The sand reckoner greek uu psammites is a work by archimedes an ancient greek mathematician of the 3rd century bc in which he set out to determine an upper bound for the number of grains of sand that fit into the universe. The sand reckoner of archimedes translated by thomas l heath original publication cambridge university press 1897 scanned proofed and formatted by john bruno hare at sacred textscom this text is in the public domain in the united states because it was published prior to 1923 i have altered the formatting of the mathematical proof areas slightly due to the limitations of html. The sand reckoner greek mathematical notation was not positional it utilized many symbols and was cumbersome to work with the m is a myriad and represents 10000the greek work is murious uncountable pl murioithe romans converted to this to myriad the sand reckoner is a remarkable work in which archimedes proposes a number system that uses powers of a myriad myriad base . In archimedes his works the sand reckoner is a small treatise that is a jeu desprit written for the layman 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. The sand reckoner of archimedes tr by thomas heath 1897 contents start reading this short treatise of archimedes on the amount of sand grains which could be contained in the ancient model of the universe is remarkable it uses some extremely large numbers given that this was antiquity and europeans did not yet have the benefit of decimal notation it also anticipates the method of