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The Sand Reckoner (Greek: Ψαμμίτης, 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. In order to do this, Archimedes had to estimate the size of the universe according to the contemporary ...
Historically, it has been read as stating that the angle subtended by the Sun's diameter is two degrees, but Archimedes states in The Sand Reckoner that Aristarchus had a value of half a degree, which is much closer to the average value of 32' or 0.53 degrees. The discrepancy may come from a misinterpretation of which unit of measure was meant ...
[21] [22] In the Sand-Reckoner, Archimedes gives his father's name as Phidias, an astronomer about whom nothing else is known. [22] [23] A biography of Archimedes was written by his friend Heracleides, but this work has been lost, leaving the details of his life obscure.
In his book The Sand Reckoner, Archimedes used the myriad as the base of a number system designed to count the grains of sand in the universe. As was noted in 2000: [5] In antiquity Archimedes gave a recipe for reducing multiplication to addition by making use of geometric progression of numbers and relating them to an arithmetic progression.
One of the earliest examples of this is The Sand Reckoner, in which Archimedes gave a system for naming large numbers. To do this, he called the numbers up to a myriad myriad (10 8) "first numbers" and called 10 8 itself the "unit of the second numbers".
Following the heliocentric ideas of Aristarcus (but not explicitly supporting them), around 250 BCE Archimedes in his work The Sand Reckoner computes the diameter of the universe centered around the Sun to be about 10 14 stadia (in modern units, about 2 light years, 18.93 × 10 12 km, 11.76 × 10 12 mi). [40] In Archimedes' own words:
3rd century BCE – Archimedes in his essay The Sand Reckoner, estimates the diameter of the cosmos to be the equivalent in stadia of what would in modern times be called two light years, if Aristarchus' theories were correct.
By Archimedes's calculation, the universe of Aristarchus (roughly 2 light years in diameter), if fully packed with sand, would contain 10 63 grains. If the much larger observable universe of today were filled with sand, it would still only equal 10 95 grains. Another 100,000 observable universes filled with sand would be necessary to make a googol.