GeoDom

When developing the Unified Substitution Method (USM) for integration (see arXiv:2505.03754 ), the primary goal was methodological: to crea...

Introduction The standard objective of a substitution involving a quadratic radical is rationalization. We replace the radical by a rational...

No llores porque ya se terminó, sonríe porque sucedió. ~ Gabriel García Márquez. En 2013 acababa de graduarme de ingeniero civil. Como les o...

This report compares the Unified Substitution Method (USM) with Mathematica’s native `Integrate` function across five families of integral...

Problema . Sea $\Gamma$ una circunferencia de centro $O$ y radio $R$. Desde un punto exterior $P$ se trazan las dos tangentes a $\Gamma$, qu...

Claim . Let $ABCD$ be a convex quadrilateral, and let $O$ be an arbitrary point in the plane. Let $M$ and $N$ be the midpoints of $BO$ and ...

Introduction  There is a tempting story one could tell about USM-style substitutions: \[\text{radical equation} \longrightarrow \text{smart ...