"Well begun is half done." - Aristotle
Philon of Byzantium (circa 100 A.D.) worked on trying to duplicate the cube (construct a cube with volume equal to twice the volume of a given cube) using only a straight edge and compass. Since he could not find a direct solution he kept searching for problems that were equivalent in the sense that one could construct the solution to one problem from the solution to the other by means of the straight edge and compass. Constructing the Philon line (as it is now known) is one such equivalent problem that he discovered. He could not find a solution to the Philon line problem either. During the past 2000 years many of the giants of computing science, including Newton, tried to solve Philon's problem with straight edge and compass without success. It was only one hundred years ago, using algebra, that this was shown to be impossible.
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