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...# triangles

## 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...## Sperner’s Lemma

Divide a triangle T into lots of baby triangles, so that baby triangles only meet at a common edge or a common...

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...## Behold! the Pythagorean Theorem

Figure 1 shows one of the simplest proofs of the Pythagorean Theorem. It is also perhaps the earliest recorded proof, known...

Continue reading...## Napoleon’s Theorem

Take any generic triangle, and construct equilateral triangles on each side whose side lengths are the same as the length...

Continue reading...## Shortest Pythagorean Proof?

Here is one of the shortest proofs of the Pythagorean Theorem. Suppose we are given any right triangle with sides of...

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