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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