The Square 169

169 = 13². Its digit reversal 961 = 31², also a perfect square — a rare property. 13 itself is a Fibonacci prime and appears in the Pythagorean triple 5-12-13. The square 169 tiles with the 5-12-13 right triangle: five of them arrange into a 13×13 square. In algebraic number theory, the prime 13 splits in the Gaussian integers as (2+3i)(2−3i) = 13, making 169 = 13² = (2+3i)²(2−3i)² — a product of four Gaussian primes. A single ordinary square conceals multiple layers of mathematical structure.