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Eratosthenes constructed a mechanical line drawing device to calculate the cube, called the mesolabio. He dedicated his solution to King Ptolemy, presenting a model in bronze with it a letter and an epigram. [28] Archimedes was Eratosthenes' friend and he, too, worked on the war instrument with mathematics.
The sieve of Eratosthenes is a popular way to benchmark computer performance. [14] The time complexity of calculating all primes below n in the random access machine model is O ( n log log n ) operations, a direct consequence of the fact that the prime harmonic series asymptotically approaches log log n .
The first known scientific measurement and calculation was done by Eratosthenes, by comparing altitudes of the mid-day sun at two places a known north–south distance apart. [3] He achieved a great degree of precision in his computation. [4] The Earth's shape deviates from spherical by flattening, but by only about 0.3%.
Eratosthenes's method to calculate the Earth's circumference has been lost; what has been preserved is the simplified version described by Cleomedes to popularise the discovery. [25] Cleomedes invites his reader to consider two Egyptian cities, Alexandria and Syene, modern Assuan:
Eratosthenes (c. 276 – c. 194/195 BC), a Greek mathematician who calculated the circumference of the Earth and also the distance from the Earth to the Sun. Hipparchus (c. 190 – c. 120 BC), a Greek mathematician who measured the radii of the Sun and the Moon as well as their distances from the Earth. On the Sizes and Distances
A prime sieve or prime number sieve is a fast type of algorithm for finding primes. There are many prime sieves. The simple sieve of Eratosthenes (250s BCE), the sieve of Sundaram (1934), the still faster but more complicated sieve of Atkin [1] (2003), sieve of Pritchard (1979), and various wheel sieves [2] are most common.
Ptolemy discussed and favored this revised figure of Posidonius over Eratosthenes in his Geographia, and during the Middle Ages scholars divided into two camps regarding the circumference of the Earth, one side identifying with Eratosthenes' calculation and the other with Posidonius' 180,000 stadion measure, which is now known to be about 33% ...
Eratosthenes calculated the circumference of the Earth based on work of Egyptian bematists. [3] [4] Pliny 6.61–62 Strabo 11.8.9 Actual distance Route Milia passuum 1)