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Solving the Cramer-Castillon problem using Pascal’s theorem

Published online by Cambridge University Press:  17 February 2025

Zian Shang  and
David Treeby
Zian Shang
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA e-mail: [email protected]
David Treeby
Affiliation:
Monash University, Melbourne, Australia e-mail: [email protected]
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Extract

In 1742 the Swiss mathematician Gabriel Cramer gave the following seemingly innocuous problem to the young Italian mathematician, Jean de Castillon:

The Cramer-Castillon problem: Given a circle and three points A, B and C, inscribe in the circle a triangle DEF whose sides (extended) pass through each of these points.

Type
Articles
Information
The Mathematical Gazette , Volume 109 , Issue 574 , March 2025 , pp. 10 - 16
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Copyright
© The Authors, 2025 Published by Cambridge University Press on behalf of The Mathematical Association

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References

Wanner, Gerhard, The Cramer-Castillon problem and Urquhart’s ‘most elementary’ theorem, Elem. Math. 61(2) (2006) pp. 58–64.CrossRefGoogle Scholar
Euler, L., Problematis cuiusdam Pappi Alexandrini constructio, Opera 26 (1783) pp. 237–242.Google Scholar
Coxeter, H. S. M., Introduction to geometry (2nd edn.), Wiley (1969). Google Scholar