Editing Archimedes (section)

=== Large numbers ===
Archimedes also developed methods for representing large numbers.

In ''[[The Sand Reckoner]]'', Archimedes devised a system of counting based on the [[myriad]],{{efn|{{Langx|grc|μυριάς|translit=murias|label=none}}}} the Greek term for the number 10,000, in order to calculate a number that was greater than the grains of sand needed to fill the universe. He proposed a number system using powers of a myriad of myriads (100 million, i.e., 10,000 x 10,000) and concluded that the number of grains of sand required to fill the universe would be 8 [[Names of large numbers|vigintillion]], or 8{{e|63}}.<ref>{{cite web |title=The Sand Reckoner |first=Bradley W |last=Carroll |publisher=Weber State University |url=http://physics.weber.edu/carroll/Archimedes/sand.htm |access-date=23 July 2007}}</ref> In doing so, he demonstrated that mathematics could represent arbitrarily large numbers.

In the ''[[Archimedes' cattle problem|Cattle Problem]]'', Archimedes challenges the mathematicians at the [[Library of Alexandria]] to count the numbers of cattle in the [[The Cattle of Helios|Herd of the Sun]], which involves solving a number of simultaneous [[Diophantine equation]]s.  A more difficult version of the problem in which some of the answers are required to be [[square number]]s, and the answer is a [[very large number]], approximately 7.760271{{e|206544}}.<ref>{{cite web |first=Keith G |last=Calkins |url=http://www.andrews.edu/~calkins/profess/cattle.htm |title=Archimedes' Problema Bovinum |publisher=[[Andrews University]] |access-date=14 September 2007 |archive-url=https://web.archive.org/web/20071012171254/http://andrews.edu/~calkins/profess/cattle.htm |archive-date=12 October 2007}}</ref>