As with many of his contemporaries, the only extant facts about the life of Aristarchus involve remarks about him and his work written by others. Only one of Aristarchus' writings survived, *On the Magnitudes and Distances of the Sun and Moon, *but in it he articulated the reasoning behind what later became modern trigonometry, and how it might be employed in astronomy and navigation. Typical of Greek mathematics was Aristarchus' primarily geometric method of approximating this strategy of triangulation. From **Archimedes**, it is known that Aristarchus had proposed the sun be considered a fixed star, with the Earth circulating around it. This view was ridiculed at the time and remained dormant until Nicolaus Copernicus devised his heliocentric theory.

Birth and death dates for Aristarchus vary, but it is agreed that he was born on the island of Samos in Greece and studied under Strato (or Straton) of Lampsacus in Alexandria, Egypt. Strato went on to succeed Theophrastus as head of the lyceum founded by Aristotle at Athens, so it is probable that Aristarchus circulated among highly intellectual and influential men. Certain of his activities can be roughly dated, as he made observations of the summer solstice around 281-280 B.C., according to Ptolemy.

### Myriad-myriads

Aristarchus favored a mathematical approach to astronomy over the descriptive one, which tended to rely on intuition and rhetoric rather than observation. An example of his commitment to observation is his reported correction of Callippus' estimate of the length of the year, adding 1/1623 of a day to it. His own observations led to six astronomical hypotheses, from which Aristarchus drew eighteen propositions. These regarded measuring the sizes and distances of various celestial objects relative to the known diameter of the Earth. He correctly concluded that the orbit of the Earth was dwarfed by the overall size of the universe and distance of its furthermost visible stars. Archimedes proved this immensity was calculable with his famous "sand reckoning," counted at the time in myriad-myriads.

By studying the relative positions of the sun, moon, and Earth, Aristarchus concluded that during the half-moon each of them occupy respective points on a right triangle. He then reasoned that the Pythagorean theorem could be applied to determine the ratio of the sun-Earth distance and the moon-Earth distance. In fact, his proof of this is best expressed today as a trigonometric formula.

Because Aristarchus did not have the tools to measure angular distances of heavenly bodies, he consequently underestimated these distances. Likewise, his estimate of the size of the moon relative to the Earth, and the size of the sun relative to the moon were inaccurate as well. Those figures were improved during the next century by **Hipparchus**, though it is only later that we learned Aristarchus underestimated the sun's size by nearly 400 times his original estimation.

Unfortunately, the idealistic Greek model called for circular orbits, which did not account for the unevenly distributed changing of seasons. These are now attributable to elliptical orbits. While Aristarchus could not completely free himself of the Greek intellectual loyalty to mathematical harmonies, he went a long way towards letting experiment rule theory rather than idealism.

### Beyond Ideals

It is from the writings of Archimedes and Plutarch that Aristarchus' heliocentric hypothesis of 260 B.C. became known. As articulated by Aristarchus, the hypothesis accounted for the apparent motion of the heavenly bodies and diurnal motion of the stars. He not only proposed that the sun is fixed and that the Earth revolves around it, but also that the Earth rotates on its own axis. Aristarchus was roundly criticized--his contemporaries marshaled Aristotelian logic to refute his premise as untenable--although he was apparently never persecuted.

Aristarchus died at the earliest estimate around 250 B.C. in Alexandria. Debunked in his own time, his contributions as a scientist and mathematician have since been reevaluated. He may have also been an inventor, making an improved design of sundial called a "skaphe" or "scaphion," which seems to have placed the shadow-throwing pointer within a hollow hemispherical base.

Aristarchus was not acknowledged by Copernicus himself, having struck out a passage referring to his distant precursor during the editing of his manuscript *De revoluntionibus orbium coelestium*. Aristarchus' most ambitious ideas could not be confirmed or denied until the time of ** Isaac Newton**, when it became possible to test the effects of the rotation of the Earth and the phenomenon of stellar aberration.

*Aristarchus of Samos on the Sizes and Distances of the Sun and Moon*. Translated and with notes by Sir Thomas Heath, 1938

- Asimov, Isaac.
*Asimov's Biographical Encyclopedia of Science and Technology*. Second Revised Edition. Garden City, NY: Doubleday, 1982, pp. 26-27. *Biographical Encyclopedia of Scientists*. Edited by Urdang and Associates. New York: Facts on File, 1981, p. 26.- Boyer, Carl B.
*A History of Mathematics*. NY: John Wiley & Sons, Inc., 1968, pp. 138-39. *The Columbia Encyclopedia*. Fifth Edition. New York: Columbia University Press, 1993, p. 2091.- Eaves, Howard.
*Great Moments in Mathematics (Before 1650)*. Mathematical Association of America, Inc., 1980, p. 96. - Greider, Ken.
*Invitation to Physics*. New York: Harcourt, Brace Jovanovich, Inc., 1973, pp. 16, 28. - Hogben, Lancelot.
*Mathematics in the Making*. Garden City, NY: Doubleday, 1962, pp. 126-9. - Ronan, Colin.
*Astronomers Royal*. Garden City, NY: Doubleday & Co., Inc., 1969, pp. 5-6. - Van Der Waerden, B.L.
*Science Awakening*. Translated by Arnold Dresden. New York: Oxford University Press, 1961, pp. 202-4. - Williams, Trevor I., editor.
*A Biographical Dictionary of Scientists*. Third Edition. New York: John Wiley & Sons, 1982, pp. 16-17. *World Who's Who in Science*. First edition. Edited by Allen G. Debus. Chicago: Marquis, 1968, p. 61.- "Aristarchus of Samos."
*MacTutor History of Mathematics Archive.* - http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Aristarchus.html
- (July 1997).