21. Theorem Of Pythagoras http://webpages.dcu.ie/~clancym/MS120/LectureNotes/File1/MS120pg02.html

22. Theorem Of Pythagoras http://webpages.dcu.ie/~clancym/MS120/LectureNotes/File1/MS120pg01.html

23. Theorem Of Pythagoras Translate this page Cuando llegues al último paso, pulsa reset para volver a empezar.Un Applet relacionado con este está en Pythagoras java applet. http://www.edu.aytolacoruna.es/aula/fisica/applets/Hwang/ntnujava/abc/Pythagoras

a + b =c Puedes variar la rapidez de cambio dando valores a Incremento de t (medido en segundos, valor por defecto=2 s) reset para volver a empezar. Pythagoras java applet hwang@phy03.phy.ntnu.edu.tw Autor: Fu-Kwun Hwang Dept. of physics National Taiwan Normal University

24. Www.digitalbrain.com The theorem of pythagoras, The theorem of pythagoras is possibly the one pieceof geometry that many people remember after school well, more. http://www.digitalbrain.com/digitalbrain/web/subjects/2. secondary/ks3mat/su4/mo

25. Template theorem of pythagoras a 2 + b 2 = c 2 This step) How ancient Chinesepeople discovers the same theorem. (much earlier than Pythagoras). http://www.phys.hawaii.edu/~teb/java/ntnujava/abc/Pythagoras.html

Theorem of Pythagoras a + b = c This java applet shows you (automatically - step by step) How ancient Chinese people discovers the same theorem. (much earlier than Pythagoras). You can change the interval delta T (in second, default value = 2 second). Click mouse button for manual control mode : Click right mouse button : show the following step Click left mouse button : show the previous step When you reach the last step, Press reset button to restart related Pythagoras java applet Your suggestions are highly appreciated! Please click hwang@phy03.phy.ntnu.edu.tw Author¡G Fu-Kwun Hwang Dept. of physics National Taiwan Normal University Last modified :¡@

26. 1300 A.C.: Theorem Of Pythagoras 1300 BC. THE theorem of pythagoras. In the tablet, of which the translationis reported, it seems really that the theorem of pythagoras is applied. http://www.maat.it/livello2-i/susa-pitagora-i.htm

HISTORY PHILOSOPHY RELIGION SCIENCE ... ITALIAN VERSION 1300 B.C. THE THEOREM OF PYTHAGORAS In the tablet, of which the translation is reported, it seems really that the theorem of Pythagoras is applied. In fact the calculation of the sides of a rectangle is exactly performed beginning from the knowledge of the diagonal (0,6666) and of the relationship existing between the width (W) and the length (L): W=L-L/4. Place: Susa (Mesopotamia) Epoch: 1300 b.C. - End of the I Dynasty of Babylon Tablet of Susa Problem We set that: - the width (of the rectangle) measures a quarter less in relationship to the length. Width = Length - Length/4 - the dimension of the diagonal is 0,6666. Diagonal = 0,6666 Which are the length and the width of the rectangle? Solution Set 1, the length, set 1 the prolongation. Arbitrary length = 1 0,25, the quarter, subtract from 1, you find 0,75. Arbitrary width = 1 - 0,25 = 0,75 Set 1 as length, set 0,75 as width, square 1, the length, you find 1. Square 0,75, the width, you find 0,5625.

27. BrochureWeb 18 THE theorem of pythagoras, DIRECTOR, AWARDS, Tom M. Apostol, GoldApple, 1989 National Educational Film and Video Festival, Oakland http://www-sfb288.math.tu-berlin.de/VideoMath/VideoMathReel/page19.html

18 T HE T HEOREM OF P YTHAGORAS D IRECTOR A WARDS Tom M. Apostol Gold Apple, 1989 National Educational Film and Video Festival, Oakland; Gold Medal, 1988 International Film and TV Festival of New York C ONTRIBUTORS Computer Animation - James F. Blinn Associate Producer - Joe Corrigan Narrator - Al Hibbs F URTHER I NFORMATION www.projmath.caltech.edu P RODUCER C ONTACT Tom M. Apostol Tom M. Apostol Project MATHEMATICS! 305 South Hill Avenue Pasadena, CA 91106, USA Tel: +1.626.395.3759 Fax: +1.626.395.3763 apostol@caltech.edu S UMMARY Several engaging animated proofs of the Pythagorean theorem are presented, with applications to real-life problems and to Pythagorean triples. The theorem is extended to 3-space, but does not hold for spherical triangles.

28. AV #83237 - Video Cassette - The Theorem Of Pythagoras AV 83237 The theorem of pythagoras. Video Cassette 22 minutes -Color - 1988. Problems from real life are used to introduce the http://www.sfsu.edu/~avitv/avcatalog/83237.htm

AV# 83237 The Theorem of Pythagoras Video Cassette - 22 minutes - Color - 1988 Problems from real life are used to introduce the mathematical problem solved by the Greek mathematician Pythagoras - how to use the known lengths of two sides of a right triangle to determine the length of the third side. Pythagorean triples, the Chinese proof, the Euclidean proof and the Pythagorean theorem in three dimensions are also explained. Access Policy for this Title Search AV Library Titles for: Last modified on January 29, 2003 by av@sfsu.edu

29. Pythagorean Theorem -- From MathWorld Dixon, R. The theorem of pythagoras. §4.1 in Mathographics. New York Dover,pp. 9295, 1991. Project Mathematics. The theorem of pythagoras. Videotape. http://mathworld.wolfram.com/PythagoreanTheorem.html

Geometry Plane Geometry Triangles Triangle Properties Pythagorean Theorem For a right triangle with legs a and b and hypotenuse c Many different proofs exist for this most fundamental of all geometric theorems. The theorem can also be generalized from a plane triangle to a trirectangular tetrahedron , in which case it is known as de Gua's theorem . The various proofs of the Pythagorean theorem all seem to require application of some version or consequence of the parallel postulate : proofs by dissection rely on the complementarity of the acute angles of the right triangle, proofs by shearing rely on explicit constructions of parallelograms, proofs by similarity require the existence of non-congruent similar triangles, and so on (S. Brodie). Based on this observation, S. Brodie has shown that the parallel postulate is equivalent to the Pythagorean theorem. A clever proof by dissection which reassembles two small squares into one larger one was given by the Arabian mathematician Thabit ibn Kurrah (Ogilvy 1994, Frederickson 1997). Another proof by dissection is due to Perigal (left figure; Pergial 1873; Dudeney 1970; Madachy 1979; Steinhaus 1999, pp. 4-5; Ball and Coxeter 1987). A related proof is accomplished using the above figure at right, in which the

30. The Theorem Of Pythagoras Pythagoras (fl. 500 BCE). The theorem of pythagoras is one of the earliest andmost important results in the history of mathematics. theorem of pythagoras. http://www.stats.uwaterloo.ca/~rwoldford/pythagoras.html

Pythagoras (fl. 500 BCE) The theorem of Pythagoras is one of the earliest and most important results in the history of mathematics. It has immense practical value and led to the discovery of irrational numbers - a right triangle with unit sides leads via Pythagoras to the square root of 2! For further history: St. Andrews' history of Mathematics site Theorem of Pythagoras Given any right angle triangle, if one forms a square on each side of that triangle then the area of the largest square (that of the hypoteneuse) is equal to the sum of the areas of the two smaller squares (those which are formed on the sides about the right or 90 degree angle). Proof of the theorem is demonstrated through the following Quicktime animation. Use the controls to animate the movie. Notes on the demonstration: Textual details of the proof are intentionally absent from the movie. This encourages the student to work through why this is in fact a proof and how they might produce a formal proof based on the demonstration. Alternatively an instructor might like to fill in these details before/during/after the demonstration.

31. The Theorem Of Pythagoras. The theorem of pythagoras. Theorem 14.2.1. Remark 14.2.2 The ndimensional theoremof Pythagoras If are such that (ie ), then . Noah Dana-Picard 2001-02-26. http://sukka.jct.ac.il/~math/tutorials/alg-tut/node55.html

Next: Various examples of the Up: Some more geometry. Previous: The triangle inequality. The theorem of Pythagoras. Theorem 14.2.1 Remark 14.2.2 The n -dimensional theorem of Pythagoras: If are such that (i.e. ), then Noah Dana-Picard

32. The Garden Of Archimedes: Pythagoras The theorem of pythagoras can also be enunciated in a different form the sum ofthe squares of the base and the altitude of a rectangle is equal to the square http://www.math.unifi.it/archimede/archimede_inglese/pitagora/exh_pitagora/sched

The Garden of Archimedes A Museum for Mathematics Pythagoras and his theorem Parallelograms and trapeziums rectangles parallelograms trapeziums right angled trapezium The theorem of Pythagoras can also be enunciated in a different form: the sum of the squares of the base and the altitude of a rectangle is equal to the square of the diagonal . In fact, the diagonal of a rectangle is the hypotenuse of the right-angled triangle having as cathets the base and the altitude. If we then take each square twice, we'll have that: the sum of the squares on the sides of a rectangle is equal to the sum of the squares on the diagonals The same result is also valid for the non right-angled parallelogram. Take the parallelogram ABCD. When the theorem of Pythagoras is applied to the right-angled triangle BED, the square of diagonal BD is equal to the sum of the squares of ED and BE, which are coloured in green and yellow. Similarly, the square of the diagonal AC is equal to the red square plus the multicolored one. The sum of the areas of the squares of the diagonals is then equal to the one of the areas of the four squares drawn in the first figure. The second figure is obtained from the first by moving some parts without altering the overall area, and therefore the sum of the areas of the four squares of the first figure (which was equal to the sum of the squares of the diagonals) is equal to the one of the six squares of the second figure. On the other hand, again with the theorem of Pythagoras, the two green squares are equal to the square of the AB, and the two red ones to the square of side AC, and thus the sum of the areas of the six squares is equal to that one of the squares of the sides. We can conclude by saying that:

33. The Garden Of Archimedes: Pythagoras In the enunciation of the theorem of pythagoras, the squares can be replaced byother figures, like for example triangles, hexagons or even irregular figures http://www.math.unifi.it/archimede/archimede_inglese/pitagora/exh_pitagora/sched

The Garden of Archimedes A Museum for Mathematics Pythagoras and his Theorem Similar figures . Similar figures stars and Pythagoras another demonstration lunes In the enunciation of the theorem of Pythagoras, the squares can be replaced by other figures, like for example triangles, hexagons or even irregular figures, as long as they are similar among themselves. Similar figures are the ones that differ only in quantity, but not in shape. In other words, two similar figures are those where one is the enlargement of the other. For example, two five pointed stars are similar, while a five pointed star is not similar to a four pointed star. Arguing from analogy, two triangles in which the sides of one are twice the sides of the other are similar, while the ones in the figure are not, because in this case the enlargement is done in only one direction. Note that all squares are similar, like all circles and all regular polygons with the same number of sides. A property of similar figures that explains why they can replace the squares in the theorem of Pythagoras, is that their areas are proportional to the squares of the corresponding segments. For example, in the case of five pointed stars, the area is proportional to the square of the distance between two consecutive points; in formulas A = kL (Naturally, side l of the star could have been taken instead of the distance between the two points; in this case it would be A =hl

34. Geometry Lesson 11 Instruction, Page 1 Instruction 111. The theorem of pythagoras Converse Special Right Triangles Distance Calculations Summary. THE theorem of pythagoras. Student's Links. http://www.etap.org/mathfiles/english/geometry/geo11/instruction1.html

Geometry Lesson 11 Pythagorean Theorem and Its Use (High School) Instruction 11-1 Converse Special Right Triangles Distance Calculations Summary THE THEOREM OF PYTHAGORAS Student's Links http://regentsprep.org/Regents/math/fpyth/PracPyth.htm (Interactive Worksheet) http://www.cut-the-knot.com/pythagoras/ (Proofs) http://www.frontiernet.net/~imaging/pythagorean.html (Interactive Explanation) http://library.thinkquest.org/20991/geo/stri.html#pythagoras (Explanation) Parents' Links http://www.purplemath.com/modules/geoform.htm (Explanation) http://etap.org/mathfiles/english/grade7/hspm9/hspm9ins5.html (Detailed Explanation with Examples) http://pc65.frontier.osrhe.edu/hs/Math/GEO/conjectures.htm#ch10 (Study C-88) Teachers' Links http://regentsprep.org/Regents/math/fpyth/TActive.htm (Lesson Ideas) http://www.mste.uiuc.edu/mathed/HumanResources/mccully/pythagoras.html (Lesson Plan) Now let's do Practice Exercise 11-1 top Next Page: Converse top

35. Theorem Of Pythagoras Translate this page Teorema de Pitágoras a 2 + b 2 = c 2. Este applet java mostra a você (automaticamente- passo a passo) Como o povo Chinês antigo descobriu o mesmo teorema. http://www.cepa.if.usp.br/fkw/abc/Pythagoras.html

Teorema de Pitágoras a + b = c Este applet java mostra a você (automaticamente - passo a passo) Como o povo Chinês antigo descobriu o mesmo teorema. (muito antes de Pitágoras). Você pode mudar o intervalo delta T (em segundos, valor original = 2 segundos). Clique no botão do mouse para obter o modo de controle manual: Clique no botão esquerdo: mostra o passo seguinte Clique no botão direito: mostra o passo anterior Quando você atingir o último passo, pressione o botão reiniciar para recomeçar applets java relacionados a Pitágoras Suas sugestões serão muito apreciadas! Por favor clique hwang@phy03.phy.ntnu.edu.tw Autor Fu-Kwun Hwang Dept. of physics National Taiwan Normal University Última modificação:

36. Caltech Bookstore And Caltech Wired Department Mixed Media Section Project Math Product(s) 014491 TheoremOf Pythagoras Video, $29.95. 014492 theorem of pythagoras Workbook, $4.95. http://bookstore2.caltech.edu/WM_VCAT.HTM?CMD=999*005*002*000

37. New Page 4 Pythagoras Systems Ltd The theorem of pythagoras is proved here, although themain business of Pythagoras SystemsLtd is to design and build websites for http://users.skynet.be/bk381647/linkpyth.html

Website met verschillende bewijzen i.v.m. de stelling van Pythagoras Andere website met verschillende bewijzen, van Alexander Bogomolny Interactieve bewijzen van de stelling van Pythagoras Pythagoras op math.be ... Pythagoras - Pythagoras of Samos Born: about 569 BC in Samos, Ionia Died: about 475...Description: Biography of Pythagoras (569BC475)with a good introduction to his beliefs and philosophyCategory: Society Philosophy Philosophers Pythagoras of Samos... Pythagoras and the Pythagoreans - Passages from Plato, Aristotle and the Doxographists referring to Pythagoras and the Pythagoreans.... Pythagoras (Internet Encyclopedia of Philosophy) - Pythagoras (fl. 530 BCE.) Pythagoras (fl. 530 BCE) must have been one of the world's greatest men, but he wrote nothing, and it is hard to say how much of the doctrine we know as Pythagorean is due to the founder of the society and how much is later development.... The School of Pythagoras - and proportion. The work of Pythagoras provides a starting point for..1998 Original version of School of Pythagoras Home page of...... Pythagoras - Pythagoras Norrtelje Photo by Peter Larsson · For information call +46 (0)176-100 50...

38. Pythagoras And The Pythagoreans http://members.tripod.co.uk/james/

39. Mexico.digitalbrain.com The theorem of pythagoras, The theorem of pythagoras is possibly the one pieceof geometry that many people remember after school well, más. http://mexico.digitalbrain.com/digitalbrain/web/subjects/2. secondary/ks3mat/su4

40. Trekantsberegning På WWW theorem of pythagoras Interaktiv figur viser hvordan kineserne opdagede Pythagoras'sætning længe før Pythagoras. A Simple Proof of Pythagoras' Theorem. http://www.mat.suite.dk/WGeom.htm

Trekantsberegning Ensvinklede trekanter Retvinklede trekanter Enhedscirklen Interaktive opgaver. Der kan vælges mellem mange opgavetyper. Fx kan vælges opgaver om retvinklede trekanter som ikke hedder ABC. Fra Interaktive opgaver, Forlaget Basis, Næstved Trigonometriske opgaver Interaktive opgaver. Retvinklet og vilkårlig trekant. "Gør det selv"- bevis for cosinusrelationerne Interaktiv opgave der går ud på at bevise cosinusrelationerne. Pythagoras - den omvendte sætning "Bevis" ved hjælp af interaktiv figur. Medianerne i en trekant Interaktiv figur og figur hvor man klikker sig frem gennem et bevis. Fra Pmh's Matematiksider Mathcad-dokumenter med interaktive opgaver om retvinklet trekant. Der skal frembringes figurer med bestemte egenskaber. Retvinklet trekant Vilkårlig trekant Interaktive opgaver. Fra Matematik på Espergærde Gymnasium Trigonometri-test Fra Amtsgymnasiet i Odder Geometri Trekantsberegning. Kortfattet teori med interaktive dele. Fra MatLex, Randers HF og VUC Pythagoras' sætning (3) Pythagorean Theorem (3) Pythagoras' sætning (4) ... The Law of Cosines (2) Interaktive sider vedrørende beviser. Fra IES-math, Amtscentret for Undervisning, Hillerød

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