GeoDom
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 $AI=k$;...
sábado, 21 de noviembre de 2020
Still very Bretschneider, isn't it?
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Given a general convex quadrilateral with sides of lengths $a$, $b$, $c$, and $d$, the area is given by $$\begin{align*} K&=\frac{1}{4}...
sábado, 31 de octubre de 2020
Two Identities and their Consequences (draft)
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Renowned British mathematician John Conway , in correspondence with Peter Doyle, used two trigonometric formulae to prove Heron's formul...
lunes, 6 de julio de 2020
Generalization of two formulae and an alternative proof of Bretschneider's formula
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"If we do not succeed in solving a mathematical problem, the reason frequently consists in our failure to recognize the more general st...
sábado, 4 de julio de 2020
Killing three birds with one stone
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In this note we derive Heron's formula, Brahmagupta's formula and the bicentric quadrilateral's area formula, $\sqrt{abcd}$, fro...
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