GeoDom

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 ...

Santo Domingo, 28 de Enero del 2026 Señor Luis Rodolfo Abinader Corona Presidente de la República Dominicana C.c.: Directores y redactores d...

"The world's sneakiest substitution."  — Michael Spivak The classical Weierstrass substitution for integrals of the form \[\i...

The problem : Solution .  We assume $x > 0$. $$\begin{aligned}I &= \int \sqrt{x^2+1+\sqrt{x^4+x^2+1}} \, dx \\ &= \int \frac{t^2-...

One man’s trick may be another man’s method, and there may be more to an apparent trick than first meets the eye.   — Todd Trimble In my som...

In these tables we benchmark the Unified Substitution Method (USM) change of variables that this arXiv draft  (version 1) calls Transformati...