Archimedes Palimpsest
The '''Archimedes Palimpsest''' is a Hotlink caller ringtones palimpsest on Mili Jay parchment, in which a copy of an otherwise unknown work of the ancient Alltel ringtones mathematician, Monica Hajkova physicist, and Samsung ringtones engineer Silvia Saint Archimedes of Real ringtones Syracuse, Italy/Syracuse, who lived in the Veronika Zemanova 3rd century BC/third century BC, was made in the Virgin mobile ringtones 10th century. In the Anetta Keys 12th century the Cingular Ringtones codex was unbound and washed, in order that the parchment leaves could be folded in half and reused for a Christian element without liturgy/liturgical text. Fortunately, the erasure was incomplete, and Archimedes' work is still legible today, using combinations of ultraviolet and visible light. It was a book of nearly 90 pages before being made a palimpsest of 177 pages; the older leaves folded so that each became two leaves of the liturgical book. In categories choosing 1906 it was briefly inspected in cello bow Constantinople and was published, from photographs, by the expensive re Denmark/Danish leroy handicap philology/philologist creating nickel Johan Ludvig Heiberg (world the 1854-punning on 1928); shortly thereafter it was translated into just written English language/English by available johnson Thomas Heath. Before that it was not widely known among mathematicians, physicists, or historians.
Media hype
Many statements on the web on the topic of the Archimedes Palimpsest are full of harbor he hyperbole. They can leave the erroneous impression that none of Archimedes' works are known except this one, or that only since the late define some 1990s, when modern techniques began to be used to fill in some spokeswoman senator lacunae, did anyone know the content of this palimpsest.
What Archimedes did
Although the only mathematical tools at its author's disposal were what we might now consider secondary-school any surplus geometry, Archimedes used those methods with rare brilliance, explicitly using played himself infinitesimals to solve problems that would now be treated by about wrongdoing integral calculus, which was independently reinvented in the 17th century. Among those problems were that of the seven strong center of gravity of a solid hemisphere, that of the center of divorce because gravity of a frustum of a circular paraboloid, and that of the area of a region bounded by a airways while parabola and one of its secant lines. Contrary to historically ignorant statements found in some religion thread 20th century calculus textbooks, he did not use anything like Riemann sums, either in the work embodied in this palimpsest or in any of his other works. For explicit details of the method used, see how Archimedes used infinitesimals.
A problem solved exclusively in the ''Method'' is the calculation of the volume of a cylindrical wedge, a result that reappears as theorem XVII (schema XIX) of Kepler's ''Stereometria''.
Some pages of the ''Method'' remained unused by the author of the Palimpsest and then they are still -surely forever- lost. Between them, an annonced result was about the volume of the intersection of two cylinders, a figure that Apostol and Mnatsakian have renamed ''n = 4 Archimedian globe'' (and the half of it, ''n = 4 Archimedian dome''), whose volume relates to the ''n''-polygonal pyramid. This is amusing because the collaboration on ''indivisibles'' between Galileo and Cavalieri—ranging between years 1626 to around 1635—has as a main argument the hull and pyramid of the ''n'' = ∞ dome. So in some sense it is true that the Method is only a theorem back from the modern infinitesimal theory.
Historian Reviel Netz of Stanford University, with technical assistance from several persons at the Rochester Institute of Technology, has been trying to fill in gaps in Heiberg's account. In Heiberg's time, much attention was paid to Archimedes' brilliant use of infinitesimals to solve problems about areas, volumes, and centers of gravity. Less attention was given to the ''Stomachion'', a problem treated in the Palimpsest that appears to deal with a children's puzzle. Netz has shown that Archimedes found that the ''number of ways'' to solve the puzzle is 17,152. This is perhaps the most sophisticated work in the field of combinatorics in classical antiquity.
The lawsuit
From the 1920s the manuscript lay unknown in the Paris apartment of an amateur of manuscripts and his heirs. In 1998 the ownership of the palimpsest was disputed in federal court in New York in the case of the ''Greek Orthodox Patriarch of Jerusalem/Patriarchate of Jerusalem versus Christie's, Inc''. At some time in the distant past, the Archimedes manuscript had lain in the library of Mar Saba, near Jerusalem, a monastery bought by the Patriarchate in 1625. The plaintiff contended that the palimpsest had been stolen from one of its monasteries in the 1920s. Judge Kimba Wood decided in favor of Christie's Auction House on laches grounds, and the palimpsest was sold for $2 million.
Now in a museum
The palimpsest is now on display at the Walters Art Museum in Baltimore, Maryland/Baltimore, where work of conservation continues, and a more accurate edition of the manuscript, including its drawn geometrical figures, is expected.
External links
* http://www.thewalters.org/archimedes/frame.html
* http://dftuz.unizar.es/~rivero/research/isisletter.htm
* http://www.pbs.org/wgbh/nova/teachers/programs/3010_archimed.html
* http://www.pbs.org/wgbh/nova/archimedes/palimpsest.html
Tag: History of mathematics
category:mathematics books
Tag: Manuscripts
Media hype
Many statements on the web on the topic of the Archimedes Palimpsest are full of harbor he hyperbole. They can leave the erroneous impression that none of Archimedes' works are known except this one, or that only since the late define some 1990s, when modern techniques began to be used to fill in some spokeswoman senator lacunae, did anyone know the content of this palimpsest.
What Archimedes did
Although the only mathematical tools at its author's disposal were what we might now consider secondary-school any surplus geometry, Archimedes used those methods with rare brilliance, explicitly using played himself infinitesimals to solve problems that would now be treated by about wrongdoing integral calculus, which was independently reinvented in the 17th century. Among those problems were that of the seven strong center of gravity of a solid hemisphere, that of the center of divorce because gravity of a frustum of a circular paraboloid, and that of the area of a region bounded by a airways while parabola and one of its secant lines. Contrary to historically ignorant statements found in some religion thread 20th century calculus textbooks, he did not use anything like Riemann sums, either in the work embodied in this palimpsest or in any of his other works. For explicit details of the method used, see how Archimedes used infinitesimals.
A problem solved exclusively in the ''Method'' is the calculation of the volume of a cylindrical wedge, a result that reappears as theorem XVII (schema XIX) of Kepler's ''Stereometria''.
Some pages of the ''Method'' remained unused by the author of the Palimpsest and then they are still -surely forever- lost. Between them, an annonced result was about the volume of the intersection of two cylinders, a figure that Apostol and Mnatsakian have renamed ''n = 4 Archimedian globe'' (and the half of it, ''n = 4 Archimedian dome''), whose volume relates to the ''n''-polygonal pyramid. This is amusing because the collaboration on ''indivisibles'' between Galileo and Cavalieri—ranging between years 1626 to around 1635—has as a main argument the hull and pyramid of the ''n'' = ∞ dome. So in some sense it is true that the Method is only a theorem back from the modern infinitesimal theory.
Historian Reviel Netz of Stanford University, with technical assistance from several persons at the Rochester Institute of Technology, has been trying to fill in gaps in Heiberg's account. In Heiberg's time, much attention was paid to Archimedes' brilliant use of infinitesimals to solve problems about areas, volumes, and centers of gravity. Less attention was given to the ''Stomachion'', a problem treated in the Palimpsest that appears to deal with a children's puzzle. Netz has shown that Archimedes found that the ''number of ways'' to solve the puzzle is 17,152. This is perhaps the most sophisticated work in the field of combinatorics in classical antiquity.
The lawsuit
From the 1920s the manuscript lay unknown in the Paris apartment of an amateur of manuscripts and his heirs. In 1998 the ownership of the palimpsest was disputed in federal court in New York in the case of the ''Greek Orthodox Patriarch of Jerusalem/Patriarchate of Jerusalem versus Christie's, Inc''. At some time in the distant past, the Archimedes manuscript had lain in the library of Mar Saba, near Jerusalem, a monastery bought by the Patriarchate in 1625. The plaintiff contended that the palimpsest had been stolen from one of its monasteries in the 1920s. Judge Kimba Wood decided in favor of Christie's Auction House on laches grounds, and the palimpsest was sold for $2 million.
Now in a museum
The palimpsest is now on display at the Walters Art Museum in Baltimore, Maryland/Baltimore, where work of conservation continues, and a more accurate edition of the manuscript, including its drawn geometrical figures, is expected.
External links
* http://www.thewalters.org/archimedes/frame.html
* http://dftuz.unizar.es/~rivero/research/isisletter.htm
* http://www.pbs.org/wgbh/nova/teachers/programs/3010_archimed.html
* http://www.pbs.org/wgbh/nova/archimedes/palimpsest.html
Tag: History of mathematics
category:mathematics books
Tag: Manuscripts
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