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

Continue reading...# geometry

## 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...

Continue reading...## 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...

Continue reading...## Reuleaux Wheel

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

Continue reading...## 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...

Continue reading...## Kakeya Needle Problem

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

Continue reading...## Isoperimetric Inequality

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

Continue reading...## 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...

Continue reading...## Eccentricity of Conics

To each conic section (ellipse, parabola, hyperbola) there is a number called the eccentricity that uniquely characterizes the shape of the curve. A circle...

Continue reading...## Volume of a Cone in N Dimensions

One of the first geometric formulas we learn in plane geometry is that the area of a triangle is: Area of a...

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