The Archimedes Palimpsest is a parchment codex palimpsest, originally a Byzantine Greek copy of a compilation of Archimedes and other authors. It contains two works of Archimedes that were thought to have been lost (the Ostomachion and the Method of Mechanical Theorems) and the only surviving original Greek edition of his work On Floating Bodies. The first version of the compilation is believed to have been produced by Isidorus of Miletus, the architect of the geometrically complex Hagia Sophia cathedral in Constantinople, sometime around AD 530. The copy found in the palimpsest was created from this original, also in Constantinople, during the Macedonian Renaissance (c. AD 950), a time when mathematics in the capital was being revived by the former Greek Orthodox bishop of Thessaloniki Leo the Geometer, a cousin of the Patriarch.
Following the sack of Constantinople by Western crusaders in 1204, the manuscript was taken to an isolated Greek monastery in Palestine, possibly to protect it from occupying crusaders, who often equated Greek script with heresy against their Latin church and either burned or looted many such texts (including two additional copies of Archimedes writing, at least). The complex manuscript was not appreciated at this remote monastery and was soon overwritten (1229) with a religious text. In 1899, nine hundred years after it was written, the manuscript was still in the possession of the Greek church, and back in Istanbul, where it was catalogued by the Greek scholar Papadopoulos-Kerameus, attracting the attention of Johan Heiberg. Heiberg visited the church library and was allowed to make detailed photographs in 1906. Most of the original text was still visible, and Heiberg published it in 1915. In 1922 the manuscript went missing in the midst of the evacuation of the Greek Orthodox library in Istanbul, during a tumultuous period following World War I. A Western businessman concealed the book for over 70 years, and at some point forged pictures were painted on top of some of the text to increase resale value.
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In geometry, Cavalieri's principle, a modern implementation of the method of indivisibles, named after Bonaventura Cavalieri, is as follows: 2-dimensional case: Suppose two regions in a plane are included between two parallel lines in that plane. If every line parallel to these two lines intersects both regions in line segments of equal length, then the two regions have equal areas. 3-dimensional case: Suppose two regions in three-space (solids) are included between two parallel planes.
Archimedes of Syracuse (ˌɑːrkᵻˈmiːdiːz, ; 287-212 BC) was an Ancient Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Considered the greatest mathematician of ancient history, and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying the concept of the infinitely small and the method of exhaustion to derive and rigorously prove a range of geometrical theorems.
Explores the triumph of determinism in modern mechanics and the methodology of scientific development, with practical exercises on estimating surgical mask usage and analyzing atomic bomb energy.
We investigate hypergraphic LP relaxations for the Steiner tree problem, primarily the partition LP relaxation introduced by Koenemann et al. [Math. Programming, 2009]. Specifically, we are interested in proving upper bounds on the integrality gap of this ...
This PhD thesis explores the way multiple and tenuous links connect collective memory and space in the contemporary city. It does so through a field enquiry carried out in Rome, Italy. This palimpsest-city has a particular relationship to the past, which c ...
A large no. of liq./solid systems is examd. on a lab. scale to find out the effect of internals (e.g. static mixers) on the expansion behavior of fluidized beds. The expansion behavior is evaluated as a function of Archimedes no. With decreasing Archimedes ...