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Journal for Geometry and Graphics 27 (2023), No. 2, 195--206
Copyright Heldermann Verlag 2023

Analytic Solution of Castillon's Problem, another Approach

Jana Chalmovianská
Dept. of Algebra and Geometry, Comenius University, Bratislava, Slovakia

We solve Castillon's problem using inversion in complex circle. This approach leads to an analytic solution to the problem similar but distinct from the standard solution due to Lagrange and Carnot. While the standard solution parametrizes the given circle by stereographic projection, the proposed approach makes use of circular inversions. Though the two approaches appear fairly different, each of them leads finally to a group of Möbius transformations, in one case over real and in the other over complex numbers.

Keywords: Castillon's problem, inversion in circle, complex circle.

MSC: 51M04; 51N10.

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