Add the odd numbers one by one. The running total is always a perfect square. Try it: 1 = 1, 1+3 = 4, 1+3+5 = 9, 1+3+5+7 = 16. No coincidence.
Sum of first n odd numbers
1 + 3 + 5 + … + (2n−1) = n²
Nicomachus knew this around 100 AD — and you can prove it by drawing dots.
Visualise it: an n × n square of dots can be split into L-shapes of 1, 3, 5, 7… dots each. Each L is one more odd number.