Hang a cube from one of its vertices. Now, if you slice it horizontally through its center, you get a...
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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...
Continue reading...Banach-Tarski Paradox
Did you know that it is possible to cut a solid ball into 5 pieces, and by re-assembling them, using...
Continue reading...Face Derivatives and Computer Vision
One challenge in robotics is the problem of computer vision: how do you program a computer to interpret and “understand”...
Continue reading...Pretzel Unlinking
Imagine that each of the ropes in the two sets of links in Figure 1 are solid (with thickness) and...
Continue reading...Unbelievable Unlinking
Imagine that the two objects in Figure 1 are solid (with thickness) and made of very flexible and stretchy rubber....
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...Prime Number Theorem
Fix some number N. What fraction of the integers less than or equal to N are prime? Thinking about it,...
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