From: Amara Graps (amara@amara.com)
Date: Sat Mar 02 2002 - 02:34:49 MST
From: "scerir" <scerir@libero.it>, Mon, 25 Feb 2002
'His discoveries were numerous and admirable; but he is said to have
requested his friends and relations that, when he was dead, they
would place over his tomb a cylinder containing a sphere, inscribing
it with the ratio which the containing solid bears to the
contained.' [Plutarch, Parallel Lives: Marcellus]
The story of Archimedes' grave is
interesting, >http://www.mcs.drexel.edu/~crorres/Archimedes/Tomb/Cicero.html
I especially like this statement:
"The Romans were so uninterested in mathematics that Cicero's act of
respect in cleaning up Archimedes' grave was perhaps the most
memorable contribution of any Roman to the history of mathematics."
Simmons, George F., Calculus Gems, McGraw-Hill, Inc., New York,
1992, page 38
But I think that Archimedes' *life* was more interesting
>http://www.mcs.drexel.edu/~crorres/Archimedes/contents.html
His contributions show that he was one of humankind's most important
mathematicians- right up there with Newton, Euclid, Gauss ...
"Give me a place to stand and I shall move the Earth"
-- Archimedes referring to the law of the lever, which he had proved
in his treatise, _Planes in Equilibrium_.
Archimedes' Palimpsest.
In October 1998, a manuscript containing some of Archimedes' works
resurfaced from long obscurity and was sold in New York for two
million dollars. The private owner agreed to make it available
for research and publication. Among its many treasures is the only
evidence we have for the treatise known as "The Method", in which
physics and mathematics are most intimately combined by Archimedes.
This text below gives some history about the manuscript:
=====================================================================
from: http://www.maa.org/news/palimp.html
Christie's to Auction
Archimedes Palimpsest on October 29
Famous auction house Christie's are announcing on their web page
that on October 29 they will hold an auction for the Archimedes
Palimpsest at their New York location. This famous manuscript was
found by paleographer Athanassios Papadopoulos-Kerameus in 1899, and
edited by J. L. Heiberg. It contains several texts by Archimedes,
including The Method, a long-lost document in which Archimedes
explains his method for discovering the value of areas and volumes
(which he would then prove using the "method of exhaustion"). An
English translation by T. L Heath was published in 1912 as a
supplement to his The Works of Archimedes and is included in more
recent editions of that book.
Historians of mathematics had known of the existence of The Method
through references by other authors, but until 1899 it was thought
to have been lost. Its rediscovery was of great importance because
it shows that Archimedes used a kind of "method of indivisibles" to
determine the areas and volumes which he wanted to compute. He did
not consider, however, such computations to be proofs, and gave
proofs using the method of exhaustion.
In addition to The Method, the manuscript contains several other
works by Archimedes, including the only known copy of On Floating
Bodies in the original Greek.
[...]
The manuscript discovered by Papadopoulos-Kerameus was a
"palimpsest," that is, a parchment on which some text had been
erased and replaced with other text. The underlying text could
nevertheless still be read and could be seen to be of a mathematical
nature. Papadopoulos-Kerameus published excerpts from the manuscript
in the hopes that experts would recognize it, and this led to
Heiberg's examination and identification of the document. The
manuscript has apparently been in the hands of a private collector
throughout most of this century, unavailable to researchers, and has
only now resurfaced. (Christie's says the palimpsest is from a
"French private collection".)
[...]
Christie's has valued the manuscript at between $800,000 and
$1,200,00.
[...]
Update on October 28
A number of sources report that the Greek Ministry of Culture and
the Greek Orthodox Patriarchate of Jerusalem are asking Christie's
to stop the sale of the manuscript, claiming that it was acquired
illegally and in fact belongs to the Patriarchate. Christie's says
it is convinced the current owner is the rightful owner and will
proceed with the sale.
Update on November 2
As expected, the auction happened on October 29. It was very quick,
perhaps some five minutes. The manuscript was bought for $2 million
by one Simon Finch, a well-known London antiquarian and rare books
dealer, who was acting for an as-yet unknown American buyer.
Christie's officials have stated that the new owner plans to make
the manuscript available to scholars.
=====================================================================
The Archimedes Palimpsest now in the care of the Walters Art Gallery
http://www.thewalters.org/archimedes/
In June 2000, Physics Today published a long article by Reviel Netz
about this manuscript. He is a science historian and a classics
professor at Stanford University, and he notes that the Palimpsest
is changing Archimedes' math from the heterogeneous 1907 translation
to something playful and creative.
At first look, the manuscript looks like an ancient prayer book
(Paliimpsestos is the Greek word for rescraped, or overwritten,
parchment). But underneath is something different. First completed
around AD 1000 by a scribe in Constantinople, the Greek manuscript
was likely a copy of a copy of a copy of the original papyrus
scroll. Two hundred years after its creation, however, the document
was given a facelift. Sometime during the Crusades, a local scribe
scrubbed off the ink, cut the book's leaves in half, and rotated the
pages 90 degrees. Then he wrote on the parchment again. The prayer
book then disappeared until 1907, when it was translated by a
classics scholar. It didn't resurface again until 1998, when it was
sold at a Christie's auction.
Imaging teams are using multispectral imaging, magnetic imaging, and
confocal microscopy to examine the palimpsest. "It's sort of a
'history of mathematics' genome project," says Bill Christens-Barry,
a physicist at Johns Hopkins and a member of the imaging team.
"We're trying to look at the foundation of elements of the whole
field by stitching together very small fragments of information to
understand the whole."
=================================================================
From Rviel Netz' June 2000 Physics Today article (pg. 36), Box 3:
"The Eurekas of Archimedes"
Archimedes made many discoveries. Some, perhaps most, he committed
to writing, and some of these writings, perhaps, most, survived.
The most remarkable of them, the Method, survives only thanks to
the Archimedes Palimpsest.
The palimpsest contains, in more or less fragmentary form, seven
works by Archimedes. The first three form a natural sequence in
mathematical physics:
* Planes in Equilibrium. Archimedes proves the law of the balance and
derives results for centers of gravity in planes.
* On Floating Bodies. Here he proves his law of buoyancy and
derives results for the flotation of solids of geometrically
interesting shapes.
*.Method. The law of the balance is used to derive geometrical
properties.
Next come four studies in pure geometry:
* Spiral Lines: Spirals are first defined and their lengths and
areas are measured.
* On sphere and Cylinder. Archimedes provides the ratios for the
surface area and volume of a sphere and then solves a series of
problems concerning spheres.
* Measurement of the Circle. An approximation of the value of pi is
obtained using a method than can, in principle, be extended
indefinitely.
* Stomachion. Only a fragment survives. Apparently this is a study
in a tangram-like game, where area are covered by given geometrical
figures (tiling!)
Three further works of Archimedes have survived in Greek in other
manuscripts:
* Quadrature of the Parabola. Related in certain ways to the Method,
this is an exploration of the applicability of the the law of the
balance to geometry.
* Sand-Reckoner. In this complex miscellany, Archimedes sets out to
measure how many grains of sand it would take to fill up the
universe, in the process contributing to astronomy as well as to the
calculation techniques.
* Conoids and Spheroids. Archimedes introduces the solids of
revolution of conic sections, and provides several measurements for
those figures.
Archimedes may also have been the author of the Cattle Problem, a
numerical problem comparable in spirit to the Sand-Reckoner,
although the attribution is nowhere directly founded. An Arabic
text, _On Lemmas_, showing various configurations of circles and
measurements concerning them, may be derived from Archimedes; the
same may be said, with even less confidence, of an Arabic treatise
on the _Construction of the Regular Heptagon_. We know for sure, on
the authority of the knowledgeable commentator Pappus, that
Archimedes had produced a work (now lost) on Semi-Regular Solids
(the faces of which are all regular, though not identical).
One may go on counting, beyond these 14 works, well into the realm
of myth, as recounted by Greek and Arabic stories on Archimedean
feats of engineering and proof. We cannot know how much the
Archimedean corpus originally contained. However, we do have a
relatively large body of surviving works, more representative,
probably, than for any other mathematician from antiquity: None of
the others appears to us with as well-defined a scientific
personality.
-- ******************************************************************** Amara Graps, PhD email: amara@amara.com Computational Physics vita: ftp://ftp.amara.com/pub/resume.txt Multiplex Answers URL: http://www.amara.com/ ******************************************************************** "Whenever I see an adult on a bicycle, I do not despair for the future of the human race." -- H. G. Wells
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