geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, the Cramer–Castillon problem is a problem stated by the

Swiss Swiss may refer to: * the adjectival form of Switzerland * Swiss people Places * Swiss, Missouri * Swiss, North Carolina *Swiss, West Virginia * Swiss, Wisconsin Other uses *Swiss-system tournament, in various games and sports *Swiss Internation ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

Gabriel Cramer Gabriel Cramer (; 31 July 1704 – 4 January 1752) was a Genevan mathematician. He was the son of physician Jean Cramer and Anne Mallet Cramer. Biography Cramer showed promise in mathematics from an early age. At 18 he received his doctorate ...

solved by the Italian mathematician, resident in Berlin,

Jean de Castillon Jean may refer to: People * Jean (female given name) * Jean (male given name) * Jean (surname) Fictional characters * Jean Grey, a Marvel Comics character * Jean Valjean, fictional character in novel ''Les Misérables'' and its adaptations * J ...

in 1776. The problem consists of (see the image): Given a circle

Z

and three points

A, B, C

in the same plane and not on

Z

, to construct every possible triangle inscribed in

Z

whose sides (or their elongations) pass through

A, B, C

respectively. Centuries before,

Pappus of Alexandria Pappus of Alexandria (; grc-gre, Πάππος ὁ Ἀλεξανδρεύς; AD) was one of the last great Greek mathematicians of antiquity known for his ''Synagoge'' (Συναγωγή) or ''Collection'' (), and for Pappus's hexagon theorem i ...

had solved a special case: when the three points are collinear. But the general case had the reputation of being very difficult. After the geometrical construction of Castillon,

Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi LagrangiaLazare Carnot Lazare Nicolas Marguerite, Count Carnot (; 13 May 1753 – 2 August 1823) was a French mathematician, physicist and politician. He was known as the "Organizer of Victory" in the French Revolutionary Wars and Napoleonic Wars. Education and early ...

generalized it to

n

points., page 176.

References

Bibliography

* * *

External links

* * {{DEFAULTSORT:Cramer-Castillon problem Geometry