Teorema lui Pitagora (Romanian Wikipedia)
Analysis of information sources in references of the Wikipedia article "Teorema lui Pitagora" in Romanian language version.
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arxiv.org
- Otto Neugebauer (). The exact sciences in antiquity (ed. Republication of 1957 Brown University Press 2nd). Courier Dover Publications. p. 36. ISBN 0-486-22332-9.. For a different view, see Dick Teresi (). Lost Discoveries: The Ancient Roots of Modern Science. Simon and Schuster. p. 52. ISBN 0-7432-4379-X., where the speculation is made that the first column of tablet 322 in the Plimpton collection supports a Babylonian knowledge of some elements of trigonometry. That notion is pretty much laid to rest, however, by Eleanor Robson (). „Words and Pictures: New Light on Plimpton 322”. The American Mathematical Monthly. Mathematical Association of America. 109 (2): 105–120. doi:10.2307/2695324. JSTOR 2695324. (pdf file Arhivat în , la Wayback Machine.). The generally accepted view today is that the Babylonians had no awareness of trigonometric functions. See also Abdulrahman A. Abdulaziz (). „The Plimpton 322 Tablet and the Babylonian Method of Generating Pythagorean Triples”. arXiv:1004.0025
[math.HO]. §2, page 7.
books.google.com
- Judith D. Sally, Paul Sally (). „Chapter 3: Pythagorean triples”. Roots to research: a vertical development of mathematical problems. American Mathematical Society Bookstore. p. 63. ISBN 0-8218-4403-2.
- Posamentier, Alfred. The Pythagorean Theorem: The Story of Its Power and Beauty, p. 23 (Prometheus Books 2010).
- George Johnston Allman (). Greek Geometry from Thales to Euclid (ed. Reprinted by Kessinger Publishing LLC 2005). Hodges, Figgis, & Co. p. 26. ISBN 1-4326-0662-X.
The discovery of the law of three squares, commonly called the "theorem of Pythagoras" is attributed to him by – amongst others – Vitruvius, Diogenes Laertius, Proclus, and Plutarch ...
- (Heath 1921, Vol I, p. 144) Heath, Sir Thomas (). „The 'Theorem of Pythagoras'”. A History of Greek Mathematics (2 Vols.) (ed. Dover Publications, Inc. (1981)). Clarendon Press, Oxford. p. 144 ff. ISBN 0-486-24073-8.
- Otto Neugebauer (). The exact sciences in antiquity (ed. Republication of 1957 Brown University Press 2nd). Courier Dover Publications. p. 36. ISBN 0-486-22332-9.. For a different view, see Dick Teresi (). Lost Discoveries: The Ancient Roots of Modern Science. Simon and Schuster. p. 52. ISBN 0-7432-4379-X., where the speculation is made that the first column of tablet 322 in the Plimpton collection supports a Babylonian knowledge of some elements of trigonometry. That notion is pretty much laid to rest, however, by Eleanor Robson (). „Words and Pictures: New Light on Plimpton 322”. The American Mathematical Monthly. Mathematical Association of America. 109 (2): 105–120. doi:10.2307/2695324. JSTOR 2695324. (pdf file Arhivat în , la Wayback Machine.). The generally accepted view today is that the Babylonians had no awareness of trigonometric functions. See also Abdulrahman A. Abdulaziz (). „The Plimpton 322 Tablet and the Babylonian Method of Generating Pythagorean Triples”. arXiv:1004.0025 [math.HO]. §2, page 7.
- Mario Livio (). The golden ratio: the story of phi, the world's most astonishing number. Random House, Inc. p. 25. ISBN 0-7679-0816-3.
- Benson, Donald. The Moment of Proof : Mathematical Epiphanies, pp. 172–173 (Oxford University Press, 1999).
- Maor, Eli. The Pythagorean Theorem: A 4,000-year History, p. 61 (Princeton University Press, 2007).
- (Maor 2007, p. 39) page 39 Maor, Eli (). The Pythagorean Theorem: A 4,000-Year History. Princeton, New Jersey: Princeton University Press. ISBN 978-0-691-12526-8.
- Stephen W. Hawking (). God created the integers: the mathematical breakthroughs that changed history. Philadelphia: Running Press Book Publishers. p. 12. ISBN 0-7624-1922-9. Această demonstrație a apărut pentru prima dată după ce un program de computer a fost programat să verifice demonstrațiile euclidiene.
- Jan Gullberg (). Mathematics: from the birth of numbers. W. W. Norton & Company. p. 435. ISBN 0-393-04002-X.
- Demonstrația lui Pitagora a fost cel mai probabil nu una generală, din moment ce teoria proporțiilor a fost dezvoltată doar două secole după Pitagora; vezi și (Maor 2007, p. 25) pagina 25 Maor, Eli (). 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: James A Garfield (). The New England Journal of Education. 3: 161. Lipsește sau este vid:
|title=(ajutor) as noted in William Dunham (). The mathematical universe: An alphabetical journey through the great proofs, problems, and personalities. Wiley. p. 96. ISBN 0-471-17661-3. and in A calendar of mathematical dates: 1 aprilie 1876 Arhivat în , la Wayback Machine. by V. Frederick Rickey - Judith D. Sally, Paul Sally (). „Theorem 2.4 (Converse of the Pythagorean Theorem).”. Cited work. p. 62. ISBN 0-8218-4403-2.
- Ernest Julius Wilczynski, Herbert Ellsworth Slaught (). „Theorem 1 and Theorem 2”. Plane trigonometry and applications. Allyn and Bacon. p. 85.
- Law, Henry (). „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.
- Shaughan Lavine (). 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 James R. Choike (). „The pentagram and the discovery of an irrational number”. The College Mathematics Journal. 11: 312–316. Heath, Sir Thomas (). „The 'Theorem of Pythagoras'”. A History of Greek Mathematics (2 Vols.) (ed. Dover Publications, Inc. (1981)). Clarendon Press, Oxford. p. 144 ff. ISBN 0-486-24073-8.
- Jon Orwant, Jarkko Hietaniemi, John Macdonald (). „Euclidean distance”. Mastering algorithms with Perl. O'Reilly Media, Inc. p. 426. ISBN 1-56592-398-7.
- Wentworth, George (). Plane Trigonometry and Tables. BiblioBazaar, LLC. p. 116. ISBN 1-103-07998-0., Exerciții, pagina 116
- Lawrence S. Leff (). PreCalculus the Easy Way (ed. 7th). Barron's Educational Series. p. 296. ISBN 0-7641-2892-2.
- Pertti Lounesto (). „§7.4 Cross product of two vectors”. Clifford algebras and spinors (ed. 2nd). Cambridge University Press. p. 96. ISBN 0-521-00551-5.[nefuncțională]
- Francis Begnaud Hildebrand (). Methods of applied mathematics (ed. Reprint of Prentice-Hall 1965 2nd). Courier Dover Publications. p. 24. ISBN 0-486-67002-3.
- Howard Whitley Eves (). „§4.8:...generalization of Pythagorean theorem”. Great moments in mathematics (before 1650). Mathematical Association of America. p. 41. ISBN 0-88385-310-8.
- Judith D. Sally, Paul Sally (). „Exercise 2.10 (ii)”. Roots to Research: A Vertical Development of Mathematical Problems. p. 62. ISBN 0-8218-4403-2.
- Lawrence S. Leff (). cited work. Barron's Educational Series. p. 326. ISBN 0-7641-2892-2.
- Rajendra Bhatia (). Matrix analysis. Springer. p. 21. ISBN 0-387-94846-5.
- Ferdinand van der Heijden, Dick de Ridder (). Classification, parameter estimation, and state estimation. Wiley. p. 357. ISBN 0-470-09013-8.
- Qun Lin, Jiafu Lin (). Finite element methods: accuracy and improvement. Elsevier. p. 23. ISBN 7-03-016656-6.
- Howard Anton, Chris Rorres (). Elementary Linear Algebra: Applications Version (ed. 10th). Wiley. p. 336. ISBN 0-470-43205-5.
- Karen Saxe (). „Theorem 1.2”. Beginning functional analysis. Springer. p. 7. ISBN 0-387-95224-1.
- Douglas, Ronald G. (). Banach Algebra Techniques in Operator Theory, 2nd edition. New York, New York: Springer-Verlag New York, Inc. pp. 60–1. ISBN 978-0-387-98377-6.
- Stephen W. Hawking (). cited work. p. 4. ISBN 0-7624-1922-9.
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Eric W. Weisstein (). CRC concise encyclopedia of mathematics (ed. 2nd). p. 2147. ISBN 1-58488-347-2.
The parallel postulate is equivalent to the Equidistance postulate, Playfair axiom, Proclus axiom, the Triangle postulate and the Pythagorean theorem.
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Alexander R. Pruss (). 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.
- Barrett O'Neill (). „Exercise 4”. Elementary differential geometry (ed. 2nd). Academic Press. p. 441. ISBN 0-12-088735-5.
- Saul Stahl (). „Theorem 8.3”. The Poincaré half-plane: a gateway to modern geometry. Jones & Bartlett Learning. p. 122. ISBN 0-86720-298-X.
- Jane Gilman (). „Hyperbolic triangles”. Two-generator discrete subgroups of PSL(2,R). American Mathematical Society Bookstore. ISBN 0-8218-0361-1.
- Tai L. Chow (). Mathematical methods for physicists: a concise introduction. Cambridge University Press. p. 52. ISBN 0-521-65544-7.[nefuncțională]
- Maor (2007), p. 47. Maor, Eli (). The Pythagorean Theorem: A 4,000-Year History. Princeton, New Jersey: Princeton University Press. ISBN 978-0-691-12526-8.
cam.ac.uk
dpmms.cam.ac.uk
- Pentru o discuție extinsă referitoare la această generalizare, vezi, de exemplu, Willie W. Wong Arhivat în , la Wayback Machine. 2002, A generalized n-dimensional Pythagorean theorem (engleză).
clarku.edu
aleph0.clarku.edu
- Euclid's Elements, Book I, Proposition 47: web page version using Java applets from Euclid's Elements de Prof. David E. Joyce, Clark University
- Euclid's Elements, Book I, Proposition 48 De la D.E. Joyce's web page la Clark University
cut-the-knot.org
- Alexander Bogomolny. „Pythagorean Theorem, proof number 10”. Cut the Knot. Accesat în .
- Alexander Bogomolny. „Cut-the-knot.org: Pythagorean theorem and its many proofs, Proof #3”. Cut the Knot. Accesat în .
- Alexander Bogomolny. „Cut-the-knot.org: Pythagorean theorem and its many proofs, Proof #4”. Cut the Knot. Accesat în .
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Bogomolny, Alexander. „Pythagorean Theorem”. Interactive Mathematics Miscellany and Puzzles. Alexander Bogomolny. Accesat în . Legătură externa în
|work=(ajutor)
doi.org
- Otto Neugebauer (). The exact sciences in antiquity (ed. Republication of 1957 Brown University Press 2nd). Courier Dover Publications. p. 36. ISBN 0-486-22332-9.. For a different view, see Dick Teresi (). Lost Discoveries: The Ancient Roots of Modern Science. Simon and Schuster. p. 52. ISBN 0-7432-4379-X., where the speculation is made that the first column of tablet 322 in the Plimpton collection supports a Babylonian knowledge of some elements of trigonometry. That notion is pretty much laid to rest, however, by Eleanor Robson (). „Words and Pictures: New Light on Plimpton 322”. The American Mathematical Monthly. Mathematical Association of America. 109 (2): 105–120. doi:10.2307/2695324. JSTOR 2695324. (pdf file Arhivat în , la Wayback Machine.). The generally accepted view today is that the Babylonians had no awareness of trigonometric functions. See also Abdulrahman A. Abdulaziz (). „The Plimpton 322 Tablet and the Babylonian Method of Generating Pythagorean Triples”. arXiv:1004.0025 [math.HO]. §2, page 7.
- Mike Staring (). „The Pythagorean proposition: A proof by means of calculus”. Mathematics Magazine. Mathematical Association of America. 69 (1): 45–46. doi:10.2307/2691395. JSTOR 2691395.
- Bruce C. Berndt (). „Ramanujan—100 years old (fashioned) or 100 years new (fangled)?”. The Mathematical Intelligencer. 10 (3): 24. doi:10.1007/BF03026638.
- WS Massey (). „Cross products of vectors in higher-dimensional Euclidean spaces”. The American Mathematical Monthly. Mathematical Association of America. 90 (10): 697–701. doi:10.2307/2323537. JSTOR 2323537.
- Aydin Sayili (). „Thâbit ibn Qurra's Generalization of the Pythagorean Theorem”. Isis. 51 (1): 35–37. doi:10.1086/348837. JSTOR 227603.
- Victor Pambuccian (decembrie 2010). „Maria Teresa Calapso's Hyperbolic Pythagorean Theorem”. The Mathematical Intelligencer. 32 (4): 2. doi:10.1007/s00283-010-9169-0.
ed.gov
eric.ed.gov
- (Loomis 1968) Loomis, Elisha Scott (). The Pythagorean proposition (ed. 2nd). The National Council of Teachers of Mathematics. ISBN 978-0-87353-036-1. For full text of 2nd edition of 1940, see Elisha Scott Loomis. „The Pythagorean proposition: its demonstrations analyzed and classified, and bibliography of sources for data of the four kinds of proofs” (PDF). Education Resources Information Center. Institute of Education Sciences (IES) of the U.S. Department of Education. Accesat în . Originally published in 1940 and reprinted in 1968 by National Council of Teachers of Mathematics, isbn=0-87353-036-5.
- (Loomis 1968, Geometric proof 22 and Figure 123, page= 113) Loomis, Elisha Scott (). The Pythagorean proposition (ed. 2nd). The National Council of Teachers of Mathematics. ISBN 978-0-87353-036-1. For full text of 2nd edition of 1940, see Elisha Scott Loomis. „The Pythagorean proposition: its demonstrations analyzed and classified, and bibliography of sources for data of the four kinds of proofs” (PDF). Education Resources Information Center. Institute of Education Sciences (IES) of the U.S. Department of Education. Accesat în . Originally published in 1940 and reprinted in 1968 by National Council of Teachers of Mathematics, isbn=0-87353-036-5.
imdb.com
- „The Scarecrow's Formula”. Internet Movie Data Base. Accesat în .
jstor.org
- Otto Neugebauer (). The exact sciences in antiquity (ed. Republication of 1957 Brown University Press 2nd). Courier Dover Publications. p. 36. ISBN 0-486-22332-9.. For a different view, see Dick Teresi (). Lost Discoveries: The Ancient Roots of Modern Science. Simon and Schuster. p. 52. ISBN 0-7432-4379-X., where the speculation is made that the first column of tablet 322 in the Plimpton collection supports a Babylonian knowledge of some elements of trigonometry. That notion is pretty much laid to rest, however, by Eleanor Robson (). „Words and Pictures: New Light on Plimpton 322”. The American Mathematical Monthly. Mathematical Association of America. 109 (2): 105–120. doi:10.2307/2695324. JSTOR 2695324. (pdf file Arhivat în , la Wayback Machine.). The generally accepted view today is that the Babylonians had no awareness of trigonometric functions. See also Abdulrahman A. Abdulaziz (). „The Plimpton 322 Tablet and the Babylonian Method of Generating Pythagorean Triples”. arXiv:1004.0025 [math.HO]. §2, page 7.
- Mike Staring (). „The Pythagorean proposition: A proof by means of calculus”. Mathematics Magazine. Mathematical Association of America. 69 (1): 45–46. doi:10.2307/2691395. JSTOR 2691395.
- O discuție detaliată despre contribuțiile lui Hippasos se găsesc în Kurt Von Fritz (). „The Discovery of Incommensurability by Hippasus of Metapontum”. Annals of Mathematics. Second Series. Annals of Mathematics. 46 (2): 242–264. JSTOR 1969021.
- WS Massey (). „Cross products of vectors in higher-dimensional Euclidean spaces”. The American Mathematical Monthly. Mathematical Association of America. 90 (10): 697–701. doi:10.2307/2323537. JSTOR 2323537.
- Aydin Sayili (). „Thâbit ibn Qurra's Generalization of the Pythagorean Theorem”. Isis. 51 (1): 35–37. doi:10.1086/348837. JSTOR 227603.
ngccoin.com
- „Uganda 2000 Shillings”. Numismatic Guaranty Corporation. Accesat în .
recreatiimatematice.ro
- Crâșmăreanu, Mircea. „Câteva probleme privind triplete pitagoreice” (pdf). Accesat în 13 martie. Parametru necunoscut
|anaccesare=ignorat (ajutor); Verificați datele pentru:|access-date=(ajutor)
slu.edu
- De exemplu, vezi Teorema lui Pitagora Arhivat în , la Wayback Machine., Saint Louis University website Java applet
tripod.com
jeff560.tripod.com
- Miller, Jeff (). „Images of Mathematicians on Postage Stamps”. Accesat în .
ulpgc.es
dma.ulpgc.es
- Otto Neugebauer (). The exact sciences in antiquity (ed. Republication of 1957 Brown University Press 2nd). Courier Dover Publications. p. 36. ISBN 0-486-22332-9.. For a different view, see Dick Teresi (). Lost Discoveries: The Ancient Roots of Modern Science. Simon and Schuster. p. 52. ISBN 0-7432-4379-X., where the speculation is made that the first column of tablet 322 in the Plimpton collection supports a Babylonian knowledge of some elements of trigonometry. That notion is pretty much laid to rest, however, by Eleanor Robson (). „Words and Pictures: New Light on Plimpton 322”. The American Mathematical Monthly. Mathematical Association of America. 109 (2): 105–120. doi:10.2307/2695324. JSTOR 2695324. (pdf file Arhivat în , la Wayback Machine.). The generally accepted view today is that the Babylonians had no awareness of trigonometric functions. See also Abdulrahman A. Abdulaziz (). „The Plimpton 322 Tablet and the Babylonian Method of Generating Pythagorean Triples”. arXiv:1004.0025 [math.HO]. §2, page 7.
usma.edu
math.usma.edu
- Published in a weekly mathematics column: James A Garfield (). The New England Journal of Education. 3: 161. Lipsește sau este vid:
|title=(ajutor) as noted in William Dunham (). The mathematical universe: An alphabetical journey through the great proofs, problems, and personalities. Wiley. p. 96. ISBN 0-471-17661-3. and in A calendar of mathematical dates: 1 aprilie 1876 Arhivat în , la Wayback Machine. by V. Frederick Rickey
visithcandersen.dk
- H.C. Andersen: Formens evige Magie (1831), visithcandersen.dk
web.archive.org
- Otto Neugebauer (). The exact sciences in antiquity (ed. Republication of 1957 Brown University Press 2nd). Courier Dover Publications. p. 36. ISBN 0-486-22332-9.. For a different view, see Dick Teresi (). Lost Discoveries: The Ancient Roots of Modern Science. Simon and Schuster. p. 52. ISBN 0-7432-4379-X., where the speculation is made that the first column of tablet 322 in the Plimpton collection supports a Babylonian knowledge of some elements of trigonometry. That notion is pretty much laid to rest, however, by Eleanor Robson (). „Words and Pictures: New Light on Plimpton 322”. The American Mathematical Monthly. Mathematical Association of America. 109 (2): 105–120. doi:10.2307/2695324. JSTOR 2695324. (pdf file Arhivat în , la Wayback Machine.). The generally accepted view today is that the Babylonians had no awareness of trigonometric functions. See also Abdulrahman A. Abdulaziz (). „The Plimpton 322 Tablet and the Babylonian Method of Generating Pythagorean Triples”. arXiv:1004.0025 [math.HO]. §2, page 7.
- „Megalithic triangles”. Arhivat din original la . Accesat în .
- De exemplu, vezi Teorema lui Pitagora Arhivat în , la Wayback Machine., Saint Louis University website Java applet
- Published in a weekly mathematics column: James A Garfield (). The New England Journal of Education. 3: 161. Lipsește sau este vid:
|title=(ajutor) as noted in William Dunham (). The mathematical universe: An alphabetical journey through the great proofs, problems, and personalities. Wiley. p. 96. ISBN 0-471-17661-3. and in A calendar of mathematical dates: 1 aprilie 1876 Arhivat în , la Wayback Machine. by V. Frederick Rickey - Pentru o discuție extinsă referitoare la această generalizare, vezi, de exemplu, Willie W. Wong Arhivat în , la Wayback Machine. 2002, A generalized n-dimensional Pythagorean theorem (engleză).
- „Le Saviez-vous?”. Arhivat din original la . Accesat în .