The Sand Reckoner is a work of Archimedes in which he creates the first known (Greek) system of number-naming that can be expanded beyond the needs of everyday life.

Archimedes attempts to calculate how many grains of sand it would take to fill the known universe, which, although much smaller than the universe of modern physics, is much larger than most people would suppose. Ptolemy, whose geocentric system is much derided, was aware that the Earth is a sphere and that the distance to the "fixed" stars was so great that the Earth could be considered a mathematical point to all intents and purposes.

In The Sand Reckoner, Archimedes invents a numeral system based on the myriad (10 000) that can deal with what some now call astronomical numbers . He uses the concept of recursion to express these astronomical numbers: thus the myriad myriad, ( 10 000 x 10 000 ), etc.

External links

• The Sand Reckoner
• The Sand Reckoner (annotated)