The Mathematics of the Great Wall of China

The Great Wall is about 21,196 km long (including branches). Its construction required surveying (geometry), slope calculation (trigonometry), and logistics (optimisation). The wall’s path follows ridgelines – a ‘minimum energy’ path determined by topography (gradient descent). The number of workers (estimated 1 million) is a scale factor problem. The wall is not visible from space (a myth). Its construction used rammed earth, brick, and stone – materials tested for strength (compressive stress). Mathematics built the wall, and mathematics now preserves it.