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Eratosthenes created a whole section devoted to the examination of Homer, and acquired original works of great tragic dramas of Aeschylus, Sophocles and Euripides. [6] Eratosthenes made several important contributions to mathematics and science, and was a friend of Archimedes. Around 255 BC, he invented the armillary sphere.
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.
Eratosthenes (c. 276–194 BC) Scymnus (fl. 180s BC) Hipparchus (c. 190–120 BC) Agatharchides (2nd century BC) Posidonius (c. 135–51 BC) Pseudo-Scymnus (c. 90 BC) Diodorus Siculus (c. 90–30 BC) Alexander Polyhistor (1st century BC) Roman Empire period 15th century reconstruction of Ptolemy's map. Periplus of the Erythraean Sea; Strabo (63 ...
The Ebstorf Map was an example of a European mappa mundi, made by Gervase of Ebstorf, who was possibly the same man as Gervase of Tilbury, [28] some time in the thirteenth century. It was a very large map: painted on 30 goatskins sewn together, it measured about 3.6 m × 3.6 m (12 ft × 12 ft).
In this example the fact that the Legendre identity is derived from the Sieve of Eratosthenes is clear: the first term is the number of integers below X, the second term removes the multiples of all primes, the third term adds back the multiples of two primes (which were miscounted by being "crossed out twice") but also adds back the multiples ...
The prototypical example of a sifted set is the set of prime numbers up to some prescribed limit X. Correspondingly, the prototypical example of a sieve is the sieve of Eratosthenes, or the more general Legendre sieve. The direct attack on prime numbers using these methods soon reaches apparently insuperable obstacles, in the way of the ...
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Furthermore, the fact that Eratosthenes's measure corresponds precisely to 252,000 stadia might be intentional, since it is a number that can be divided by all natural numbers from 1 to 10: some historians believe that Eratosthenes changed from the 250,000 value written by Cleomedes to this new value to simplify calculations; [27] other ...