What does a cube look like in higher dimensions? Well, we can extrapolate by looking at lower dimensions. A 0-dimensional cube is a...

Continue reading...# geometry

## Arclength Surprise

Consider a unit circle, and any arc S on the unit circle in the first quadrant. No matter where S is...

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...## Sums of Two Squares Ways

In the Fun Fact Sums of Two Squares, we’ve seen which numbers can be written as the sum of two squares....

Continue reading...## Misleading Sequence

Place n points along a unit circle, in such a way that when you draw all lines connecting every pair of...

Continue reading...## Polyhedral Face Vectors

A polyhedron is any closed region of 3-space cut out by a finite set of planes. Take any polyhedron and do the...

Continue reading...## Mug Trick

Take a mug that has a handle, and fill it with coffee. Hold the mug in your hand. Now, without...

Continue reading...## Chords of a Unit Circle

Take N equidistant points on the unit circle. Pick one of those points, then draw chords from it to all...

Continue reading...## Sine of (1/55555….)

Take your calculator, and enter a number consisting of several 5’s, such as 5555555. Now take the reciprocal of this number. Now take the...

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...

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