Archive for the ‘Misc. Math’ Category

Proof Without Words: Nine-Point Circle Property

The “Nine-Point Circle” of a triangle \(\triangle ABC\) contains the vertices of the medial triangle (\(\triangle RST \)) and orthic triangle (\(\triangle UVW \)), as well as points \(X\), \(Y\), \(Z\) that bisect segments from \(\triangle ABC\)’s orthocenter (\(H\)) to its vertices. A question on Math.StackExchange.comĀ asked for proof that the center of the nine-point circle […]

Limits are about the journey …


Posted 29 April, 2013 by Blue in Classroom, Misc. Math

A Ceva-like Theorem for Tetrahedra

A question at Math.StackExchange asked about “Ceva’s Theorem in three dimensions”. So I derived one. The result (which I believe may be new, although it could very well exist in the hundreds of years of mathematical literature since Ceva) replaces the traditional ratios of segment lengths with “triple-ratios” of triangle areas, to satisfying effect. Whereas […]

Posted 20 April, 2013 by Blue in Classroom, Misc. Math, Open Question

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

Master of the Puniverse

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

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