Here’s a quick way to square numbers between 40 and 60. You know the squares of 40, 50, and 60,...
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Social Choice and the Condorcet Paradox
How should one select the winner of an election? If there are only two candidates, the answer is clear— choose the...
Continue reading...Fermat’s Little Theorem
Fermat’s little theorem gives a condition that a prime must satisfy: Theorem. If P is a prime, then for any...
Continue reading...Derivative Paradox
Here’s a fun (but untrue) fact. You know from calculus that the derivative of x2 is 2x. But what’s wrong with the following...
Continue reading...Shortest Pythagorean Proof?
Here is one of the shortest proofs of the Pythagorean Theorem. Suppose we are given any right triangle with sides of...
Continue reading...Multiplying Complementary Pairs
Quick! What’s 23 x 27? 621 There’s a trick to doing this quickly. Can you see a pattern in these...
Continue reading...Four Fours Problem
Here’s a challenge that you may wish to try: can you express all the numbers from 1 to 100 using...
Continue reading...Wilson’s Theorem
Here’s an interesting characterization of primes: Wilson’s Theorem. A number P is prime if and only if (P-1)! + 1...
Continue reading...Area of an Ellipse
You know the formula for the area of a circle of radius R. It is Pi * R2. But what...
Continue reading...Regular Solids
A regular polygon is a polygon whose angles are equal and side lengths are equal. A 3-D polyhedron is said to be regular if all its faces are...
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