What’s the largest possible amount of money you can win in a single game of TV’s “Jeopardy!”? Read my note This … is … “Maximal Jeopardy!” to find out.

## Author Archive

## This … is … “Maximal Jeopardy!”

## A Hedronometric Theorem of Menger

In 1928, Karl Menger outlined necessary and sufficient conditions for a set of edge lengths to determine an actual, non-degenerate, tetrahedron. The conditions amount to dead-simple sanity checks that the consequent face areas and volume have to be positive real numbers. In the short note “A Hedronometric Theorem of Menger”, I derive (as the title […]

## What I know about hyperbolic tetrahedra

Inspired by Mednykh and Pashkevich’s “Elementary Formulas for a Hyperbolic Tetrahedron”, I have compiled most of my disparate notes about hyperbolic hedronometry into one document: “Hedronometric Formulas for a Hyperbolic Tetrahedron”. I consider this a “living document” that I will update as I learn more about the subject matter. It’s primarily a formula look-up list […]

## Master of the Puniverse

… for non-negative \(x\) and real \(n\), not both zero.

## The Descartes Rule of Sweeps

Something about Descartes’ Rule of Signs had bothered me ever since my exposure to it in high school. As you know, the Rule of Signs runs something like this: For a polynomial with non-zero real coefficients, the number of positive roots is, at most, the number of sign changes in the coefficient sequence (ordered by power); more […]