lunes, 26 de mayo de 2025

USM Transform #3 vs. Mathematica Integrate

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Warning : The 19-example table is an eye-catching demo, but it is not large or diverse enough to qualify as a “representative” benchmark in ...
miércoles, 17 de julio de 2024

Showing $\frac{1}{e^{i\alpha_2}} + \frac{1}{e^{i\beta_2}} + \frac{1}{e^{i\gamma_2}} = \frac{1}{e^{i(\alpha_2+\beta_2+\gamma_2)}}$

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Let $x$ be any of $\alpha_1$, $\beta_1$, or $\gamma_1$ and suppose $\alpha_1+\beta_1+\gamma_1=\pi$. Then $$e^{i(\alpha_2+\beta_2)}+e^{i(\alp...
jueves, 21 de marzo de 2024

A new integration technique via Euler-like identities

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"Complexification formulas are great and it seems like this simplifies the right away." - Ninad Munshi Warning : a more refined ...
miércoles, 28 de febrero de 2024

A family of trigonometric formulas for the roots of quadratic equations

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  This note presents alternative trigonometric formulas for finding the roots of quadratic equations where $a$, $b$, and $c$ are non-zero re...
jueves, 15 de febrero de 2024

Integrals yielding $e^{\pi}$ or $e^{-\pi}$

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 Lately, I've been playing a lot with integrals , and coincidentally (with a bit of algebraic manipulation), I've come across these ...
jueves, 4 de enero de 2024

A generalization of Burlet's theorem to cyclic quadrilaterals

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 The Burlet's theorem is a result in Euclidean geometry, which can be formulated as follows: Theorem 1 . Consider triangle $ABC$ with $...
martes, 19 de diciembre de 2023

The half-angle formulas are central!

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 As the title suggests, the half-angle formulas are central . Even more central than the law of cosines, which is nothing more than the half...