Geodesic
Analytic Solution of Castillon's Problem, another Approach
Journal for geometry and graphics, Tome 27 (2023) no. 2, pp. 195-206 Cet article a éte moissonné depuis la source Heldermann Verlag

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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 M�bius transformations, in one case over real and in the other over complex numbers.
Classification : 51M04, 51N10
Mots-clés : Castillon's problem, inversion in circle, complex circle 
@article{JGG_2023_27_2_JGG_2023_27_2_a7,
     author = {J. Chalmoviansk\'a },
     title = {Analytic {Solution} of {Castillon's} {Problem,} another {Approach}},
     journal = {Journal for geometry and graphics},
     pages = {195--206},
     year = {2023},
     volume = {27},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2023_27_2_JGG_2023_27_2_a7/}
}
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J. Chalmovianská . Analytic Solution of Castillon's Problem, another Approach. Journal for geometry and graphics, Tome 27 (2023) no. 2, pp. 195-206. http://geodesic.mathdoc.fr/item/JGG_2023_27_2_JGG_2023_27_2_a7/