An arithmetic progression is a sequence of 3 or more integers whose terms differ by a constant, e.g., 20, 23, 26, 29...
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Van der Waerden Theorem
Can you color the integers red and blue such that there are no monochromatic arithmetic progressions (AP’s) extending infintely in...
Continue reading...Devil’s Staircase
Here is a strange continuous function on the unit interval, whose derivative is 0 almost everywhere, but it somehow magically...
Continue reading...Slices of Hanging Cubes
Hang a cube from one of its vertices. Now, if you slice it horizontally through its center, you get a...
Continue reading...All Horses are the Same Color
If you know how to prove things by induction, then here is an amazing fact: Theorem. All horses are the...
Continue reading...Klein Bottle
A Klein bottle is a surface with a very strange property. A surface is any object that is locally 2-dimensional;...
Continue reading...Medical Tests and Bayes’ Theorem
Suppose that you are worried that you might have a rare disease. You decide to get tested, and suppose that...
Continue reading...Riemann Hypothesis
If you know about complex numbers, you will be able to appreciate one of the great unsolved problems of our...
Continue reading...Dinner Party Problem
How many people must you have at dinner to ensure that there are a subset of 3 people who all...
Continue reading...Continuum Hypothesis
We have seen in the Fun Fact Cantor Diagonalization that the real numbers (the “continuum”) cannot be placed in 1-1 correspondence with...
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