The Sand-Reckoner

Archimedes said in his Sand-Reckoner that Aristarchus had proposed a new theory which, if true, would make the universe vastly larger than was then believed. (This is because a moving Earth should produce a parallax, or annual shift, in the apparent positions of the fixed stars, unless the stars…

The Sand-Reckoner is a small treatise that is a jeu d’esprit written for the layperson—it is addressed to Gelon, son of Hieron—that nevertheless contains some profoundly original mathematics. Its object is to remedy the inadequacies of the Greek numerical notation system by showing how to…