Hang a cube from one of its vertices. Now, if you slice it horizontally through its center, you get a...

Continue reading...# geometry

## Koch Tetrahedron

In Koch Snowflake we saw an interesting fractal snowflake-like object that is obtained when gluing smaller triangles iteratively to the sides of...

Continue reading...## Hyperbolic Geometry

In the Fun Fact on Spherical Geometry, we saw an example of a space which is curved in such a way...

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

The unit ball in Rn is defined as the set of points (x1,…,xn) such that x12 + … + xn2 <= 1. What...

Continue reading...## Sphere Eversions

If you take a loop of string in the plane and place an arrow along it pointing clockwise, is it...

Continue reading...## Sierpinski-Mazurkiewicz Paradox

If you’ve seen the Banach-Tarski paradox, you know that it is possible to cut a solid 3-dimensional ball into 5 pieces...

Continue reading...## Area of a Circle or Regular Polygon

There’s a nice way to see why the formula for the area of a circle of radius R is: Pi...

Continue reading...## Chords of an Ellipse

Consider N equally spaced on points on the unit circle, with the point P=(1,0) as one of these equally spaced...

Continue reading...## Sliding Chords

Take a circle C, and a chord in the circle. Now slide the chord around the circle. As you do this, the...

Continue reading...## 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...

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