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Penrose triangle

The Penrose triangle known as the Penrose tribar, or the impossible tribar, is a triangular impossible object, an optical illusion consisting of an object which can be depicted in a perspective drawing, but cannot exist as a solid object. It was first created by the Swedish artist Oscar Reutersvärd in 1934. Independently from Reutersvärd, the triangle was devised and popularized in the 1950s by psychiatrist Lionel Penrose and his son, prominent mathematician Roger Penrose, who described it as "impossibility in its purest form", it is featured prominently in the works of artist M. C. Escher, whose earlier depictions of impossible objects inspired it; the tribar appears to be a solid object, made of three straight beams of square cross-section which meet pairwise at right angles at the vertices of the triangle they form. The beams may be broken, forming cuboids; this combination of properties cannot be realized by any three-dimensional object in ordinary Euclidean space. Such an object can exist in certain Euclidean 3-manifolds.

There exist three-dimensional solid shapes each of which, when viewed from a certain angle, appears the same as the 2-dimensional depiction of the Penrose triangle on this page. The term "Penrose triangle" can refer to the 2-dimensional depiction or the impossible object itself. M. C. Escher's lithograph Waterfall depicts a watercourse that flows in a zigzag along the long sides of two elongated Penrose triangles, so that it ends up two stories higher than it began; the resulting waterfall, forming the short sides of both triangles, drives a water wheel. Escher helpfully points out that in order to keep the wheel turning some water must be added to compensate for evaporation. If a line is traced around the Penrose triangle, a 4-loop Möbius strip is formed.. Although the tribar is named one of the impossible objects, there exist many more that fit into the same category. Other impossible objects include the devil's fork, the Shepard elephant, impossible arch. While it is possible to construct analogies to the Penrose triangle with other shapes and regular polygons to create a Penrose polygon, the visual effect is not as striking, as the sides increase, the object seems to be warped or twisted.

Three hares Penrose steps Penrose square root law An article about impossible triangle sculpture in Perth Escher for Real constructions

Levante UD

Levante Unión Deportiva, S. A. D. is a Spanish football club in Valencia, in the namesake autonomous community. Founded on 9 September 1909, it plays in La Liga, holding home games at Ciutat de Valencia Stadium. Levante UD was registered as Levante Football Club on 9 September 1909. Levante Union Deportiva has the eastern region of the Iberian Peninsula as its namesake. Levante is the coast where the sun always rises. Levante UD's name is attributed to the Levant wind that comes from the east and reminiscent of the Levante beach in La Malvarrosa, where Levante Football Club clashed some of its earliest fixtures. Backed, Levante Union Deportiva is the most senior football club in Valencia. Local rival team Valencia CF was not formed until 1919. Levante's earliest games were played at La Platjeta, near the docks on a plot of land owned by a perfume entrepreneur, its next ground was near the port area, the club began to become associated with the working class. In 1919, the side played Valencia CF for the first time, losing 0–1.

In 1928, Levante FC won the Valencian Championship. 1909 saw the birth of Gimnástico Football Club, which played at Patronato de la Juventud Obrera, being named Gimnástico-Patronato. In 1919, Gimnástico became the champion of the Campeonato de Valencia, beating CD Castellón in two leg finals. In 1931, with the emergence of the Second Spanish Republic, the club dropped the Real from its name. In 1934–35, both Levante and Gimnástico debuted in the second division, when the league was expanded from 10 teams to 24. In 1935, Levante won the Campeonato Levante-Sur, a competition that featured teams from Valencia and Andalusia, subsequently reached the semi-finals of the Spanish Cup, consecutively beating Valencia and Barcelona before losing to eventual runners-up Sabadell. During the Spanish Civil War and Gimnástico played in the Mediterranean League, finishing fifth and sixth – teams from this league competed in the Copa de la España Libre, it was intended that the top four teams from the league would enter the cup, but Barcelona opted to tour Mexico and the United States, as a result, Levante took its place.

The first round of the competition was a mini-league with the top two teams and Valencia, qualifying for the final. On 18 July 1937, Levante defeated. During the Civil War, Levante's ground was destroyed. In contrast, Gimnástico had lost most of their players; as a result, in 1939 Levante FC and Gimnástico FC merged into Levante Unión Deportiva. Levante UD thus having origin from at least 1909 from both Levante FC and Gimnástico FC. At first being named Unión Deportiva Levante-Gimnástico changing it a few years to Levante Unión Deportiva, with current club colours dating from this era. Moreover, Levante UD not only inherited their colors from Gimnástico FC but their nickname, "Granota", the Frogs. Levante had to wait until the 1960s to make its La Liga debut. In 1963, the club finished runner-up in Group II of the second division, defeating Deportivo de La Coruña 4–2 on aggregate in the promotion play-offs. During the first top flight season, it managed to win both games against Valencia, managing a 5–1 home win against Barcelona in the 1964–65 campaign but being relegated nonetheless after losing in the playoffs against Málaga.

It spent most of the following two decades in the third divisions. In the early 1980s, Dutch superstar Johan Cruyff played half a season for the club, retiring three years later. After winning 2003–04's second division, Levante returned to the top level but survived only one season. Finishing third in 2005–06, it returned for two additional campaigns, the decisive match in the 2006–07 season being a 4–2 home win against Valencia courtesy of Riga Mustapha and Laurent Courtois. Levante's financial status worsened and there were reports that the players had only received one-fifth of their contractual payments. News reports stated that the club had incurred a debt of over €18 million in payments due to its players; the team plummeted down the standings, it was confirmed that the club would be playing in the second division in 2008–09, with several matches to go. The players protested at their lack of payments at one point, refusing to move for several seconds after the opening whistle against Deportivo and announcing that they would issue a job action during the season-ending game at Real Madrid.

The action was resolved when league officials announced that a benefit game would be played between Levante team members, a team made up of players from the first division, with all benefits going to pay the wages due to the players. On 13 June 2010, Levante returned to La Liga after a 3–1 home win against relegated Castellón, it lost in the final round 0–4 at Real Betis, but its opponents only managed to finis