A sufficient condition for reciprocal Jacobi triangles

Sandra Lieven, Márcio Fabiano da Silva

Resumo


Given a triangleABCletA′B′C′be a Jacobi triangle forABC. When∠BA′C′=∠CA′B′=α′,∠AB′C′=∠CB′A′=β′and∠AC′B′=∠BC′A′=γ′, the triangleABCisa Jacobi triangle forA′B′C′. In this case we say thatABCandA′B′C′are reciprocal Jacobitriangles. In 2015, G.T. Vickers presented a necessary condition for two triangles to be reciprocal,but the question whether that condition was also sufficient remained open. In this work we proveit by using basically trigonometric relations.

Palavras-chave


Jacobi’s Theorem; Triangle; Geometry

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Referências


Lieven, S. Triˆangulo de Jacobi, Disserta ̧c ̃ao de Mestrado, UFABC, 2019.

Vickers, G. T. Reciprocal Jacobi Triangles and the McCay Cubic,Forum Geometricorum, 15:179–183, 2015.




DOI: https://doi.org/10.5540/03.2021.008.01.0348

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