The lune of Hippocrates is the upper left shaded area. It has the same area as the lower right shaded triangle.
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 was the first curved figure to have its exact area calculated mathematically.[1]
^Postnikov, M. M. (2000), "The problem of squarable lunes", American Mathematical Monthly, 107 (7): 645–651, doi:10.2307/2589121, JSTOR 2589121. Translated from Postnikov's 1963 Russian book on Galois theory.
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In geometry, the luneofHippocrates, named after Hippocratesof Chios, is a lune bounded by arcs of two circles, the smaller of which has as its diameter...
Quadrature of the Circle and Hippocrates' Lunes at Convergence Mesolabe Compass and Square Roots - Numberphile video explaining Hippocrates' mesolabe compass...
it while in prison. Hippocratesof Chios attacked the problem by finding a shape bounded by circular arcs, the luneofHippocrates, that could be squared...
LuneofHippocrates, in geometry, a plane region bounded by arcs of circles and amenable to quadrature Spherical lune, a 3-dimensional lune Ted Lune (1920–1968)...
quadrature of the circle, LuneofHippocrates, The Quadrature of the Parabola. This construction must be performed only by means of compass and straightedge...
combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocratesof Chios, Thales and Theaetetus....
one of Archimedes' creations, with symmetry along the y-axis. LuneofHippocrates Heath, T. L. (1897). "On the Salinon of Archimedes". The Journal of Philology...
part of his quadrature of the luneofHippocrates, but did not identify the constant of proportionality. A variety of arguments have been advanced historically...
A History of Greek Mathematics is a book by English historian of mathematics Thomas Heath about history of Greek mathematics. It was published in Oxford...
include Hippocratesof Chios (c. 470–410 BC), Theaetetus (c. 417–369 BC), and Eudoxus (c. 408–355 BC). Greek mathematics also drew the attention of philosophers...
its diameter, as part of his quadrature of the luneofHippocrates, but did not identify the constant of proportionality. Eudoxus of Cnidus, also in the...
triples, contain of a number of geometrical proofs, and approximate π at 3.16 5th century BC – Hippocratesof Chios utilizes lunes in an attempt to square...
'declension' from κλίσις, etc. Examples of Romance language expressions calqued from foreign languages include: French lune de miel, Catalan lluna de mel, Spanish...
purpose of systematizing the grammar of Sanskrit. c. 500 BC – Greece, Oenopides of Chios 470 BC – 410 BC – Greece, Hippocratesof Chios utilizes lunes in an...
im Glück). 2300 years of medical costume : distinctive garb of the medical and related professions from the time ofHippocrates to the Napoleonic era...
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