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 …

claimtoken-51808748be339

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

Master of the Puniverse

… for non-negative $$x$$ and real $$n$$, not both zero.

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