Divide a triangle T into lots of baby triangles, so that baby triangles only meet at a common edge or a common...
Continue reading...medium
Rising Sequences in Card Shuffling
In Seven Shuffles we saw that it takes about 7 random riffle shuffles to randomize a deck of 52 cards. This means...
Continue reading...Gabriel’s Trumpet
The surface of revolution of y = 1/xfor x greater than 1, has finite volume but infinite surface area! Put another way, this...
Continue reading...e is irrational
If e were rational, then e = n/m for some integers m, n. So then 1/e = m/n. But the series expansion for 1/e is 1/e =...
Continue reading...Spherical Geometry
Remember high school geometry? The sum of the angles of a planar triangle is always 180 degrees or Pi radians. However, triangles...
Continue reading...Sums of Two Squares Ways
In the Fun Fact Sums of Two Squares, we’ve seen which numbers can be written as the sum of two squares....
Continue reading...Misleading Sequence
Place n points along a unit circle, in such a way that when you draw all lines connecting every pair of...
Continue reading...Polyhedral Face Vectors
A polyhedron is any closed region of 3-space cut out by a finite set of planes. Take any polyhedron and do the...
Continue reading...Descartes’ Rule of Signs
Given a polynomial such as: x4 + 7×3 – 4×2 – x – 7 it is possible to say anything about how many positive real...
Continue reading...Fundamental Group
You are abducted by space aliens and dumped, blindfolded, on a strange asteroid! Removing your blindfold, you decide to play...
Continue reading...