Cramer–Castillon problem

Two solutions whose sides pass through $A,B,C$

In geometry, the Cramer–Castillon problem is a problem stated by the Genevan mathematician Gabriel Cramer solved by the Italian mathematician, resident in Berlin, Jean de Castillon in 1776.Template:Sfnp

The problem is as follows (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 had solved a special case: when the three points are collinear. But the general case had the reputation of being very difficult.Template:Sfnp 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 $n$ points.Template:Sfnp

Bibliography

• Template:Cite book
• Template:Cite journal
• Template:Cite web
• Template:Cite book

External links

• Template:Commons category-inline