magazines does not list a single Yiddish, Hebrew or Jewish publication.

Latvianisation policies were followed in the area of education, cutting and removing subsidies for minority education. During Ulmanis' rule, education was strongly emphasized and literacy rates in Latvia reached high levels. Especially in eastern Latvia Latgale region however, education was actively used as a tool of assimilation of minorities. Many new schools were built, but they were Latvian schools and minority children were thus assimilated.

Economy
Economic historians are divided as whether Latvia experienced economic stagnation or prosperity during the Ulmanis regime. The state assumed a larger role in the economy and state capitalism was introduced by purchasing and uniting smaller competing private companies into larger state enterprises. This process was controlled by Latvijas Kredītbanka, a state bank established in 1935. Many large-scale building projects were undertaken—new schools, administrative buildings, Ķegums Hydroelectric Power Station. Due to an application of the economics of comparative advantage, the United Kingdom and Germany became Latvia's major trade partners, while trade with the USSR was reduced. The economy, especially the agriculture and manufacturing sectors, was micromanaged to an extreme degree. Ulmanis nationalised many industries. This resulted in rapid economic growth, during which Latvia attained a very high standard of living. At a time when most of the world's economy was still suffering from the effects of the Great Depression, Latvia could point to increases in both gross national product (GNP) and in exports of Latvian goods overseas. This, however, came at the cost of liberty and civil rights.

The policy of Ulmanis, even before his accession to power, was openly directed toward eliminating the minority groups from economic life and of giving Latvians of Latvian ethnicity access to all positions in the national economy. This was sometimes referred to as "Lettization". According to some estimates, about 90% of the banks and credit establishments in Latvia were state-owned or under Latvian management in 1939, against 20% in 1933. Alfrēds Birznieks, the minister of agriculture, in a speech delivered in Ventspils on 26 January 1936, said: "Latvian people are the only masters of this country; Latvians will themselves promulgate the laws and judge for themselves what justice is."

As a result, the economic and cultural influence of minorities—Germans, Jews, Russians, Poles—declined.

Latvia's first full-length sound movie Fishermans' Son (1939) was a tale of a young fisherman who tries to free other local fishermen from the power of a middleman and shows them that the future lies in cooperative work. The movie was based on a widely popular novel written by Vilis Lācis who in 1940 became the Prime Minister of the Soviet-occupied Latvian SSR.

Later life and death
On 23 August 1939 Adolf Hitler's Germany and Joseph Stalin's USSR signed a non-aggression agreement, known as the Molotov–Ribbentrop Pact, which contained a secret addendum (revealed only in 1945), dividing Eastern Europe into spheres of influence. Latvia was thereby assigned to the Soviet sphere. Following a Soviet ultimatum in October 1939, Ulmanis signed the Soviet–Latvian Mutual Assistance Treaty and allowed the formation of Soviet military bases in Latvia. On 17 June 1940 Latvia was completely occupied by the Soviet Union. Rather than risk an unwinnable war, Ulmanis gave a nationwide radio address ordering no resistance to the Red Army, saying "I will remain in my place and you remain in yours".

For the next month, Ulmanis cooperated with the Soviets. He resigned as prime minister three days after the coup, and appointed a left-wing government headed by Augusts Kirhenšteins—which, in truth, had been chosen by the Soviet embassy. Soviet-controlled elections for a "People's Saeima" were held on 14–15 July, in which voters were presented with a single list from a Communist-dominated alliance. The new "People's Saeima" met on 21 July with only one order of business—a resolution proclaiming Latvia a Soviet republic and seeking admission to the Soviet Union, which carried unanimously. This move was illegal under the Latvian Constitution, which stipulated that a major change to the basic constitutional order could only be enacted after two-thirds of the electorate approved it via a plebiscite. Since Latvia seceded from the Soviet Union in 1990, it has argued that the resolution seeking admission to the Soviet Union was illegal, and that the People's Saeima was elected in accordance with an illegal and unconstitutional election law.

Also on 21 July, Ulmanis was forced to resign and asked the Soviet government for a pension and permission to emigrate to Switzerland. Instead, he was arrested and sent to Stavropol in Russian SFSR, where he worked in his original profession as an agronom for a year. After the start of Operation Barbarossa, he was imprisoned in July 1941. A year later, as German armies were closing in on Stavropol, he and other inmates were evacuated to prison in Krasnovodsk, Turkmen SSR (present-day Türkmenbaşy in Turkmenistan). On the way there, he contracted dysentery and soon died on 20 September 1942. For a long time, his burial place was unknown. In 2011 Georgian media reported that Ulmanis may be buried in Gori City Cemetery, according to a former gravedigger who claimed that he was convoyed by KGB officers and had to dig the grave for Ulmanis. However, in 2017, Ulmanis' grand-nephew, Guntis Ulmanis, announced that the search had been called off as it was apparent the site would be impossible to find.

Later assessments
Kārlis Ulmanis's legacy for Latvia and Latvians is a complex one. In the postwar Latvian SSR the Soviet régime labelled Ulmanis a fascist, indistinguishable from the Nazis, accusing him of corruption and of bloody repressions against Latvian workers.

Among the postwar Latvian émigrés of Latvian cultural background in exile, Ulmanis was idealised by many of those who viewed his 6-year authoritarian rule as a Golden Age of the Latvian nation. Some traditions created by Ulmanis, such as the so-called Friendly invitation, a charitable donations to one's former school, continued to be upheld.

In independent Latvia today, Ulmanis remains a popular, if also controversial figure. Many Latvians view him as a symbol of Latvia's independence in pre-World War II Latvia, and historians are generally in agreement about his positive early role as prime minister during the country's formative years. With regard to the authoritarian period, opinions diverge, however. On the one hand, it is possible to credit Ulmanis for the rise of ethnic Latvians' economic prosperity during the 1930s, and stress that under his rule there was not the same level of militarism or mass political oppression that characterized other dictatorships of the day. On the other hand, historians such as Ulmanis' biographer Edgars Dunsdorfs are of the view that someone who disbanded Parliament and adopted authoritarian rule cannot be regarded as a positive figure, even if that rule was in some terms a prosperous one.

One sign that Ulmanis was still very popular in Latvia during the first years of regained independence was the election of his grand-nephew Guntis Ulmanis as President of Latvia in 1993.

One of the major traffic routes in Riga, the capital of Latvia, is named after him (Kārļa Ulmaņa gatve, previously named after Ernst Thälmann). In 2003, a monument of Ulmanis was unveiled in a park in Riga centre.

Personal life and family
Not much is known about the personal life of Ulmanis. It is known that he never married and there are no records of him dating anyone. When once asked about why he was not married or did not have a significant other, his response was "I am married to Latvia, and that is enough for me." During his lifetime, there were rumors over his sexuality, with some claims that he might have been homosexual. The rumors were also fueled by Ulmanis' close relationships with two of his male employees. The rumors were also fueled by Ulmanis himself not giving any information about his personal life. He did not have any offspring, although his brother did, with Ulmanis' grandnephew Guntis Ulmanis later becoming the president of Latvia.

title: Kārlis Ulmanis


text:
List of rocket-powered aircraft

 * Arado E.381 Kleinstjäger || Germany || Air launch || Fighter || 1944 || Project || 0 || Carried by an Arado Ar 234.
 * Avro 720 || UK || CTOL || || 1956 || Project || 0 || Mixed power.
 * Bachem Ba 349 "Natter" || Germany || VTOL || Fighter || 1945 || Production || 36 || Point defence interceptor. Never saw action (debatable footage, seems to show a Ba 349 in combat. ).
 * Bell X-1 || USA || Air launch || Research || 1947 || Prototype || 7 || First aircraft to break the sound barrier in level flight.
 * Bell X-2 || USA || Air launch || Research || 1955 || Prototype || 2 || Supersonic.
 * Bereznyak-Isayev BI-1 || USSR || CTOL || Fighter || 1942 || || 9 ||
 * Bisnovat 5 || USSR || CTOL || || 1948 || Project || || Based on captured DFS 346. Never flew under power.
 * Cattaneo Magni RR || Italy || CTOL || Research || 1931 || Prototype || ||
 * Cheranovsky RP-1 || USSR|| CTOL || Research || 1932 || Prototype || || Test in 1933 ended in engine failure.
 * DFS 194 || Germany || CTOL || Experimental || 1940 || Operational || 1 || Tailless, direct predecessor of Me 163 series.
 * Douglas D-558-2 Skyrocket || USA || Air launch || Research || 1953 || Operational || 3 || Supersonic.
 * EZ-Rocket || USA || CTOL || Experimental || 2001 || Prototype || 1 || Rocket-powered variant of Rutan Long-EZ.
 * Focke-Wulf Volksjäger || Germany || CTOL || Fighter || 1944 || Project || 0 || Three rocket-powered variants under construction at the end of hostilities.
 * Hawker P.1072 || UK || CTOL || || 1949 || Prototype || 1 || Mixed power.
 * Heinkel He 112R || Germany || CTOL || Experimental || 1937 || Operational || 1 || Rocket and piston engines.
 * Heinkel He 176 || Germany || CTOL || Research || 1939 || Prototype || 1 || Pioneering liquid-fueled rocket propulsion aircraft.
 * He P.1077 Julia || Germany || CTOL || Fighter || 1944 || Project || 0 ||
 * Ju EF.127 Walli || Germany || CTOL || Fighter || 1944 || Project || 0 ||
 * Korolyov RP-318 || USSR || CTOL || Research || 1940 || || 1 ||
 * Lavochkin La-7R || USSR || CTOL || || 1945 || || 1 || Rocket and piston engines.
 * Lippisch Ente || Germany || CTOL || Research || 1928 || Prototype Opel-RAK program || 1 || First rocket-powered aircraft, part of Opel-RAK program.
 * Lockheed NF-104A || USA || CTOL || Trainer || 1963 || || 3 || Rocket and jet engines.
 * Martin Marietta X-24A || USA || Air launch || Research || 1969 || Prototype || 1 || Lifting body.
 * Martin Marietta X-24B || USA || Air launch || Research || 1973 || Prototype || 1 || Lifting body.
 * Messerschmitt Me 163 || Germany || CTOL || Fighter || 1941 ||Production || 10 A-subtype ~360 B-subtype || Tailless, B-version saw combat May 1944-May 1945.
 * Messerschmitt Me 263 || Germany || CTOL || Fighter || 1944 || || 3 || Also known as Ju 248, development of Me 163.
 * Messerschmitt P.1104 || Germany || Air launch || Fighter || 1944 || Project || 0 ||
 * Mitsubishi J8M || Japan || CTOL || Fighter || 1945 || || 7 || Was to have been a licensed Messerschmitt Me 163 but the plans were lost so was only similar.
 * Mizuno Shinryu II || Japan || CTOL || || 1945 || Project || 0 || Second aircraft developed in Japan to use a canard design after the J7W1.
 * North American X-15 || USA || Air launch || Research || 1959 || Operational || 3 || Hypersonic. Later variants capable of sub-orbital space flight.
 * Northrop XP-79 || USA || CTOL || Fighter || 1944 || Prototype || 1 || Flying wing. Converted to jet power for first and only flight.
 * Opel RAK.1 || Germany || CTOL || Research || 1929 || Operational || 1 || First purpose-built rocket-powered aircraft, Opel-RAK program.
 * Republic XF-91 Thunderceptor || USA || CTOL || || 1949 || || 2 || Rocket and jet engines.
 * Rikugun Ki-202 || Japan || CTOL || Fighter || 1945 || || 0 || Improved J8M/Ki-200 with the elongated fuselage.
 * RRL Mark-III X-racer || USA || CTOL || Racer || 2010 || || 1 ||
 * RRL Mark I X-racer || USA || CTOL || Racer || 2006 || || 1 || Customized Velocity SE, prototype for Rocket Racing League.
 * Saunders-Roe SR.53 || UK || CTOL || Fighter || 1957 || Prototype || 2 || Jet and rocket power.
 * Saunders-Roe SR.177 || UK || CTOL || Fighter || 1958 || Project || 0 || Jet and rocket power. Development of SR.53.
 * SNCASO Trident || France || CTOL || Experimental || 1953 || Prototype || 8 || Jet and rocket power.
 * SNCASE SE.212 Durandal || France || CTOL || Fighter || 1956 || Prototype || 2 || Mixed power.
 * Sombold So 344 || Germany || Air launch || || 1944 || Project || 0 || bomber box buster with a detachable explosive nose.
 * Sukhoi Su-7 || USSR || CTOL || || 1944 || || 1 || Sukhoi Su-6 with rocket and piston engines.
 * Yakovlev Yak-3RD || USSR || CTOL || || 1945 || Prototype || 1 || Modified Yakovlev Yak-3 with rocket and piston engines.
 * Yokosuka MXY7 Ohka || Japan || Air launch || Attack || 1945 || Production || || Kamikaze aircraft.
 * Zeppelin Fliegende Panzerfaust || Germany || Air launch || || 1944 || Project || 0 || Towed behind a Messerschmitt Bf 109G.
 * Zeppelin Rammer || Germany || Air launch || Fighter || 1944 || Project || 0 || Designed to use the aerial ramming technique against Allied bombers.
 * }
 * Martin Marietta X-24B || USA || Air launch || Research || 1973 || Prototype || 1 || Lifting body.
 * Messerschmitt Me 163 || Germany || CTOL || Fighter || 1941 ||Production || 10 A-subtype ~360 B-subtype || Tailless, B-version saw combat May 1944-May 1945.
 * Messerschmitt Me 263 || Germany || CTOL || Fighter || 1944 || || 3 || Also known as Ju 248, development of Me 163.
 * Messerschmitt P.1104 || Germany || Air launch || Fighter || 1944 || Project || 0 ||
 * Mitsubishi J8M || Japan || CTOL || Fighter || 1945 || || 7 || Was to have been a licensed Messerschmitt Me 163 but the plans were lost so was only similar.
 * Mizuno Shinryu II || Japan || CTOL || || 1945 || Project || 0 || Second aircraft developed in Japan to use a canard design after the J7W1.
 * North American X-15 || USA || Air launch || Research || 1959 || Operational || 3 || Hypersonic. Later variants capable of sub-orbital space flight.
 * Northrop XP-79 || USA || CTOL || Fighter || 1944 || Prototype || 1 || Flying wing. Converted to jet power for first and only flight.
 * Opel RAK.1 || Germany || CTOL || Research || 1929 || Operational || 1 || First purpose-built rocket-powered aircraft, Opel-RAK program.
 * Republic XF-91 Thunderceptor || USA || CTOL || || 1949 || || 2 || Rocket and jet engines.
 * Rikugun Ki-202 || Japan || CTOL || Fighter || 1945 || || 0 || Improved J8M/Ki-200 with the elongated fuselage.
 * RRL Mark-III X-racer || USA || CTOL || Racer || 2010 || || 1 ||
 * RRL Mark I X-racer || USA || CTOL || Racer || 2006 || || 1 || Customized Velocity SE, prototype for Rocket Racing League.
 * Saunders-Roe SR.53 || UK || CTOL || Fighter || 1957 || Prototype || 2 || Jet and rocket power.
 * Saunders-Roe SR.177 || UK || CTOL || Fighter || 1958 || Project || 0 || Jet and rocket power. Development of SR.53.
 * SNCASO Trident || France || CTOL || Experimental || 1953 || Prototype || 8 || Jet and rocket power.
 * SNCASE SE.212 Durandal || France || CTOL || Fighter || 1956 || Prototype || 2 || Mixed power.
 * Sombold So 344 || Germany || Air launch || || 1944 || Project || 0 || bomber box buster with a detachable explosive nose.
 * Sukhoi Su-7 || USSR || CTOL || || 1944 || || 1 || Sukhoi Su-6 with rocket and piston engines.
 * Yakovlev Yak-3RD || USSR || CTOL || || 1945 || Prototype || 1 || Modified Yakovlev Yak-3 with rocket and piston engines.
 * Yokosuka MXY7 Ohka || Japan || Air launch || Attack || 1945 || Production || || Kamikaze aircraft.
 * Zeppelin Fliegende Panzerfaust || Germany || Air launch || || 1944 || Project || 0 || Towed behind a Messerschmitt Bf 109G.
 * Zeppelin Rammer || Germany || Air launch || Fighter || 1944 || Project || 0 || Designed to use the aerial ramming technique against Allied bombers.
 * }
 * RRL Mark I X-racer || USA || CTOL || Racer || 2006 || || 1 || Customized Velocity SE, prototype for Rocket Racing League.
 * Saunders-Roe SR.53 || UK || CTOL || Fighter || 1957 || Prototype || 2 || Jet and rocket power.
 * Saunders-Roe SR.177 || UK || CTOL || Fighter || 1958 || Project || 0 || Jet and rocket power. Development of SR.53.
 * SNCASO Trident || France || CTOL || Experimental || 1953 || Prototype || 8 || Jet and rocket power.
 * SNCASE SE.212 Durandal || France || CTOL || Fighter || 1956 || Prototype || 2 || Mixed power.
 * Sombold So 344 || Germany || Air launch || || 1944 || Project || 0 || bomber box buster with a detachable explosive nose.
 * Sukhoi Su-7 || USSR || CTOL || || 1944 || || 1 || Sukhoi Su-6 with rocket and piston engines.
 * Yakovlev Yak-3RD || USSR || CTOL || || 1945 || Prototype || 1 || Modified Yakovlev Yak-3 with rocket and piston engines.
 * Yokosuka MXY7 Ohka || Japan || Air launch || Attack || 1945 || Production || || Kamikaze aircraft.
 * Zeppelin Fliegende Panzerfaust || Germany || Air launch || || 1944 || Project || 0 || Towed behind a Messerschmitt Bf 109G.
 * Zeppelin Rammer || Germany || Air launch || Fighter || 1944 || Project || 0 || Designed to use the aerial ramming technique against Allied bombers.
 * }
 * Sukhoi Su-7 || USSR || CTOL || || 1944 || || 1 || Sukhoi Su-6 with rocket and piston engines.
 * Yakovlev Yak-3RD || USSR || CTOL || || 1945 || Prototype || 1 || Modified Yakovlev Yak-3 with rocket and piston engines.
 * Yokosuka MXY7 Ohka || Japan || Air launch || Attack || 1945 || Production || || Kamikaze aircraft.
 * Zeppelin Fliegende Panzerfaust || Germany || Air launch || || 1944 || Project || 0 || Towed behind a Messerschmitt Bf 109G.
 * Zeppelin Rammer || Germany || Air launch || Fighter || 1944 || Project || 0 || Designed to use the aerial ramming technique against Allied bombers.
 * }
 * Zeppelin Fliegende Panzerfaust || Germany || Air launch || || 1944 || Project || 0 || Towed behind a Messerschmitt Bf 109G.
 * Zeppelin Rammer || Germany || Air launch || Fighter || 1944 || Project || 0 || Designed to use the aerial ramming technique against Allied bombers.
 * }
 * }

title: List of rocket-powered aircraft


text: User talk:64.175.247.182

title: User talk:64.175.247.182


text:
Tsushima, Ehime

Tsushima (津島町) was a town located in Kitauwa District, Ehime Prefecture, Japan.

As of 2003, the town had an estimated population of 13,284 and a density of 60.10 persons per km2. The total area was 221.05 km2.

On August 1, 2005, Tsushima, along with the towns of Mima and Yoshida (all from Kitauwa District), was merged into the expanded city of Uwajima.

Tsushima residents are also known for pearl farming and fish farming, as well as being part of the prefecture's mikan growing industry.

Nanryakuen Park is a beautiful place to go for a walk when you're there. There's also a children's amusement area called Playland across the street.

Tourism
Tsushima is known for the Iwamatsu River and the festival, "Shirauo Matsuri", they have each year where people eat tiny, live fish. Another festival is "Tsushima Summer Matsuri" which is held in August.

Iwamatsu Machinami in Iwamatsu is a historic street that is promoted by Uwajima City as a tourist attraction with a reference to Shishi Bunroku's novel "Ten'ya Wan'ya". There are approximately 20 historic houses from the Meiji era (1868–1911) and additional 30 other historic buildings. Iwamatsu was listed as one of 25 sites of the 2020 World Monuments Watch published by World Monuments Fund (WMF) for preservation efforts.

title: Tsushima, Ehime


text:
Kitauwa District, Ehime

Kitauwa (北宇和郡) is a district located in Ehime Prefecture, Japan. As of 2004, the district has an estimated population of 17,299. The total area is 340.37 km2.

The district has two towns:
 * Kihoku
 * Matsuno

History

 * Due to 1878 land reforms, the district was founded when it broke off from the Uwa District. (2 towns, 31 villages)
 * July 1, 1895 — The village of Tsushima broke up into the villages of Takachika and Iwamatsu. (2 towns, 32 villages)
 * July 1, 1899 — The village of Kiyomitsu broke up into the villages of Mimaki and Kiyomitsu. (2 towns, 33 villages)
 * May 1, 1917 — The village of Maruho merged into the town of Uwajima. (2 towns, 32 villages)
 * October 3, 1919 — The village of Iwamatsu gained town status. (3 towns, 31 villages)
 * August 1, 1921 — The town of Uwajima and the village of Yawata merged to form the city of Uwajima. (2 towns, 30 villages)
 * September 1, 1934 — The village of Kushima merged into the city of Uwajima. (2 towns, 29 villages)
 * February 11, 1938 — The village of Tamajiri merged into the town of Yoshida. (2 towns, 28 villages)
 * September 10, 1938 — The village of Takachika merged into the town of Iwamatsu. (2 towns, 27 villages)
 * November 10, 1940 — The village of Akeharu was renamed and gained town status to become the town of Matsumaru. (3 towns, 26 villages)
 * November 10, 1941 — The village of Asahi was renamed and gained town status to become the town of Chikanaga. (4 towns, 25 villages)
 * April 1, 1951 — Parts of the village of Kitanada merged into the town of Iwamatsu.
 * October 10, 1954 — The villages of Mima, Narutae, and Futana merged to become the town of Mima. (5 towns, 22 villages)
 * February 11, 1955 — The villages of Kiyomitsu, Mimami, Kitanada, Hataji, Shimonada the town of Iwamatsu merged to form the town of Tsushima. (5 towns, 17 villages)
 * March 1, 1955 — The villages of Tachima, Kisakata, and Okuna merged into the town of Yoshida. (5 towns, 14 villages)
 * March 31, 1955
 * Parts of the village of Takamitsu and the village of Tamatsu from Higashiuwa District merged into the town of Yoshida.
 * The villages of Takamitsu (excluding parts) and Miura merged into the city of Uwajima. (5 towns, 12 villages)
 * The villages of Yoshifuji, Aiji, Izumi, Mishima, and the town of Chikanaga merged to become the town of Hiromi. (5 towns, 8 villages)
 * The village of Yoshinobu and the town of Matsumaru merged to become the town of Matsuno. (5 towns, 7 villages)
 * January 1, 1957 — The village of Kuno merged into the city of Uwajima. (5 towns, 6 villages)
 * April 1, 1958 — The villages of Shitaba, Komobuchi, Yusu, Tojima and Hiburijima merged to become the village of Uwaumi. (5 towns, 2 villages)
 * August 1, 1958 — Parts of the town of Hiromi merged into the town of Mima.
 * April 1, 1974 — The village of Uwaumi merged into the city of Uwajima. (5 towns, 1 village)
 * January 1, 2005 — The town of Hiromi and the village of Hiyoshi merged to become the town of Kihoku. (5 towns)
 * August 1, 2005 — The towns of Mima, Tsushima and Yoshida merged into the expanded city of Uwajima. (2 towns)

title: Kitauwa District, Ehime


text:
Uchiumi, Ehime

Uchiumi (内海村) was a village located in Minamiuwa District, Ehime Prefecture, Japan. Pearl culturing flourishes here, as Uchiumi produces the highest pearl output in Japan.

As of 2003, the village had an estimated population of 2,351 and a density of 119.10 per km2. The total area was 19.74 km2.

On October 1, 2004, Uchiumi, along with the towns of Ipponmatsu, Jōhen, Mishō and Nishiumi (all from Minamiuwa District), was merged to create the town of Ainan.

title: Uchiumi, Ehime


text:
Mishō, Ehime

Misho (御荘町) was a town located in Minamiuwa District, Ehime Prefecture, Japan.

As of 2003, the town had an estimated population of 9,471 and a density of 188.18 persons per km2. The total area was 50.33 km2.

On October 1, 2004, Mishō, along with the towns of Ipponmatsu, Jōhen and Nishiumi, and the village of Uchiumi (all from Minamiuwa District), was merged to create the town of Ainan.

Kanjizaiji, one of the Shikoku Pilgrimage temples, is located in the town.

title: Mishō, Ehime


text:
Jōhen, Ehime

Jōhen (城辺町) was a town located in Minamiuwa District, Ehime Prefecture, Japan.

As of 2004, the town of Jōhen had an estimated population of 9,751 and a density of 129.37 persons per km2. The total area was 75.37 km2.

On October 1, 2004, Jōhen, along with the towns of Ipponmatsu, Mishō and Nishiumi, and the village of Uchiumi (all from Minamiuwa District), was merged to create the town of Ainan.

title: Jōhen, Ehime