Did You Know?
Every positive integer can be represented as the sum of at most three triangular numbers.
Proved by Gauss in 1796, this theorem shows how complex numbers can be built from simple geometric patterns. It's an example of how visual patterns relate to number theory.
Did You Know?
A pentagon contains exactly five different golden rectangles.
Each diagonal of a regular pentagon, when combined with its sides, forms a golden rectangle. This multiple occurrence...
Did You Know?
Prime numbers become increasingly rare, yet there are infinitely many of them.
The gaps between prime numbers generally get larger as numbers get bigger, but we can always find more...
Did You Know?
The birthday paradox shows that in a room of just 23 people, there’s a 50% chance two share a birthday.
This counterintuitive probability demonstrates how our intuition about statistics can be wrong. The chance rises to 99.9% with...