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around 850

Ibn Qurra's Pythagorean Theorem Proofs

Pythagorean theorem proofs by dissection

Arab polymath Thābit ibn Qurra revised an earlier translation of the Elements and translated several other Greek works from the times of Euclid to Ptolemy. He also produced two original proofs of the Pythagorean theorem as well a generalization of the theorem (which, while valid, was stated without proof).

Ibn Qurra's Pythagorean Theorem Proofs

Thābit ibn Qurra presented two original proofs of the Pythagorean theorem using a method of dissection which he called the method of reduction to triangles and rearrangement by juxtaposition. These proofs appeared in a letter to a friend written around around 850 CE and are preserved in the library of the Hagia Sophia Museum in Istanbul, Turkey.

Artifact origin

Baghdad, Iraq

Current artifact location

Hagia Sophia, Istanbul

Catalog number

4832

Timeline

PythagoreanTheorem timeline Babylonian Mud Wall Tablet Babylonian Inner Diagonal Tablet Babylonian Square Root of 2 Tablet Berlin Pythagorean Theorem Papyrus Plimpton 322 Vedic Fire Altar Rectangle Diagonal Vedic Fire Altar Square Diagonal Euclid's Elements Ptolemy's Quadrilateral Theorem Zhoubi Suanjing Pythagorean Theorem Proof Ibn Qurra's Pythagorean Theorem Proofs Lilāvatī of Bhāskara II

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Computational Explanation

Other Resources

Additional Reading

  • Beggren, J. L. "Mathematics in Medieval Islam." Ch. 5 in The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook (Ed. V. J. Katz). Princeton, NJ: Princeton University Press, pp. 517 and 547, 2007.
  • Colburn, A. R. "The Pons Asinorum.—II. New Solutions of the Pythagorean Theorem." Scientific American Supplement, Vol. 70, No. 1823, p. 382–383, 1910.
  • Eves, H. An Introduction to the History of Mathematics, 6th ed. Cengage Learning, p. 73, 1990.
  • Maor, E. The Pythagorean Theorem: A 4000-Year History. Princeton, NJ: Princeton University Press, pp. 69–71, 2007.
  • Merzbach, U. C. and Boyer, C. B. A History of Mathematics, 3rd ed. Hoboken, NJ: Wiley, pp. 213–214, 2011.
  • Perigal, H. "On Geometric Dissections and Transformations." Messenger of Mathematics, Vol. 2, pp. 103–106, 1873.
  • Sayili, A. "Thabat ibn Qurra's Generalization of the Pythagorean Theorem." Isis, Vol, 51, 35–37, 1960.
  • Scribs, C. J. "John Wallis' Treament of Angular Sections and Thābit ibn Qurra's Generalization of the Pythagorean Theorem." Isis, Vol. 56, pp. 56–67, XXX.
  • Shloming, S. "Thabit ibn Qurra and the Pythagorean Theorem." The Mathematics Teacher, Vol. 63, pp. 519–528, 1970.
  • Suter, H. Die Mathematiker und Astronomen der Araber und Ihre Werke. Leipzig, Germany: Teubner, p. 37, 1900.