**Aristarchus** was a Greek mathematician and astronomer who is celebrated as the exponent of a Sun-centred universe and for his pioneering attempt to determine the sizes and distances of the Sun and Moon.

- The Greeks knew better; they called him 'Aristarchus the mathematician'.
- Let us try in this article to do more than 'mention one or two facts' and to indicate both the magnitude and originality of Aristarchus's achievements and also his role in the development of mathematical astronomy.
- Aristarchus was certainly both a mathematician and astronomer and he is most celebrated as the first to propose a sun-centred universe.
- Aristarchus was a student of Strato of Lampsacus, who was head of Aristotle's Lyceum.
- However, it is not thought that Aristarchus studied with Strato in Athens but rather that he studied with him in Alexandria.
- Strato became head of the Lyceum at Alexandria in 287 BC and it is thought that Aristarchus studied with him there starting his studies shortly after that date.
- Aristarchus is mentioned by Vitruvius (1st century BC) who was famous as a Roman architect and engineer.
- Of course there is the immediate question of what Aristarchus invented, and Vitruvius explains that he invented a sundial in the shape of a hemispherical bowl with a pointer to cast shadows placed in the middle of the bowl.
- There is little existing evidence concerning the origin of Aristarchus's belief in a heliocentric system.
- We only know of Aristarchus's theory because of a summary statement made in Archimedes' The Sand-Reckoner and a similar reference by Plutarch.
- But Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than the 'universe' just mentioned.
- Archimedes having reported the views of Aristarchus, criticised those views as giving mathematically meaningless proportions.
- The way that Aristarchus expresses his proportions is, according to Heath, similar to other expressions which occur in Greek writings and indicated that Aristarchus considered that the radius of the sphere of the fixed stars was infinitely large compared with the orbit of the earth.
- Of course, Aristarchus had to make some such assumption, for otherwise parallax effects would be visible.
- Plutarch gives us a little extra information, for he reports that Aristarchus followed Heraclides of Pontus in believing that the apparent daily rotation of the fixed stars was due to the rotation of the earth on its axis.
- The only surviving work of Aristarchus, On the Sizes and Distances of the Sun and Moon, is not based on the sun centred theory and unfortunately his work on that sun centred theory referred to by Archimedes has been lost.
- Both these estimates were an order of magnitude too small, but the fault was in Aristarchus's lack of accurate instruments rather than in his correct method of reasoning.
- The diagram shows an argument used by Aristarchus.
- Aristarchus estimated that the angle at the time of half illumination was 87° so the ratio of the distances is sin 3°.
- Of course, we have translated this into modern notation for Aristarchus did not use degrees nor had trigonometry been invented so he did not have the sine function at his disposal.
- Aristarchus was then faced with calculating an approximation for what is in our notation sin 3°.
- Rather strangely Aristarchus uses values for the angle subtended by the sun and moon to be 2°.
- We can only assume that Aristarchus wrote On the Sizes and Distances of the Sun and Moon early in his career, then later on he adopted his hypothesis of a sun centred universe and computed a much more accurate value of the angle subtended by the sun.
- One has to assume Aristarchus was able to develop instruments to make accurate astronomical measurements later in his career.
- Rather Neugebauer suggests, Aristarchus was only interested in the mathematical theory behind finding the distances and diameters.
- There are one or two other references to work of Aristarchus which have been investigated recently.

Born about 310 BC, Samos, Greece. Died about 230 BC, Greece.

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Ancient Greek, Applied Maths, Astronomy, Geography, Origin Greece, Physics, Special Numbers And Numerals

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**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive