Author Archive

This … is … “Maximal Jeopardy!”

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.

Posted 2 February, 2013 by Blue in Classroom, Misc. Math

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 […]

Posted 24 November, 2012 by Blue in Hedronometry, Open Question

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 […]

Posted 16 September, 2012 by Blue in Hedronometry, Open Question

Master of the Puniverse

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

Posted 15 August, 2012 by Blue in Classroom, Misc. Math

The Descartes Rule of Sweeps

Something about┬áDescartes’ Rule of Signs┬áhad 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 […]

Posted 20 July, 2012 by Blue in Misc. Math, Open Question