Lucas’ Theorem: If p is a prime number, and N has base p representation (aj,…,a1,a0) and k has base p...
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Space-filling Curves
Consider a square in the plane. Is it possible to draw a curve in the square that touches every point inside the...
Continue reading...Rational Irrational Power
If you raise an irrational number to a rational power, it is possible to get something rational. For instance, raise Sqrt[2] to...
Continue reading...Koch Tetrahedron
In Koch Snowflake we saw an interesting fractal snowflake-like object that is obtained when gluing smaller triangles iteratively to the sides of...
Continue reading...Squaring Quickly
You may have seen the Fun Fact on squares ending in 5; Here’s a trick that can help you square ANY...
Continue reading...Multidimensional Newton’s Method
You’ve probably heard of Newton’s Method from your calculus course. It can be used to locate zeros of real-valued functions. But did...
Continue reading...Equidecomposability
Two sets A and B are said to be equidecomposable if you can partition set A into a finite number of subsets...
Continue reading...Projective Planes
Most of you know how to make a Mobius band—take a strip of paper and glue the ends with a...
Continue reading...St. Petersburg Paradox
A new casino offers the following game: you toss a coin until it comes up heads. If the first heads...
Continue reading...Sum of Cubes and Beyond
We saw this wonderful identity in Sum of Cubes: 13 + 23 + … + n3 = (1 + 2 + … + n)2. Hence the set of numbers {1,2,…,n} has the...
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