Pythagorean theorem (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Pythagorean theorem" in English language version.

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archive.org

van der Waerden (1983), p. 26 believed that this material "was certainly based on earlier traditions". Carl Boyer states that the Pythagorean theorem in the Śulba-sũtram may have been influenced by ancient Mesopotamian math, but there is no conclusive evidence in favor or opposition of this possibility.^[13]
Plutarch (1936). Moralia V: Isis and Osiris. Loeb Classical Library. Vol. 306. Translated by Babbitt, Frank Cole. Harvard University Press. p. 135.
An extensive discussion of the historical evidence is provided in (Euclid 1956, p. 351) page=351 Euclid (1956). The Thirteen Books of Euclid's Elements, Translated from the Text of Heiberg, with Introduction and Commentary. Vol. 1 (Books I and II). Translated by Heath, Thomas L. (Reprint of 2nd (1925) ed.). Dover.
Crease, Robert P. (2008). The Great Equations: Breakthroughs in Science From Pythagoras to Heisenberg. W W Norton & Co. p. 25. ISBN 978-0-393-06204-5.
Euclid 1956, pp. 351–352. Euclid (1956). The Thirteen Books of Euclid's Elements, Translated from the Text of Heiberg, with Introduction and Commentary. Vol. 1 (Books I and II). Translated by Heath, Thomas L. (Reprint of 2nd (1925) ed.). Dover.
Loomis 1940. Loomis, Elisha Scott (1940). The Pythagorean Proposition (2nd ed.). Ann Arbor, Michigan: Edwards Brothers. Reprinted, 1968, National Council of Teachers of Mathematics, ISBN 9780873530361.
Gullberg, Jan (1997). Mathematics: from the birth of numbers. W. W. Norton & Company. p. 435. ISBN 0-393-04002-X.
(Loomis 1940, p. 113, Geometric proof 22 and Figure 123) Loomis, Elisha Scott (1940). The Pythagorean Proposition (2nd ed.). Ann Arbor, Michigan: Edwards Brothers. Reprinted, 1968, National Council of Teachers of Mathematics, ISBN 9780873530361.
Wilczynski, Ernest Julius; Slaught, Herbert Ellsworth (1914). "Theorem 1 and Theorem 2". Plane Trigonometry and Applications. Allyn and Bacon. p. 85.
Lawrence S. Leff (2005). PreCalculus the Easy Way (7th ed.). Barron's Educational Series. p. 296. ISBN 0-7641-2892-2.
Howard Whitley Eves (1983). "§4.8:...generalization of Pythagorean theorem". Great moments in mathematics (before 1650). Mathematical Association of America. p. 41. ISBN 0-88385-310-8.
For the details of such a construction, see Jennings, George (1997). "Figure 1.32: The generalized Pythagorean theorem". Modern geometry with applications: with 150 figures (3rd ed.). Springer. p. 23. ISBN 0-387-94222-X.
Weisstein, Eric W. (1999). "Parallel Postulate". CRC Concise Encyclopedia of Mathematics. CRC Press. p. 1313. ISBN 0-8493-9640-9. The parallel postulate is equivalent to the Equidistance postulate, Playfair axiom, Proclus axiom, the Triangle postulate and the Pythagorean theorem.

ia800501.us.archive.org

Wentworth & Smith (1914), p. 116: "the Law of Cosines may be stated as follows: [...] In other words we have the Pythagorean Theorem as a special case. Hence this is sometimes called the Generalized Pythagorean Theorem." Wentworth, George; Smith, David Eugene (1914). Plane Trigonometry and Tables (PDF). Boston: Ginn and Company.

arxiv.org (Global: 69^th place; English: 59^th place)

Saikia 2013. Saikia, Manjil P. (22 October 2013). "The Pythagoras's Theorem". p. 5. arXiv:1310.0986 [math.HO]. Brief historical overview of the Pythagoras's theorem and its discoverer, Pythagoras. Simple proof of the result and discussion of some extensions.

books.google.com (Global: 3^rd place; English: 3^rd place)

The proof by Pythagoras probably was not a general one, as the theory of proportions was developed only two centuries after Pythagoras; see Maor (2007), p. 25. Maor, Eli (2007). The Pythagorean Theorem: A 4,000-Year History. Princeton, New Jersey: Princeton University Press. ISBN 978-0-691-12526-8.
Sally & Sally (2007), p. 63, Chapter 3: Pythagorean triples. Sally, Judith D.; Sally, Paul J. Jr. (21 December 2007). Roots to Research: A Vertical Development of Mathematical Problems. American Mathematical Society. ISBN 978-0-8218-4403-8.
Neugebauer 1969, p. 36. Neugebauer, Otto (1969). The exact sciences in antiquity (2nd ed.). Courier Dover Publications. ISBN 0-486-22332-9. OCLC 638685764.
Neugebauer 1969: p. 36 "In other words it was known during the whole duration of Babylonian mathematics that the sum of the squares on the lengths of the sides of a right triangle equals the square of the length of the hypotenuse." Neugebauer, Otto (1969). The exact sciences in antiquity (2nd ed.). Courier Dover Publications. ISBN 0-486-22332-9. OCLC 638685764.
Kim Plofker (2009). Mathematics in India. Princeton University Press. pp. 17–18. ISBN 978-0-691-12067-6.
Boyer & Merzbach (2011), p. 187: "[In Sulba-sutras,] we find rules for the construction of right angles by means of triples of cords the lengths of which form Pythagorean triages, such as 3, 4, and 5, or 5, 12, and 13, or 8, 15, and 17, or 12, 35, and 37. Although Mesopotamian influence in the Sulvasũtras is not unlikely, we know of no conclusive evidence for or against this. Aspastamba knew that the square on the diagonal of a rectangle is equal to the sum of the squares on the two adjacent sides. Less easily explained is another rule given by Apastamba – one that strongly resembles some of the geometric algebra in Book II of Euclid's Elements. (...)" Boyer, Carl Benjamin; Merzbach, Uta C. (2011). A History of Mathematics (3rd ed.). Wiley. ISBN 978-0470525487.
"Introduction and books 1,2". The University Press. 25 March 1908 – via Google Books.
(Heath 1921, Vol I, p. 144): "Though this is the proposition universally associated by tradition with the name of Pythagoras, no really trustworthy evidence exists that it was actually discovered by him. The comparatively late writers who attribute it to him add the story that he sacrificed an ox to celebrate his discovery." Heath, Thomas (1921). "The 'Theorem of Pythagoras'". A History of Greek Mathematics (2 Vols.). Oxford: Clarendon Press. pp. 144 ff. Reprinted, Dover Publications, 1981, ISBN 0-486-24073-8.
An extensive discussion of the historical evidence is provided in (Euclid 1956, p. 351) page=351 Euclid (1956). The Thirteen Books of Euclid's Elements, Translated from the Text of Heiberg, with Introduction and Commentary. Vol. 1 (Books I and II). Translated by Heath, Thomas L. (Reprint of 2nd (1925) ed.). Dover.
Aaboe, Asger (1997). Episodes From the Early History of Mathematics. Mathematical Association of America. p. 51. ISBN 0-88385-613-1. ... it is not until Euclid that we find a logical sequence of general theorems with proper proofs.
This work is a compilation of 246 problems, some of which survived the book burning of 213 BC, and was put in final form before 100 AD. It was extensively commented upon by Liu Hui in 263 AD. Straffin, Philip D. Jr. (2004). "Liu Hui and the First Golden Age of Chinese Mathematics". In Anderson, Marlow; Katz, Victor J.; Wilson, Robin J. (eds.). Sherlock Holmes in Babylon: and Other Tales of Mathematical History. Mathematical Association of America. pp. 69 ff. ISBN 0-88385-546-1. See particularly §3: Nine chapters on the mathematical art, pp. 71 ff.
Shen, Kangshen; Crossley, John N.; Lun, Anthony Wah-Cheung (1999). The Nine Chapters on the Mathematical Art: Companion and Commentary. Oxford University Press. p. 488. ISBN 0-19-853936-3.
In particular, Li Jimin; see Centaurus, Volume 39. Copenhagen: Munksgaard. 1997. pp. 193, 205.
Chen, Cheng-Yih (1996). "§3.3.4 Chén Zǐ's formula and the Chóng-Chã method; Figure 40". Early Chinese Work in Natural Science: a Re-examination of the Physics of Motion, Acoustics, Astronomy and Scientific Thoughts. Hong Kong University Press. p. 142. ISBN 962-209-385-X.
Wu, Wen-tsün (2008). "The Gougu Theorem". Selected works of Wen-tsün Wu. World Scientific. p. 158. ISBN 978-981-279-107-8.
Benson, Donald (1999). The Moment of Proof: Mathematical Epiphanies. Oxford University Press. pp. 172–173.
Maor (2007), p. 39. Maor, Eli (2007). The Pythagorean Theorem: A 4,000-Year History. Princeton, New Jersey: Princeton University Press. ISBN 978-0-691-12526-8.
Published in a weekly mathematics column: Garfield, James A. (1876). "Pons Asinorum". The New England Journal of Education. 3 (14): 161; as noted in Dunham, William (1997). The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems, and Personalities. Wiley. p. 96. ISBN 0-471-17661-3.
Maor (2007), pp. 106–107. Maor, Eli (2007). The Pythagorean Theorem: A 4,000-Year History. Princeton, New Jersey: Princeton University Press. ISBN 978-0-691-12526-8.
Sally & Sally (2007), pp. 54–55, Theorem 2.4 (Converse of the Pythagorean theorem). Sally, Judith D.; Sally, Paul J. Jr. (21 December 2007). Roots to Research: A Vertical Development of Mathematical Problems. American Mathematical Society. ISBN 978-0-8218-4403-8.
Law, Henry (1853). "Corollary 5 of Proposition XLVII (Pythagoras's Theorem)". The Elements of Euclid: with many additional propositions, and explanatory notes, to which is prefixed an introductory essay on logic. John Weale. p. 49.
Lavine, Shaughan (1994). Understanding the infinite. Harvard University Press. p. 13. ISBN 0-674-92096-1.
Heath (1921), Vol I, pp. 65; Hippasus was on a voyage at the time, and his fellows cast him overboard. See Choike, James R. (1980). "The Pentagram and the Discovery of an Irrational Number". The College Mathematics Journal. 11: 312–316. Heath, Thomas (1921). "The 'Theorem of Pythagoras'". A History of Greek Mathematics (2 Vols.). Oxford: Clarendon Press. pp. 144 ff. Reprinted, Dover Publications, 1981, ISBN 0-486-24073-8.
Jon Orwant; Jarkko Hietaniemi; John Macdonald (1999). "Euclidean distance". Mastering algorithms with Perl. O'Reilly Media, Inc. p. 426. ISBN 1-56592-398-7.
Pertti Lounesto (2001). "§7.4 Cross product of two vectors". Clifford algebras and spinors (2nd ed.). Cambridge University Press. p. 96. ISBN 0-521-00551-5.
Francis Begnaud Hildebrand (1992). Methods of applied mathematics (Reprint of Prentice-Hall 1965 2nd ed.). Courier Dover Publications. p. 24. ISBN 0-486-67002-3.
Lawrence S. Leff (1 May 2005). cited work. Barron's Educational Series. p. 326. ISBN 0-7641-2892-2.
Sally & Sally (2007), p. 62, Exercise 2.10 (ii). Sally, Judith D.; Sally, Paul J. Jr. (21 December 2007). Roots to Research: A Vertical Development of Mathematical Problems. American Mathematical Society. ISBN 978-0-8218-4403-8.
Claudi Alsina, Roger B. Nelsen: Charming Proofs: A Journey Into Elegant Mathematics. MAA, 2010, ISBN 9780883853481, pp. 77–78 (excerpt, p. 77, at Google Books)
Rajendra Bhatia (1997). Matrix analysis. Springer. p. 21. ISBN 0-387-94846-5.
Ferdinand van der Heijden; Dick de Ridder (2004). Classification, parameter estimation, and state estimation. Wiley. p. 357. ISBN 0-470-09013-8.
Qun Lin; Jiafu Lin (2006). Finite element methods: accuracy and improvement. Elsevier. p. 23. ISBN 7-03-016656-6.
Howard Anton; Chris Rorres (2010). Elementary Linear Algebra: Applications Version (10th ed.). Wiley. p. 336. ISBN 978-0-470-43205-1.
Karen Saxe (2002). "Theorem 1.2". Beginning functional analysis. Springer. p. 7. ISBN 0-387-95224-1.
Douglas, Ronald G. (1998). Banach Algebra Techniques in Operator Theory (2nd ed.). New York, New York: Springer-Verlag New York, Inc. pp. 60–61. ISBN 978-0-387-98377-6.
Pruss, Alexander R. (2006). The Principle of Sufficient Reason: A Reassessment. Cambridge University Press. p. 11. ISBN 0-521-85959-X. We could include ... the parallel postulate and derive the Pythagorean theorem. Or we could instead make the Pythagorean theorem among the other axioms and derive the parallel postulate.
O'Neill, Barrett (2006). "Exercise 4". Elementary Differential Geometry (2nd ed.). Academic Press. p. 441. ISBN 0-12-088735-5.
Stahl, Saul (1993). "Theorem 8.3". The Poincaré Half-Plane: A Gateway to Modern Geometry. Jones & Bartlett Learning. p. 122. ISBN 0-86720-298-X.
Gilman, Jane (1995). "Hyperbolic triangles". Two-generator Discrete Subgroups of PSL(2,R). American Mathematical Society. ISBN 0-8218-0361-1.

cam.ac.uk (Global: 670^th place; English: 480^th place)

dpmms.cam.ac.uk

For an extended discussion of this generalization, see, for example, Willie W. Wong Archived 2009-12-29 at the Wayback Machine 2002, A generalized n-dimensional Pythagorean theorem.

clarku.edu (Global: 6,602^nd place; English: 6,109^th place)

aleph0.clarku.edu

"Euclid's Elements, Book I, Proposition 47". See also a web page version using Java applets by David E. Joyce, Clark University.
Euclid's Elements, Book I, Proposition 48 From D.E. Joyce's web page at Clark University

colgate.edu (Global: low place; English: 9,382^nd place)

math.colgate.edu

Lantz, David (2008). "Garfield's proof of the Pythagorean Theorem". Colgate University Faculty Pages. Archived from the original on 28 August 2013. Retrieved 14 January 2018.

cut-the-knot.org (Global: low place; English: low place)

Bogomolny (2016), Proof #4. Bogomolny, Alexander (2016). "Pythagorean Theorem". Cut the Knot. Archived from the original on 6 October 2025. Retrieved 10 November 2025.
Bogomolny (2016), Proof #3. Bogomolny, Alexander (2016). "Pythagorean Theorem". Cut the Knot. Archived from the original on 6 October 2025. Retrieved 10 November 2025.
Bogomolny (2016), Proof #10. Bogomolny, Alexander (2016). "Pythagorean Theorem". Cut the Knot. Archived from the original on 6 October 2025. Retrieved 10 November 2025.
Bogomolny (2016), Proof #40 (by M. Hardy). Bogomolny, Alexander (2016). "Pythagorean Theorem". Cut the Knot. Archived from the original on 6 October 2025. Retrieved 10 November 2025.
Bogomolny, Alexander (2018). "Pythagorean Theorem for the Reciprocals". Cut the Knot. Archived from the original on 3 December 2024. Retrieved 10 November 2025.

doi.org (Global: 2^nd place; English: 2^nd place)

Friberg, Jöran (1981). "Methods and traditions of Babylonian mathematics: Plimpton 322, Pythagorean triples, and the Babylonian triangle parameter equations". Historia Mathematica. 8: 277–318. doi:10.1016/0315-0860(81)90069-0.: p. 306 "Although Plimpton 322 is a unique text of its kind, there are several other known texts testifying that the Pythagorean theorem was well known to the mathematicians of the Old Babylonian period."
Robson 2001. Robson, Eleanor (2001). "Neither Sherlock Holmes nor Babylon: a reassessment of Plimpton 322". Historia Mathematica. 28 (3): 167–206. doi:10.1006/hmat.2001.2317.
Mackinnon, Nick (March 1992). "Homage to Babylonia". The Mathematical Gazette. 76 (475): 158–178. doi:10.2307/3620389. JSTOR 3620389.
Fritz (1945), p. 252. von Fritz, Kurt (April 1945). "The Discovery of Incommensurability by Hippasus of Metapontum". Annals of Mathematics. Second Series. 46 (2): 242–264. doi:10.2307/1969021. JSTOR 1969021.
Staring, Mike (1996). "The Pythagorean proposition: A proof by means of calculus". Mathematics Magazine. 69 (1). Mathematical Association of America: 45–46. doi:10.2307/2691395. JSTOR 2691395.
Berndt, Bruce C. (1988). "Ramanujan – 100 years old (fashioned) or 100 years new (fangled)?". The Mathematical Intelligencer. 10 (3): 24–31. doi:10.1007/BF03026638. S2CID 123311054.
Fritz (1945). von Fritz, Kurt (April 1945). "The Discovery of Incommensurability by Hippasus of Metapontum". Annals of Mathematics. Second Series. 46 (2): 242–264. doi:10.2307/1969021. JSTOR 1969021.
WS Massey (December 1983). "Cross products of vectors in higher-dimensional Euclidean spaces" (PDF). The American Mathematical Monthly. 90 (10). Mathematical Association of America: 697–701. doi:10.2307/2323537. JSTOR 2323537. S2CID 43318100. Archived from the original (PDF) on 26 February 2021.
Sayili, Aydin (March 1960). "Thâbit ibn Qurra's Generalization of the Pythagorean Theorem". Isis. 51 (1): 35–37. doi:10.1086/348837. JSTOR 227603. S2CID 119868978.
Donald R Conant & William A Beyer (March 1974). "Generalized Pythagorean Theorem". The American Mathematical Monthly. 81 (3). Mathematical Association of America: 262–265. doi:10.2307/2319528. JSTOR 2319528.
Pambuccian, Victor (December 2010). "Maria Teresa Calapso's Hyperbolic Pythagorean Theorem". The Mathematical Intelligencer. 32 (4): 2. doi:10.1007/s00283-010-9169-0.

jstor.org (Global: 26^th place; English: 20^th place)

Mackinnon, Nick (March 1992). "Homage to Babylonia". The Mathematical Gazette. 76 (475): 158–178. doi:10.2307/3620389. JSTOR 3620389.
Fritz (1945), p. 252. von Fritz, Kurt (April 1945). "The Discovery of Incommensurability by Hippasus of Metapontum". Annals of Mathematics. Second Series. 46 (2): 242–264. doi:10.2307/1969021. JSTOR 1969021.
Staring, Mike (1996). "The Pythagorean proposition: A proof by means of calculus". Mathematics Magazine. 69 (1). Mathematical Association of America: 45–46. doi:10.2307/2691395. JSTOR 2691395.
Fritz (1945). von Fritz, Kurt (April 1945). "The Discovery of Incommensurability by Hippasus of Metapontum". Annals of Mathematics. Second Series. 46 (2): 242–264. doi:10.2307/1969021. JSTOR 1969021.
WS Massey (December 1983). "Cross products of vectors in higher-dimensional Euclidean spaces" (PDF). The American Mathematical Monthly. 90 (10). Mathematical Association of America: 697–701. doi:10.2307/2323537. JSTOR 2323537. S2CID 43318100. Archived from the original (PDF) on 26 February 2021.
Sayili, Aydin (March 1960). "Thâbit ibn Qurra's Generalization of the Pythagorean Theorem". Isis. 51 (1): 35–37. doi:10.1086/348837. JSTOR 227603. S2CID 119868978.
Donald R Conant & William A Beyer (March 1974). "Generalized Pythagorean Theorem". The American Mathematical Monthly. 81 (3). Mathematical Association of America: 262–265. doi:10.2307/2319528. JSTOR 2319528.

maa.org (Global: 3,479^th place; English: 2,444^th place)

Published in a weekly mathematics column: Garfield, James A. (1876). "Pons Asinorum". The New England Journal of Education. 3 (14): 161; as noted in Dunham, William (1997). The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems, and Personalities. Wiley. p. 96. ISBN 0-471-17661-3.

ox.ac.uk (Global: 613^th place; English: 456^th place)

ora.ox.ac.uk

Robson 2001. Robson, Eleanor (2001). "Neither Sherlock Holmes nor Babylon: a reassessment of Plimpton 322". Historia Mathematica. 28 (3): 167–206. doi:10.1006/hmat.2001.2317.

researchgate.net (Global: 120^th place; English: 125^th place)

Friberg, Jöran (1981). "Methods and traditions of Babylonian mathematics: Plimpton 322, Pythagorean triples, and the Babylonian triangle parameter equations". Historia Mathematica. 8: 277–318. doi:10.1016/0315-0860(81)90069-0.: p. 306 "Although Plimpton 322 is a unique text of its kind, there are several other known texts testifying that the Pythagorean theorem was well known to the mathematicians of the Old Babylonian period."

ruc.dk (Global: low place; English: low place)

akira.ruc.dk

Høyrup, Jens (1999). "Pythagorean 'Rule' and 'Theorem' – Mirror of the Relation Between Babylonian and Greek Mathematics". In Renger, Johannes (ed.). Babylon: Focus mesopotamischer Geschichte, Wiege früher Gelehrsamkeit, Mythos in der Moderne. 2. Internationales Colloquium der Deutschen Orient-Gesellschaft 24.–26. März 1998 in Berlin (PDF). Berlin: Deutsche Orient-Gesellschaft / Saarbrücken: SDV Saarbrücker Druckerei und Verlag. pp. 393–407., p. 406, "To judge from this evidence alone it is therefore likely that the Pythagorean rule was discovered within the lay surveyors' environment, possibly as a spin-off from the problem treated in Db₂-146, somewhere between 2300 and 1825 BC." (Db₂-146 is an Old Babylonian clay tablet from Eshnunna concerning the computation of the sides of a rectangle given its area and diagonal.)

semanticscholar.org (Global: 11^th place; English: 8^th place)

api.semanticscholar.org

Berndt, Bruce C. (1988). "Ramanujan – 100 years old (fashioned) or 100 years new (fangled)?". The Mathematical Intelligencer. 10 (3): 24–31. doi:10.1007/BF03026638. S2CID 123311054.
WS Massey (December 1983). "Cross products of vectors in higher-dimensional Euclidean spaces" (PDF). The American Mathematical Monthly. 90 (10). Mathematical Association of America: 697–701. doi:10.2307/2323537. JSTOR 2323537. S2CID 43318100. Archived from the original (PDF) on 26 February 2021.
Sayili, Aydin (March 1960). "Thâbit ibn Qurra's Generalization of the Pythagorean Theorem". Isis. 51 (1): 35–37. doi:10.1086/348837. JSTOR 227603. S2CID 119868978.

pdfs.semanticscholar.org

WS Massey (December 1983). "Cross products of vectors in higher-dimensional Euclidean spaces" (PDF). The American Mathematical Monthly. 90 (10). Mathematical Association of America: 697–701. doi:10.2307/2323537. JSTOR 2323537. S2CID 43318100. Archived from the original (PDF) on 26 February 2021.

slu.edu (Global: low place; English: 7,846^th place)

See for example Pythagorean theorem by shear mapping Archived 2016-10-14 at the Wayback Machine, Saint Louis University website Java applet

stanford.edu (Global: 179^th place; English: 183^rd place)

plato.stanford.edu

Huffman, Carl (23 February 2005). "Pythagoras". In Zalta, Edward N. (ed.). The Stanford Encyclopedia of Philosophy (Winter 2018 Edition) (Winter 2018 ed.). It should now be clear that decisions about sources are crucial in addressing the question of whether Pythagoras was a mathematician and scientist. The view of Pythagoras's cosmos sketched in the first five paragraphs of this section, according to which he was neither a mathematician nor a scientist, remains the consensus.

utexas.edu (Global: 916^th place; English: 706^th place)

farside.ph.utexas.edu

Heiberg, J. L. "Euclid's Elements of Geometry" (PDF). pp. 46–47.

cs.utexas.edu

Dijkstra, Edsger W. (7 September 1986). "On the theorem of Pythagoras". EWD975. E. W. Dijkstra Archive.

web.archive.org (Global: 1^st place; English: 1^st place)

Bogomolny (2016), Proof #4. Bogomolny, Alexander (2016). "Pythagorean Theorem". Cut the Knot. Archived from the original on 6 October 2025. Retrieved 10 November 2025.
Bogomolny (2016), Proof #3. Bogomolny, Alexander (2016). "Pythagorean Theorem". Cut the Knot. Archived from the original on 6 October 2025. Retrieved 10 November 2025.
See for example Pythagorean theorem by shear mapping Archived 2016-10-14 at the Wayback Machine, Saint Louis University website Java applet
Bogomolny (2016), Proof #10. Bogomolny, Alexander (2016). "Pythagorean Theorem". Cut the Knot. Archived from the original on 6 October 2025. Retrieved 10 November 2025.
Lantz, David (2008). "Garfield's proof of the Pythagorean Theorem". Colgate University Faculty Pages. Archived from the original on 28 August 2013. Retrieved 14 January 2018.
Bogomolny (2016), Proof #40 (by M. Hardy). Bogomolny, Alexander (2016). "Pythagorean Theorem". Cut the Knot. Archived from the original on 6 October 2025. Retrieved 10 November 2025.
Bogomolny, Alexander (2018). "Pythagorean Theorem for the Reciprocals". Cut the Knot. Archived from the original on 3 December 2024. Retrieved 10 November 2025.
WS Massey (December 1983). "Cross products of vectors in higher-dimensional Euclidean spaces" (PDF). The American Mathematical Monthly. 90 (10). Mathematical Association of America: 697–701. doi:10.2307/2323537. JSTOR 2323537. S2CID 43318100. Archived from the original (PDF) on 26 February 2021.
For an extended discussion of this generalization, see, for example, Willie W. Wong Archived 2009-12-29 at the Wayback Machine 2002, A generalized n-dimensional Pythagorean theorem.

worldcat.org (Global: 5^th place; English: 5^th place)

search.worldcat.org

Neugebauer 1969, p. 36. Neugebauer, Otto (1969). The exact sciences in antiquity (2nd ed.). Courier Dover Publications. ISBN 0-486-22332-9. OCLC 638685764.
Neugebauer 1969: p. 36 "In other words it was known during the whole duration of Babylonian mathematics that the sum of the squares on the lengths of the sides of a right triangle equals the square of the length of the hypotenuse." Neugebauer, Otto (1969). The exact sciences in antiquity (2nd ed.). Courier Dover Publications. ISBN 0-486-22332-9. OCLC 638685764.

Pythagorean theorem (English Wikipedia)

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archive.org (Global: 6^th place; English: 6^th place)

arxiv.org (Global: 69^th place; English: 59^th place)

books.google.com (Global: 3^rd place; English: 3^rd place)

cam.ac.uk (Global: 670^th place; English: 480^th place)

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colgate.edu (Global: low place; English: 9,382^nd place)

doi.org (Global: 2^nd place; English: 2^nd place)

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ox.ac.uk (Global: 613^th place; English: 456^th place)

researchgate.net (Global: 120^th place; English: 125^th place)

semanticscholar.org (Global: 11^th place; English: 8^th place)

slu.edu (Global: low place; English: 7,846^th place)

stanford.edu (Global: 179^th place; English: 183^rd place)

utexas.edu (Global: 916^th place; English: 706^th place)

web.archive.org (Global: 1^st place; English: 1^st place)

worldcat.org (Global: 5^th place; English: 5^th place)