If you know how to multiply 2×2 matrices, and know about complex numbers, then you’ll enjoy this connection. Any complex number...
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Taylor-made Pi
After learning about the Taylor series for 1/(1+x) in calculus, you can find an interesting expression for Pi very easily. Start 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...Sierpinski-Mazurkiewicz Paradox
If you’ve seen the Banach-Tarski paradox, you know that it is possible to cut a solid 3-dimensional ball into 5 pieces...
Continue reading...Fourier Ears Only
Did you know that every sufficiently smooth function on an interval can be expressed as an infinite sum of sines...
Continue reading...Brouwer Fixed Point Theorem
One of the most useful theorems in mathematics is an amazing topological result known as the Brouwer Fixed Point Theorem....
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