21. BrochureWeb 18 THE theorem of pythagoras. DIRECTOR. AWARDS. Tom M. Apostol. Gold Apple, 1989National Educational Film and Video Festival, Oakland; Gold Medal, 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.

22. Math Forum - Mathematics Teacher Bibliography: Right Triangles, Pythagorean Theo Geometry Bibliography Right Triangles and the theorem of pythagoras Group presentations of different proofs of the theorem of pythagoras. http://mathforum.org/mathed/mtbib/right.triangles.html

Mathematics Teacher Geometry Bibliography: Right Triangles and the Theorem of Pythagoras Hubert Ludwig, Ball State University Back to Geometry Bibliography: Contents 00hjludwig@bsu.edu home page: http://www.cs.bsu.edu/~hjludwig/ Home The Math Library Quick Reference ... Help http://mathforum.org/

23. About "The Theorem Of Pythagoras" The theorem of pythagoras. _ Library Home Full Table of Contents Suggest a Link Library Help http://mathforum.org/library/view/7534.html

The Theorem of Pythagoras Library Home Full Table of Contents Suggest a Link Library Help Visit this site: http://www.projectmathematics.com/pythag.htm Author: Project MATHEMATICS!, California Institute of Technology Description: A videotape-and-workbook module that explores a basic topic in high school mathematics in ways that cannot be done at the chalkboard or in a textbook. Several 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. Levels: High School (9-12) Languages: English Resource Types: Multimedia Video Lesson Plans and Activities Textbooks Math Topics: Higher-Dimensional Geometry Triangles and Other Polygons Math Ed Topics: Audiovisual/Multimedia Curriculum/Materials Development Home The Math Library ... Help http://mathforum.org/

24. An Easy Approach To The Theorem Of Pythagoras An Easy Approach to the theorem of pythagoras. Pythagoras’ theorem is usuallypresented as a theorem about triangles in a right triangle, the square on the http://it.stlawu.edu/~dmelvill/mesomath/Pythagoras/EasyPythagoras.html

An Easy Approach to the Theorem of Pythagoras Pythagoras’ theorem is usually presented as a theorem about triangles: in a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. It is perhaps easier to think of it as a nice result relating rectangles and squares: in a rectangle, the square on the diagonal is equal to the sum of the squares on the long and short sides. There are many proofs of the theorem, most of them not as well-known as they might be. Euclid’s proof in Elements I, 47 (see David Joyce’s excellent website ) is an elegant argument in cut-and-paste geometry. If it seems a little daunting at first, it can be tamed by using shaded triangles to keep track of the steps. My purpose here is to give a simple approach to the theorem using metric geometry, that is, geometry where the lengths and areas have values that can be calculated. I make no claims to originality in the approach, but it seems to be one that is not readily accessible. Mathematical arguments are generally easier to follow if you work along with them, and if you want to do that here, all you need is some squared paper and a pencil.

25. An Easy Approach To The Theorem Of Pythagoras An Easy Approach to the theorem of pythagoras. We have seen that a triangle linkstwo ways of dividing the area of a square into two. http://it.stlawu.edu/~dmelvill/mesomath/Pythagoras/EasyPythagoras2.html

An Easy Approach to the Theorem of Pythagoras We have seen that a triangle links two ways of dividing the area of a square into two. Now we look at what happens in some more complicated example. First, a 3x3 grid. With a three-by-three grid, we can view the two squares on the left of the top row as forming a 2x1 rectangle, and add the diagonal to form a triangle with sides of lengths 2 and 1. The squares on the sides of the rectangle have areas 1 and 4, so the total area is 5 squares. Now we have to find the area of the square on the diagonal, or the hypotenuse of the triangle. First, construct the square and color it in. What is the area of the red square? It includes 1 whole small square and a lot of bits of the outer squares. But the outer bits are made up of four copies of the original triangle, and that was just half of the 2x1 rectangle. The rectangle has area 2, so half of it has area 1 and four copies then have area 4. The total area is the one central square, plus 4 from the outside to make 5. The red and the blue areas are the same.

26. Theorem Of Pythagoras Before introducing the theorem of pythagoras, we begin with some perfect The theorem of pythagoras is one of the most important formulas in all of http://www2.scc-fl.edu/rrapalje/Tech-Prep-Math/Theorem of Pythagoras/Theorem of

Special Quadratic Equations Theorem of Pythagoras (Better, but Still Under Construction! Check back next year!) from Basic Algebra: One Step at a Time p. 193 - 200 Dr. Robert J. Rapalje Seminole Community CollegeHunt Club Center Before introducing the Theorem of Pythagoras, we begin with some perfect square equations. Perfect square equations (see the first example and the exercises that follow) can be solved by taking the square root of both sides of the equation. This is called the square root property of equations. When you use this property, you must include a "±" (that is, "+" or "-") in order to obtain both solutions of the equation. EXAMPLE 1. Solve the equation x Solution: The solution is essentially to answer the question, "What number can be squared (multiplied times itself!) in order to get 16. There are actually two answers: x = 4 and also x = -4. This answer may be also written as x = ± 4. EXAMPLE 2. Solve the equation x

27. Pythagoras Theorem (8) Pythagoras Theorem (8). Proving theorem of pythagoras by Dissection. The figureshows a dissection method of proving the theorem of pythagoras. http://www.ies.co.jp/math/java/geo/pythashi/pythashi.html

Pythagoras Theorem (8) Proving Theorem of Pythagoras by Dissection The figure shows a dissection method of proving the Theorem of Pythagoras. The method seems to be very complex, but it can be understood as one special case of simple dissection methods. Using the applet, we can obtain infinitely many methods of dissection. Perigal's proof is classified in the same category. Applet How to use the Applet Drag the red point in the left figure to decide the bases of the right triangle ( lengths of a and b). Drag the red point in the left figure to observe various patterns of dissection.

28. Theorem Of Pythagoras From Tarquin Books - Books, Posters And Educational Materi Tarquin Books provides books, newsletters and electronic publishing for legaland professional sectors in the UK and elsewhere. http://www.xplpublishing.co.uk/tqn/default.asp?cid=&id=675&productname=Theorem o

29. Theorem Of Pythagoras Laminated Poster From Tarquin Books - Books, Posters And E Tarquin Books provides books, newsletters and electronic publishing for legaland professional sectors in the UK and elsewhere. http://www.xplpublishing.co.uk/tqn/default.asp?cid=&id=676&productname=Theorem o

30. PinkMonkey.com Geometry Study Guide - 6.2 The Theorem Of Pythagoras PinkMonkey.comFree Online Geometry StudyGuide -The World s largest source ofFree Booknotes/Literature summaries. http://www.pinkmonkey.com/studyguides/subjects/geometry/chap6/g0606201.asp

Support the Monkey! Tell All your Friends and Teachers Free College Search Click Here Get the "Dirt" on your College! Get a Scholarship! See What's New on the Message Boards today! The Unofficial Guide to College Home ... New Title Request Win a $1000 or more Scholarship to college! Please Take our User Survey WebMasters Click Here 6.2 The Theorem of Pythagoras Figure 6.3 D ABC is a right triangle. l (AB) = c l (BC) = a l (CA) = b CD is perpendicular to AB such that D ABC ~ D CBD or l (BC) l (AB) l (CD) a = c x = cx D ABC ~ D ACD or l (AC) l (AB) l (AD) b = c Therefore, from (1) and (2) a + b = cx + cy = c ( x + y ) = c c = c a + b = c The square of the hypotenuse is equal to the sum of the squares of the legs. Converse of Pythagoras Theorem : In a triangle if the square of the longest side is equal to the sum of the squares of the remaining two sides then the longest side is the hypotenuse and the angle opposite to it, is a right angle. Figure 6.4 Given that in D ABC l (AC) l (AB) l (BC) To prove that D ABC is a right triangle or that m ABC = 90 Construct a D PQR such that l (QR) = l (BC)

31. PinkMonkey.com Geometry Study Guide - CHAPTER 6 : THEOREM OF PYTHAGORAS AND THE CHAPTER 6 theorem of pythagoras AND THE RIGHT TRIANGLE. 6.1 The Right Triangle.Figure 6.1. D ABC is a right triangle, hence m Ð ABC = 900. http://www.pinkmonkey.com/studyguides/subjects/geometry/chap6/g0606101.asp

Support the Monkey! Tell All your Friends and Teachers Free College Search Click Here Get the "Dirt" on your College! Get a Scholarship! See What's New on the Message Boards today! The Unofficial Guide to College Home ... New Title Request Win a $1000 or more Scholarship to college! Please Take our User Survey WebMasters Click Here CHAPTER 6 : THEOREM OF PYTHAGORAS AND THE RIGHT TRIANGLE 6.1 The Right Triangle Figure 6.1 D ABC is a right triangle, hence m ABC = 90 . Therefore m A and m C are complementary ( figure 6.1). Now seg.BD is a perpendicular onto seg.AC (figure 6.2). Figure 6.2 Seg.BD divides D ABC into two right triangles D BDC and D ADB ( figure 6.2). It can be easily proven that these two triangles are similar to the parent D ABC and therefore similar to each other. Proof : Consider D ABC and D BDC ABC BCA D ABC ~ D BDC Similarly consider D ABC and D ADB. ABC CAB D ABC ~ D ADB from (1) and (2) D ABC ~ D ADB ~ D BDC. Since D ABC ~ D BDC and D ABC ~ D ADB In (A) l (BC) is repeated and in (B) l (seg.AB) is repeated at the means. This is referred to as the geometric mean.

32. Kids.net.au - Site Profile For The Theorem Of Pythagoras , Brief description and proof ofthe Pythagorean theorem. Url, http//wwwspof.gsfc.nasa.gov/stargaze/Spyth.......Title, The theorem of pythagoras. http://www.kids.net.au/siteprofile/13636

Web kids.net.au Thesaurus Dictionary Kids Categories Encyclopedia ... Toys The American Experience: The Presidents Site Profile Title: The American Experience: The Presidents Description: A collection of research developed for the PBS television series. Includes a review of all 20th century chief executives, a collection of Presidential quotes, links to related sites, a comprehensive collection of primary source materials, and a teachers' Url: http://www.pbs.org/wgbh/amex/presidents/ Category: Kids_and_Teens/School_Time/Social_Studies/History/By_Region/North_America/United_States/Presidents Printer safe version Link to Kids.Net.Au About Us ... Add Kids.net.au to your site! Kids.net.au - Search engine for kids, children, educators and teachers - Searching sites designed for kids that are child safe and clean. Information on this site is sourced from Dmoz.org, Wikipedia.org and Kids.net.au

33. 1300 A.C.: Theorem Of Pythagoras theorem of pythagoras. In the tablet, of which the translation is reported, itseems really that the theorem of pythagoras is applied. http://web.genie.it/utenti/i/inanna/livello2-i/susa-pitagora-i.htm

HISTORY PHILOSOPHY RELIGION SCIENCE ... VERSIONE ITALIANA 1300 b.C. 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.

34. Theorem Of Pythagoras - A² + B² = C² Record set of the pythagoras theorem of pythagoras a² + b² = c².Home Search Forum Links Contact Imprint Sitemap. German English http://www.mathematik-wissen.de/us/theorem_of_pythagoras.htm

th grade th grade th grade th grade th grade th grade Theorem of Pythagoras a² + b² = c² [Home] [Search] [Forum] [Links] ... German [English How big is the hypotenuse of a right angles triangle, when both lengths of the sides are known? Questioned differently: How big is the diagonal d of a right angle? The possibilities to calculate the diagonal in a square through the area are known but in this example, there no square is given. Four of these rectangles are placed next to each other in a way that the four diagonals make a square (square, so that later on the length can be calculated with help from the root). Three squares result: = (a - b)² = d² = (a + b)² The right angled triangle: Sought: d² 1. First possibility One time the yellow square plus four times the eight angled triangle, make the red square. 2. Second possibility One time the green square minus four times the right angled triangle make the red square. The root of d² is the sought diagonal in the right angle or the hypotenuse of the right angled triangle. previous site superordinate site next site Mathematik-Wissen.de

35. Euclid’s Height Theorem Condition theorem of pythagoras. The height divides the triangle into two right So, the following is obtained according to the theorem of pythagoras http://www.mathematik-wissen.de/us/euclid_s_height_theorem.htm

th grade th grade th grade th grade th grade th grade Euclid's height theorem h² = p · q [Home] [Search] [Forum] [Links] ... German [English Ass ertions h² = p·q Evidence Condition - theorem of Pythagoras: The height divides the triangle into two right angled triangles: ahp and bqh. So, the following is obtained according to the theorem of Pythagoras: h² + p² = a² h² + q² = b² Hypotenuse squared, is the same as both hypotenuse sections added to the second power: c² = (p+q)² c² = p² + 2pq + q² Theorem of Pythagoras, insert and sum up: previous site superordinate site next site Mathematik-Wissen.de ... /Math-knowledge.com

36. 1300 A.C.: Theorem Of Pythagoras THE theorem of pythagoras. In the tablet, of which the translation is 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.

37. Pythagoras Theorem Pythagoras Theorem. File List This page contains activities to promote anunderstanding and application of the theorem of pythagoras. http://smard.cqu.edu.au/Database/Junior/Measurement/Pythagoras_Theorem/upload.ht

Pythagoras Theorem File List This page contains activities to promote an understanding and application of the Theorem of Pythagoras. If you have developed activities applying to this area you may like to share them with other mathematics teachers. Note: To DOWNLOAD a file, click on the FILENAME. To contribute a file to the database click UPLOAD. File Upload Filename: Title: Submitted by: Email Address: Description: File List This page contains activities to promote an understanding and application of the Theorem of Pythagoras. If you have developed activities applying to this area you may like to share them with other mathematics teachers. Note: To DOWNLOAD a file, click on the FILENAME. To contribute a file to the database click UPLOAD. URL: http://smard.cqu.edu.au/Database/Junior/Measurement/Pythagoras_Theorem/ Last Modified: Sun Apr 29 12:56:02 2001 by g.morgan

38. MathLove Pythagoras theorem A Pythagoras Proof. How did Pythagoras prove Pythagorean Try to fit 1,2,3,4 and 5 on 6, thus verifying the theorem of pythagoras. http://www.mathlove.com/new3/tools/detail.php?pid=PZL0B

39. BCIT Math 11 Competency Test: The Theorem Of Pythagoras With Applications British Columbia Institute of Technology. The theorem of pythagoras With Applications.Copyright © British Columbia Institute of Technology, http://www.math.bcit.ca/competency_testing/testinfo/testsyll11/trigonometry/pyth

The Theorem of Pythagoras With Applications Privacy Statement 3700 Willingdon Avenue, Burnaby, British Columbia, Canada, V5G 3H2, Phone: 604-434-5734 This page is maintained by Andrew_McConnell@bcit.ca and was last updated Wed Oct 22 16:17:28 2003

40. Template theorem of pythagoras a2 + b2 = c2 How ancient Chinese people discovers thesame 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 :¡@

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