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'Archimedes' calculus'
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| Title of object: |
Archimedes' calculus |
| Canonical Name: |
ArchimedesCalculus |
| Type: |
Definition |
| Created on: |
2008-07-14 09:44:18 |
| Modified on: |
2008-07-14 09:44:18 |
| Classification: |
msc:01A20 |
| Synonyms: |
Archimedes' calculus=differential calculus |
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Content:
The differential calculus of Archimedes has been passed down to the modern era within one text, an erasable parchment (palimpsest). The information had not been recorded in Archimedes' handwriting. Worse, the parchment's calculus information had been copied over hundred's of years, and later erased by 1,100 AD Byzanatine priests. Byzantines used the vellum paper to write a religious text.
In 1906 Heiberg ran across a copy of the text, decoding large chunks of the erased information. He found a calculus method that exactly sum an infinite slice of a parabola. The method did not use the method of exhaustion, as often misreported in math history texts. \PMlinkexternal{E.J. Dijksterhuis}{http://mathforum.org/kb/message.jspa?messageID=5847373&tstart=90} included Heilberg's view of the information in a 1987 biography of Archimedes, published by Princeton Press. Dijksterhuis cited a 1/4 geometric infinite series:
$$4A/3 = A + A/4 + A/16 + A/64 + ... $$
written as a finite Egyptian fraction series:
$$4A/3 = A + A/4 + A/12$$
The document came on the open market a few years ago. It was auctioned for 2,000,000 dollars. NOVA reported a revised analysis of the text that was suggested by its new owners. The NOVA program that did not include Heiberg and Dijksterhuis' 1/4 geometric series method in its review. A Stanford University investigator has possessed the document for five years. Hopefully a final version of the text will be published by its new owners so that a debate can commence on the actual details of Archimedes' differential calculus.
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