Lune of Hippocrates

In geometry, the lune of Hippocrates, named after Hippocrates of Chios, is a lune bounded by arcs of two circles, the smaller of which has as its diameter a chord spanning a right angle on the larger circle. Equivalently, it is a non-convex plane region bounded by one 180-degree circular arc and one 90-degree circular arc. It is the first curved figure to have its exact area calculated mathematically.

Read more about Lune Of HippocratesHistory, Proof, Generalizations

Other articles related to "lune of hippocrates, hippocrates, lunes":

Lune Of Hippocrates - Generalizations
... As Hippocrates showed using a similar proof to the one above, if two lunes are formed on the two sides of a right triangle, whose outer boundaries are semicircles and whose inner boundaries are ... The quadrature of the lune of Hippocrates is the special case of this result for an isosceles right triangle ... The lunes formed in this way from a right triangle are known as the lunes of Alhazen, named after the 10th and 11th century Arabic and Persian ...
Lune (mathematics) - Lune of Hippocrates
... In the 5th century BC, Hippocrates of Chios showed that certain lunes could be exactly squared by straightedge and compass ... See Lune of Hippocrates ...