Stop trying to calculate Pi squared

What happens when you multiply an infinite, non-repeating decimal by itself? With numbers like the square root of two, squaring them instantly cures the chaos—snapping an endless mess right back into a clean, well-behaved whole number. But what about the most famous irrational number of all: $\pi$? Could $\pi^2$ secretly collapse into a neat, hidden fraction that mathematicians just haven’t calculated far enough to see?

Calculating decimals forever won’t give you the answer. To solve the mystery once and for all, 18th-century mathematician Adrien-Marie Legendre devised an ingenious mathematical trap using infinite continued fractions and trigonometry. Discover how a simple 45-degree angle created an inescapable paradox, proving why $\pi^2$ can never be tamed into a simple fraction!