That's Maths:Archimedes of Syracuse was the greatest mathematician of antiquity. He was also a brilliant physicist, engineer and astronomer, famed for founding hydrostatics, for formulating the law of the lever, for designing the helical pump that bears his name, for designing engines of war, and for much more. Generations of children have learned how, upon discovering a way to assay King Hieron's crown, Archimedes ran naked through the street crying "Eureka".
Archimedes estimated the value of pi, the ratio of the circumference to the diameter of a circle, to remarkable accuracy using polygons of 96 sides within and around a circle. And he found the volume of a sphere, showing that it is two-thirds of the volume of the smallest cylinder in which it is contained. He asked that an image of a sphere within a cylinder be inscribed on his tombstone. Centuries later, the Roman orator Cicero found such a carving on a grave in Syracuse.
Many of Archimedes’ writings are lost, being known to us only through references made to them by later writers. Other works have reached us by a circuitous route: they were translated into Arabic in the ninth century, and from Arabic into Latin during the Renaissance. But some of Archimedes’s most important work remained hidden from us until the remarkable discovery of the Archimedes Palimpsest.
Palimpsests were works written on parchment that had been scraped clean of earlier writing. This was common practice in the Middle Ages, as vellum was very expensive. In 1906 a prayer book written in the 13th century AD came to light in Constantinople. Upon close examination by the Danish philologist Johan Heiberg, the incompletely erased work underlying the text was recognised as a 10th-century copy of several works of Archimedes, which had been thought to have been lost forever.
The palimpsest is the only source we have of The Method of Mechanical Theorems, in which Archimedes uses infinitesimal quantities to calculate the volumes of various bodies. This method foreshadowed integral calculus, invented independently by Newton and Leibniz nearly two thousand years later.
The Archimedes Palimpsest is the earliest extant manuscript of Archimedes' work; it includes copies of the geometric diagrams that he drew in the sand in the third century BC. It contains several treatises by Archimedes, including The Method. The Palimpsest was bought at auction in New York in 1998 for $2 million. The German magazine Der Spiegel reported that the purchaser was Jeff Bezos, founder of amazon.com.
The palimpsest has been intensively analysed over the past 10 years, using advanced imaging methods. A recent exhibition at the Walters Art Museum in Baltimore, Lost and Found: The Secrets of Archimedes, was devoted to the analysis of the palimpsest and to the outcome of the project to study it. All the images and translations are freely available on the Digital Palimpsest Web Page ( archimedespalimpsest.org), providing a treasure trove for scholars of mathematics.
* Peter Lynch is professor of meteorology at University College Dublin. He blogs at thatsmaths.com
