Problem: Eratosthenes of Cyrene (; Greek: Eratosthenes o Kurenaios, IPA:

Eratosthenes was described by the Suda Lexicon as a Pentathlos (Pentathlos) which can be translated as "All-Rounder", for he was skilled in a variety of things: He was a true polymath. He was nicknamed Beta because he was great at many things and tried to get his hands on every bit of information but never achieved the highest rank in anything; Strabo accounts Eratosthenes as a mathematician among geographers and a geographer among mathematicians.  Eusebius of Caesarea in his Preparatio Evangelica includes a brief chapter of three sentences on celestial distances (Book XV, Chapter 53). He states simply that Eratosthenes found the distance to the Sun to be "stadion muriadas tetrakosias kai oktokismurias" (literally "of stadia myriads 400 and 80,000") and the distance to the Moon to be 780,000 stadia. The expression for the distance to the Sun has been translated either as 4,080,000 stadia (1903 translation by E. H. Gifford), or as 804,000,000 stadia (edition of Edouard des Places, dated 1974-1991). The meaning depends on whether Eusebius meant 400 myriad plus 80,000 or "400 and 80,000" myriad. With a stade of 185 m, 804,000,000 stadia is 149,000,000 km, approximately the distance from the Earth to the Sun.  Eratosthenes also calculated the Sun's diameter. According to Macrobious, Eratosthenes made the diameter of the Sun to be about 27 times that of the Earth. The actual figure is approximately 109 times.  During his time at the Library of Alexandria, Eratosthenes devised a calendar using his predictions about the ecliptic of the Earth. He calculated that there are 365 days in a year and that every fourth year there would be 366 days.  He was also very proud of his solution for Doubling the Cube. His motivation was that he wanted to produce catapults. 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. Archimedes was Eratosthenes' friend and he, too, worked on the war instrument with mathematics. Archimedes dedicated his book The Method to Eratosthenes, knowing his love for learning and mathematics.

What else about the Library of Alexandria?

Answer with quotes: He calculated that there are 365 days in a year and that every fourth year there would be 366 days.


Problem: Armando Anthony "Chick" Corea (born June 12, 1941) is an American jazz pianist/electric keyboardist and composer. His compositions "Spain", "500 Miles High", "La Fiesta" and "Windows", are considered jazz standards. As a member of Miles Davis's band in the late 1960s, he participated in the birth of jazz fusion. In the 1970s he formed the fusion band Return to Forever.

In the early 1970s, Corea took a profound stylistic turn from avant-garde to a crossover jazz fusion style that incorporated Latin jazz with Return to Forever. Named after their eponymous 1972 album, the band relied on both acoustic and electronic instrumentation and drew upon Latin American styles more than on rock music. On their first two records, Return to Forever consisted of Flora Purim on vocals, Joe Farrell on flute and soprano saxophone, Airto Moreira on drums , and Stanley Clarke on double bass. Drummer Lenny White and guitarist Bill Connors later joined Corea and Clarke to form the second version of the group, which expanded the earlier Latin jazz elements with a more rock and funk-oriented sound inspired by the Mahavishnu Orchestra, led by his Bitches Brew bandmate John McLaughlin. This incarnation of the group recorded the album Hymn of the Seventh Galaxy, before Connors' departure and replacement by Al Di Meola, who was present on the subsequent releases Where Have I Known You Before, No Mystery, and Romantic Warrior.  Corea's composition "Spain" appeared on the 1972 Return to Forever album Light as a Feather. This is probably his most popular piece, and it has been recorded by a variety of artists. There are also a variety of recordings by Corea himself. These included an arrangement for piano and symphony orchestra that appeared in 1999 and a collabration with vocalist Bobby McFerrin on the 1992 album Play. Corea usually performs "Spain" with a prelude based on Joaquin Rodrigo's Concierto de Aranjuez (1940), which earlier received a jazz orchestration on Davis and Gil Evans' Sketches of Spain.  In 1976, he issued My Spanish Heart, influenced by Latin American music and featuring vocalist Gayle Moran (Corea's wife) and electric violinist Jean-Luc Ponty. The album combined jazz and flamenco, supported by Minimoog backup and a horn section.

Did he work with any other artists on this album?

Answer with quotes:
Gayle Moran (Corea's wife) and electric violinist Jean-Luc Ponty.