Sunday, February 7, 2010



Pythagoras of Samos (569 - 475 BC) combined science and religion in equal measure. He travelled to both Egypt and Babylon. He is the father of number theory and recognised, among other things, that the Earth was a sphere. Pythagoras and his inner circle of followers (the mathematikoi) held that, fundamentally, reality is mathematical in nature, with each number having its own 'personality.'

Euclid (325 - 265BC) of Alexandria brought together the work of several predecessors. The 13 books of The Elements became the primary source of geometric reasoning for two thousand years. Euclid's other works included Optics (on perspective) and The Book of Fallacies (which sounds delightful but is lost).

Neo-Platonist Proclus Diadochus (died 485), one of the last great philosophers of Plato's Academy at Athens, wrote a commentary on Euclid's Elements which today is our principal source of early Greek geometry.

Aristarchus (310 - 230 BC) applied Alexandrian trigonometry to estimate the distances and sizes of the sun and moon, and also postulated a heliocentric universe.

Archimedes of Syracuse (287 - 212 BC) is credited with the discovery of pi.

Eratosthenes (275-194 BC), the third librarian of Alexandria, calculated the circumference of the earth to within 1% accuracy, based on the measured distance from Aswan to Alexandria and the fraction of the whole arc determined by differing shadow-lengths at noon in those two locations. He deduced that the length of the year should be 365 1/4 days and put forward the idea of adding a "leap day" every four years. He cataloged 44 constellations and 475 fixed stars.

Eratosthenes also suggested that the seas were connected, that Africa might be circumnavigated, and that "India could be reached by sailing westward from Spain."

Apollonius of Perga (262 -190 BC), in his famous book Conics, introduced terms which are familiar to us today, such as parabola, ellipse, hyperbola and polyhedron. In another work On the Burning Mirror he described the focal properties of a parabolic mirror. When it came to planetary theory, Apollonius developed systems of eccentric and epicyclical motion to explain the apparent motion of the planets across the sky.

No mere theoretician, Apollonius developed the hemicyclium, a sundial which has the hour lines drawn on the surface of a conic section giving greater accuracy.

Hipparchus (190 - 120 BC) of Bithynia, during the reign of Ptolemy VII, discovered and measured the precession of the equinoxes, the size and trajectory of the sun, and the moon's path. He charted constellations and speculated that stars might have both births and deaths. He is credited with inventing longitude and latitude, importing the 360° circular system from Babylonia, and calculating the length of a year within six minutes accuracy.

Ptolemy (Claudius Ptolemaeus) 87 -150 AD worked out mathematically his elegant system of epicycles to support the geocentric, Aristotelian view, and wrote a treatise on astrology, both of which were to become the medieval paradigm.

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