domingo, 17 de octubre de 2021

PAGMO 2021 - Problemas 2, 6

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Estas son mis soluciones a los problemas $2$ y $6$ de la  Olimpiada Panamericana Femenil de Matemáticas . Problema 2 . Considere el triángul...
lunes, 14 de junio de 2021

Generalized half-angle formulas - Hyperbolic version

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In Mathoverflow I wonder about the possibility of finding non-Euclidean versions of the generalized half-angle formulas $[1]$. The Russian ...
martes, 1 de junio de 2021

Using the half-angle formula for cosine to derive Zelich's lemma on mixtilinear incircles

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Lemma ( Ivan Zelich ) . Let $w$ be the $A$- mixtilinear incircle in $\triangle{ABC}$ touching side $AB$ at $E$, side $AC$ at $F$. Then $$AE...
viernes, 7 de mayo de 2021

Using the half-angle formulas to derive Mahavira's identities

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In a cyclic quadrilateral $ABCD$, let $a$, $b$, $c$, $d$ denote the lengths of sides $AB$, $BC$, $CD$, $DA$, and $m$, $n$ the lengths of the...
martes, 30 de marzo de 2021

Length of angle bisector: yet another application of the half-angle formulas

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Let $\triangle{ABC}$ be a triangle. Let $AD$ be the angle bisector of $\angle{BAC}$ in $\triangle{ABC}$. Let $d$ be the length of $AD$. Then...
domingo, 28 de marzo de 2021

Publicaciones, reportajes y entrevistas

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En arXiv (Cornell) A Unified Substitution Method for Integration  En  Mathematics Magazine A Generalization of the Law of Tangents . En  The...
sábado, 5 de diciembre de 2020

The Pythagorean Theorem from the Half-Angle Formula for Cosine

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I've been trying to rescue the Half-Angle Formulas  from oblivion and give them the status they deserve by showing its many applications...