Medieval Origins

The cross-multiplication behind the butterfly is centuries old. Comparing two fractions by multiplying diagonally is closely related to the rule of three, a calculating shortcut taught to merchants and students across medieval Islamic and European math for trade, inheritance, and currency.

The word "algorithm" comes from the Persian mathematician Al-Khwarizmi, whose work helped carry these methods into Europe. The visual trick simply repackages a long-standing idea: to compare a/b and c/d, multiply diagonally, and the larger cross-product marks the larger fraction.