There are clearly many interesting whole numbers. For instance, 2 is the only even prime number, 3 is the first...
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Connected Sums
A surface is any object which is locally like a piece of the plane. A sphere, a projective plane, a Klein bottle,...
Continue reading...Fibonacci GCD’s, please
Fibonacci numbers exhibit striking patterns. Here’s one that may not be so obvious, but is striking when you see it....
Continue reading...Dominoes on a Chessboard
A standard 8×8 chessboard can easily be covered (tiled) with non-overlapping dominoes (1×2 pieces): simply use 4 dominoes in each...
Continue reading...Cantor Set
Start with the interval [0,1]. Remove the (open) middle third of it, i.e. get (1/3, 2/3). Now remove the middle...
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...Red-Black Pairs Card Trick
Here’s a terrific mathematical card trick that will impress your friends. When you do this trick, the effect of the...
Continue reading...Borsuk-Ulam Theorem
The Borsuk-Ulam theorem is another amazing theorem from topology. An informal version of the theorem says that at any given...
Continue reading...Poker Probability Paradox
In poker, there is a hierarchy of desirable hands which relate to how unlikely the hand is. For instance, a...
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