Random interesting math facts .
Complex numbers are in a sense perfect while there is little doubt that perfect numbers are complex.
You can position 10 defenders of a square castle so that on every side there will be 5 men. A torus may be brushed smooth but a sphere can not. A circle may be quite useful in drawing straight lines. In the sequence of all integers, there are arbitrary long runs with no primes. With just one caveat, anything you can do with a compass and a ruler you can do with the ruler alone.