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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