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Many statements on the web on the topic of the Archimedes Palimpsest are full of hyperbole. They can leave the erroneous impression that none of Archimedes' works are known except this one, or that only since the late 1990sCenturies: 19th century 20th century 21st century Decades: 1940s 1950s 1960s 1970s 1980s 1990s 2000s 2010s 2020s 2030s 2040s Years: Events and trends Computers, technology Explosive growth of the Internet; decrease in the cost of computers and other techn, when modern techniques began to be used to fill in some lacunaA lacuna is a gap in a manuscript or text. The word is Latin for hole or pit''.e, did anyone know the content of this palimpsest.
Although the only mathematical tools at its author's disposal were what we might now consider secondary-school geometryGeometry is the branch of mathematics dealing with spatial relationships. From experience, or possibly intuitively, people characterize space by certain fundamental qualities, which are termed axioms in geometry. Such axioms are insusceptible to proof, bu, Archimedes used those methods with rare brilliance, explicitly using infinitesimals to solve problems that would now be treated by integral calculus, which was independently reinvented in the 17th century. Among those problems were that of the center of gravity of a solid hemisphere, that of the center of gravity of a frustum of a circular paraboloid, and that of the area of a region bounded by a parabola and one of its secant lines. Contrary to historically ignorant statements found in some 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.
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.