GeoDom

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...
domingo, 29 de noviembre de 2020

An Alternative Form of Bretschneider's Formula

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If you are already familiar with Bretschneider's Formula, have you ever wonder how would it like if we interchange the cosine-part by a ...
jueves, 26 de noviembre de 2020

La importancia de tener un amigo matemático

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La mayoría de nosotros, enfrentados ante un problema matemático de esos de “cuánto tardarían dos trenes en chocar si uno sale de la estación...

The product AI*BI*CI

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Consider a triangle $\triangle{ABC}$ and its Incenter, $I$. Denote $R$ and $r$ the circumradius and inradius, respectively. Also let $AI=k$;...
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Hi, here you can find solved and open geometry problems in English and Spanish (and other stuffs).

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Emmanuel José García
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