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Archimedes: Archimedes Palimpsest
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In 1998, the Archimedes palimpsest suddenly resurfaced from a private collection. An anonymous U.S. billionaire bought it for $2 million at Christie's auction house in New York and made it available to scholars. Mathematical historians have now come up with a guess about what Archimedes was thinking 2,200 years ago.
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The foremost document containing the work of Archimedes is the Archimedes Palimpsest. A palimpsest, from the Greek word palimpsestos meaning "scraped again", is a manuscript written on parchment that has another text written over it, leaving two or more layers of visible writing. Palimpsests were common in antiquity because parchment was scarce and costly. As certain kinds of texts went in and out of literary fashion the manuscripts were recycled and reused, with their original content being rubbed away and overwritten. In 1906, the Danish professor Johan Ludvig Heiberg realized that a 174-page goatskin parchment of prayers written in the 13th century AD ... carried an older work written in the 10th century AD, which he identified as previously unknown copies of works by Archimedes.[44] The parchment spent hundreds of years in a monastery library in Constantinople before being sold to a private collector in the 1920s. On October 29, 1998 it was sold at auction to an anonymous buyer for $2 million at Christie's in New York.
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These images, produced in 2006, show scans of the Archimedes palimpsest. The first (marked 078v) shows two facing pages of the book. It was created using a technique called image subtraction. The second (081v), made at Stanford's synchrotron radiation laboratory, shows two views of the same page. The left image was created with high-intensity X rays that scanned the front of the page, peering through the paint and gold-leaf of a painting to reveal the original writings beneath. The right image shows a scan made through the back of the same page.
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This is a dissection puzzle similar to a Tangram, and the treatise describing it was found in more complete form in the Archimedes Palimpsest. Archimedes calculates the areas of the 14 pieces which can be assembled to form a square. Research published by Dr. Reviel Netz of Stanford University in 2003 argued that Archimedes was attempting to determine how many ways the pieces of paper could be assembled into the shape of a square. The figure given by Dr. Netz is that the pieces can be made into a square in 17,152 ways. The number of arrangements is 536 when solutions that are equivalent by rotation and reflection have been excluded. The Stomachion represents an example of an early problem in combinatorics.
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The Stomachion fragment offered only tantalizing glimpses into Archimedes thinking. The parchment, probably first written on in the 10th century in Constantinople, is a palimpsest—a document whose surface has been scraped and reused. In 1204, the Fourth Crusade sacked Constantinople, and shortly thereafter monks unbound the Archimedes's parchment, did their best to erase the mathematical text, and recycled the volume as a Christian prayer book. Only the beginning pages of the Stomachion made it into the new book, and on those pages, the underlying math text was faint and hard to read.
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The French owners of the Archimedes palimpsest confidentially approach an expert at Christie's in Paris to ask for an appraisal. After the appraiser discovers that the manuscript is the lost Archimedes palimpsest (in part by comparing it to Heiberg's photographs), he values it at between $800,000 and $1.2 million.
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Archimedes Palimpsest