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According to historical documents, it is challenging to establish whether a proof of Th¯abit’s theorem exists based exclusively on equidecomposibility, as in the case of the Pythagorean and Pappus theorems. This article presents the corresponding proof. Key Words: Euclidean geometry, generalization of Pythagorean theorem, equide-
THABIT IBN QURRA AND THE PYTHAGOREAN THEOREM By Robert Shloming, Brooklyn College, Brooklyn, New York DURING the Dark Ages of Western Europe, Islam was very much mathemati cally alive. The Arabs were able to solve the most difficult problems of Archimedes and Apollonius at a time when Latin mathematical knowledge was at a level
The proof of Thabit’s generalization is identical to one of the standard ways of proving the theorem of Pythagoras using similar triangles, and provides a very accessible generalisation with which to challenge learners.
In http://math.ucr.edu/~res/math153/history05f.pdf we presented a generalization of the Pythagorean Theorem due to Pappus. As with nearly all fundamental theorems, there are many possible generalizations and analogs, and here we are concerned with one which is due to Thabit ibn Qurra.
The Pythagorean (or Pythagoras') Theorem is the statement that the sum of (the areas of) the two small squares equals (the area of) the big one. In algebraic terms, a² + b² = c² where c is the hypotenuse while a and b are the legs of the triangle.
Request PDF | On a Proof of the Thābit Ibn Qurra's Generalization of the Pythagorean Theorem | One of the most interesting generalizations of the Pythagorean theorem was stated by Thābit in the...
6 ημέρες πριν · Figure 3. : since a c = x a and b c = y b, we have c = x + y = a 2 c + b 2 c so that a 2 + b 2 = c 2. Figure 3: Proof by similar triangles. Display full size. But this proof is easily rewritten as trigonometry. Since a c = x a = sin α we have x = a sin α = (c sin α) sin α = c sin 2 α, and similarly y = c cos 2 α.
