# geometry

## High-Dimensional Spheres in Cubes

How good is your intuition in high dimensions? Take a square and divide it into its four quadrants. Inscribe a circle...

## Rolling Polygons

Perhaps you’ve learned from a calculus class that as you roll a circular disk along a straight line, that the area under...

## Spherical Pythagorean Theorem

Did you know there is a version of the Pythagorean Theorem for right triangles on spheres? First, let’s define precisely what we...

## Reuleaux Wheel

A Reuleaux Triangle is a plump triangle with rounded edges, formed in the following way: take the three points at the corners...

## One, Two, Three, Pi

Here’s an interesting formula: Arctan(1) + Arctan(2) + Arctan(3) = Pi. (Everything’s in radians, of course). Presentation Suggestions:Challenge students to prove...

## Kakeya Needle Problem

What is the smallest-area convex set in the plane inside which a needle (unit straight line segment) can be reversed...

## Isoperimetric Inequality

What’s the largest volume that can be enclosed by a bubble of surface area A? If V is the volume...

## Surface Area of a Sphere

The area of a disk enclosed by a circle of radius R is Pi*R2. The formula for the circumference of a...