math.GM

This is an arXiv category tag for "general mathematics".

Volume of Simplices

How to compute the volume of a simplex using the Cayley-Menger determinant, and a higher dimensional Pythagorean theorem

Logical Formulae

Since the COVID-19 crisis and the university moving to online instruction, I've spent too much time programming WeBWorK assignments. …

A Criterion for Real Roots

When does a polynomial with real coefficients have only real roots? Here's one way to determine it.

You are 23 times more likely to crash

Driving down the highway in upstate Michigan yesterday, I saw a State Police billboard that states (I paraphrase) Drivers who text are …

A Tangent Identity

Here's a slightly non-obvious relation between some angles, that I ran into accidentally. Claim: (angles below given in degrees) \[ …

An Implicit Assumption about Expectation Values

A short note about an implicit assumption behind the notion of expectation values, and how it relates to economics applications.

A Better Estimate of Kempner's Series

The Kempner series recently regained some notoriety due to a Saturday Morning Breakfast Cereal comic (the last panel). The observation …

Mariş's Theorem

We describe a theorem due to Mihai Mariş concerning the symmetries of ground states.

Repeating Decimals

When does the decimal expansion of a number end with one digit repeated?

Irrationality of a common constant

We give a proof of the irrationality of π.