If you liked the Fun Fact Multiplication by 11, you’ll enjoy seeing how to take that idea one step farther. Here’s...

Continue reading...# medium

These fun facts are at the medium level.

## i to the i is a Real Number

If you are familiar with complex numbers, the “imaginary” number i has the property that the square of i is -1....

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...## Square Root of Two is Irrational

An irrational number is a number that cannot be expressed as a fraction. But are there any irrational numbers? It was known to...

Continue reading...## Finding the N-th digit of Pi

Here is a very interesting formula for pi, discovered by David Bailey, Peter Borwein, and Simon Plouffe in 1995:Pi =...

Continue reading...## Ellipsoidal Paths

Given an ellipse, and a smaller ellipse strictly inside it, start at a point on the outer ellipse, and in a...

Continue reading...## Large Counterexample

A positive integer is said to be of even type if its factorization into primes has an even number of primes. Otherwise it is...

Continue reading...## Whiffle Ball

Does a ball take longer to come down than go up, or does it take the same amount of time...

Continue reading...## Area of a Circle or Regular Polygon

There’s a nice way to see why the formula for the area of a circle of radius R is: Pi...

Continue reading...## Pretzel Unlinking

Imagine that each of the ropes in the two sets of links in Figure 1 are solid (with thickness) and...

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