Английская Википедия:Cramer–Castillon problem
In geometry, the Cramer–Castillon problem is a problem stated by the Swiss mathematician Gabriel Cramer solved by the Italian mathematician, resident in Berlin, Jean de Castillon in 1776.[1]
The problem consists of (see the image):
Given a circle <math>Z</math> and three points <math>A, B, C</math> in the same plane and not on <math>Z</math>, to construct every possible triangle inscribed in <math>Z</math> whose sides (or their elongations) pass through <math>A, B, C</math> respectively.
Centuries before, Pappus of Alexandria had solved a special case: when the three points are collinear. But the general case had the reputation of being very difficult.[2]
After the geometrical construction of Castillon, Lagrange found an analytic solution, easier than Castillon's. In the beginning of the 19th century, Lazare Carnot generalized it to <math>n</math> points.[3]
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External links
- ↑ Шаблон:Smallcaps, page 1.
- ↑ Шаблон:Smallcaps, page 59.
- ↑ Шаблон:Smallcaps, page 176.
