A Sample of Mathematical Pseudoeponyms
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Muhammad Yusuf
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1. The
Pythagorean theorem
The Pythagorean
theorem states that in a right triangle, the sum of the squares of the legs
equals the square of the hypotenuse. It would be difficult to overestimate the importance
of this result. It is generally acknowledged that this remarkable theorem was
known before the time of Pythagoras of Samos (ca. 582–500 B.C.), the Greek philosopher
and mathematician (see, e.g., NCTM [1969], Swetz and Kao [1977], Ang [1978]).
Van der Waerden (1983) hypothesized that since the Pythagorean theorem was
known in four ancient civilizations—Babylonia, India, Greece, and China—it is probable
that a common origin of the whole theory of right triangles exists. Using both
written sources and archeological evidence, he constructed an interesting and compelling
argument that led him to the following conclusion (van der Waerden 1983, 29): “I
am convinced that the excellent neolithic mathematician who discovered the Theorem
of Pythagoras had a proof of the theorem.” He also remarked that the best account
of mathematical science in the Neolithic Age is to be found in Chinese texts.
2. Euler's
polyhedral theorem
One of the most
interesting formulas relating to simple polyhedra is F + V – E = 2, where F is the number of faces, V is
the number of vertices, and E is the number of edges. The five simple
polyhedra are tetrahedron (pyramid), hexahedron (cube), octahedron,
dodecahedron, and icosahedron. For the cube, F = 6, V = 8 and E = 12.
Although this
formula may have been known to Archimedes (ca. 225 B.C.), René Descartes, the
French mathematician and philosopher, was the first to state this concept (ca.
1635). Leonard Euler independently discovered the theorem and announced his finding
in Petrograd in 1752. Since Descartes's findings were not generally known until
his unpublished mathematical works were made available in 1860, the polyhedral
formula became known as Euler’s theorem rather than Descartes’s theorem (Smith
1958, 296).
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