1. Theorem Of Pythagoras Demonstration of theorem of pythagoras.Category Science Math Algebra High School......Pythagore Demonstration of the theorem http://www.alphaquark.com/Traduction/Pythagore.htm

Pythagore Demonstration of the theorem homepage Source of this page Author : Thibaut Bernard Number of visitor Update: Thursday 16 August 2001. Alphaquark author's Note : This page is a translation of with the help of Altavista translation I hope this translation is good, but if there are any errors, you can write me If this translation is successful, perhaps I will try to translate another document of Alphaquark Construction of the geometrical figure which will be used for the demonstration Let us take a rectangle of width is and height B This rectangle which we make swivel of 90 o in the following way : For each rectangle, let us divide into two in the following way : Let us make swivel of 90 o the right-angled triangles in the following way yellow and purple : We thus find ourselves with four right-angled triangles. We note that one finds oneself with a square inside another. Demonstration Notation Let us take again our last diagram to indicate each of with dimensions by the following letters: One has four right-angled triangles of which : the with dimensions one opposed by a

2. The Theorem Of Pythagoras Pythagoras' Theorem. 41 proofs of the Pythagorean theorem. on the sides of a right triangle. The Pythagoras' Theorem then claims that the sum of (areas of) the two small squares http://www.math.uwaterloo.ca/navigation/ideas/grains/pythagoras.shtml

Use Menus 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. Note that the area of a given colour remains the same in the animation - no matter how the shape of the figure changes! 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.

3. Pythagorean Problem A method of disproving the theorem of pythagoras is presented. The author is adamant that this is intended only as a puzzle to find the mistake in the arguments, and not as a serious proposal. http://www.geocities.com/ResearchTriangle/System/8956/problems/pyth.htm

PLEASE NOTE: The following work is presented as a mathematical puzzle. It is NOT a valid proof, but serves to illustrate the problems that can arise if one is not familiar with postulates and conditions of various theorems. Read it and try to find the problem, but PLEASE do not preach to the world that Pythagoras' Theorem is false. A Disproof of Pythagoras' Theorem The Theorem of Pythagoras In a right triangle, the sum of the squares of the lengths of the two side sides is equal to the square of the hypotenuse. a + b = c DISPROOF: Start by defining a coordinate system with a along the x-axis and b along the y-axis. Let y = f(x) define the hypotenuse. Furthermore define a sequence of functions f n n n (x) converges uniformly to f(x). Clearly the length of the path defined by f (x) is a+b (or length a depending upon exactly how defines the path). Similarly, for any value of n the length of the path defined by f n (x) is also a+b. Since the functions f n (x) converge uniformly to f(x) the length of the path defined by f(x) is a+b.

4. The Theorem Of Pythagoras Brief description and proof of the Pythagorean theorem.Category Kids and Teens School Time Math Mathematicians Pythagoras......(M6) The theorem of pythagoras. Pythagoras of Samos was a Greek philosopher wholived around 530 BC, mostly in the Greek colony of Crotona in southern Italy. http://www-istp.gsfc.nasa.gov/stargaze/Spyth.htm

(M-6) The Theorem of Pythagoras Pythagoras of Samos was a Greek philosopher who lived around 530 BC, mostly in the Greek colony of Crotona in southern Italy. According to tradition he was the first to prove the assertion (theorem) which today bears his name: If a triangle has sides of length ( a,b,c ), with sides ( a,b ) enclosing an angle of 90 degrees ("right angle"), then a + b = c A right angle can be defined here as the angle formed when two straight lines cross each other in such a way that all 4 angles produced are equal. The theorem also works the other way around: if the lengths of the three sides ( a,b,c ) of a triangle satisfy the above relation, then the angle between sides a and b must be of 90 degrees. For instance, a triangle with sides a b c = 5 (inches, feet, meterswhatever) is right-angled, because a + b = 9 + 16 = 25 = c Ancient Egyptian builders may have known the (3,4,5) triangle and used it (with measured rods or strings) to construct right angles; even today builders may still nail together boards of those lengths to help align a corner. Many proofs exist and the easiest ones are probably the ones based on algebra, using the elementary identities discussed in the preceding section, namely

5. Theorem Of Pythagoras How ancient Chinese people discovers the same theorem. (much earlier than Pythagoras). http://www.phy.ntnu.edu.tw/java/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 :¡@

6. Project MATHEMATICS!--Theorem Of Pythagoras The theorem of pythagoras. Video Segments. 1. Three questions from real life.2. Discovering the theorem of pythagoras. 3. Geometric interpretation. http://www.projectmathematics.com/pythag.htm

The Theorem of Pythagoras Video Segments Three questions from real life Discovering the Theorem of Pythagoras Geometric interpretation Pythagoras Applying the Theorem of Pythagoras Pythagorean triples The Chinese proof Euclid's elements Euclid's proof A dissection proof Euclid's Book VI, Proposition 31 The Pythagorean Theorem in 3D Contents The program begins with three real-life situations that lead to the same mathematical problem: Find the length of one side of a right triangle if the lengths of the other two sides are known. The problem is solved by a simple computer-animated derivation of the Pythagorean theorem (based on similar triangles): In any right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs. The algebraic formula a + b = c is interpreted geometrically in terms of areas of squares, and is then used to solve the three real-life problems posed earlier. Historical context is provided through stills showing Babylonian clay tablets and various editions of Euclid's Elements . Several different computer-animated proofs of the Pythagorean theorem are presented, and the theorem is extended to 3-space.

7. Project MATHEMATICS!--Contest For student activities, recorded on videotape, related to the modules on Polynomials,the theorem of pythagoras, The Story of Pi, Similarity, and Sines http://www.projectmathematics.com/contest.htm

Project MATHEMATICS! Contest Project MATHEMATICS! conducted a contest in 1994 open to all teachers who had used project materials (videotapes and workbooks). Entries were judged on the basis of innovative and effective use of these materials in the classroom. Through the generosity of The Hewlett-Packard Company and The Intel Foundation eight prizes totaling $13,000 were awarded. They consisted of five first-place awards of $1,000 each to teachers, with an additional $1,000 presented to the awardee's school to be used in a manner determined by the awardee. In addition, second-place awards of $500 each went to three teachers, with another $500 presented to the awardee's school to be used in a manner determined by the awardee. The names of the winners are listed on the next page. A videotape was prepared showing classroom implementation of the entries of the first-place winners. This booklet describes these entries in more detail and also describes the entries of the second-place winners. The Hewlett-Packard Company and The Intel Foundation jointly provided financial support to produce the videotape and the booklet and to distribute 1,000 complimentary copies to teachers nationwide. Entries were received from various parts of the country, from Canada, and from overseas. Grade levels ranged from grade 8 in middle school to first-year community college. The contest entries show that teachers who are free to experiment can adapt to new ideas and new technology in creative ways that enhance their teaching and motivate their students to become excited about learning mathematics.

8. Theorem Of Pythagoras This java applet shows you (automatically step by step) How ancient Chinesepeople discovers the same theorem. (much earlier than Pythagoras). http://webphysics.ph.msstate.edu/javamirror/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 :¡@

9. The Theorem Of Pythagoras Brief description and proof of the Pythagorean theorem. http://www-spof.gsfc.nasa.gov/stargaze/Spyth.htm

(M-6) The Theorem of Pythagoras Pythagoras of Samos was a Greek philosopher who lived around 530 BC, mostly in the Greek colony of Crotona in southern Italy. According to tradition he was the first to prove the assertion (theorem) which today bears his name: If a triangle has sides of length ( a,b,c ), with sides ( a,b ) enclosing an angle of 90 degrees ("right angle"), then a + b = c A right angle can be defined here as the angle formed when two straight lines cross each other in such a way that all 4 angles produced are equal. The theorem also works the other way around: if the lengths of the three sides ( a,b,c ) of a triangle satisfy the above relation, then the angle between sides a and b must be of 90 degrees. For instance, a triangle with sides a b c = 5 (inches, feet, meterswhatever) is right-angled, because a + b = 9 + 16 = 25 = c Ancient Egyptian builders may have known the (3,4,5) triangle and used it (with measured rods or strings) to construct right angles; even today builders may still nail together boards of those lengths to help align a corner. Many proofs exist and the easiest ones are probably the ones based on algebra, using the elementary identities discussed in the preceding section, namely

10. The Theorem Of Pythagoras The theorem of pythagoras. Several engaging animated proofs of thePythagorean theorem are presented with applications to reallife http://www.maa.org/pubs/books/tpyvid.html

The Theorem of Pythagoras 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 minutes) List: $34.90 for video and workbook Catalog Code for Video and Workbook: TPYVID/W Workbook sold separately: $4.95 Catalog Code for Workbook: TPYWO/W How to Order Go to Subject Index Go to Publications Search © 1998 The Mathematical Association of America Please send comments, suggestions, or corrections about this page to webmaster@maa.org.

11. The Theorem Of Pythagoras ... Key To Proof Use Menus, The key to the proof of the theorem of pythagoras. Thetheorem states that the area of the large white square (square of http://www.math.uwaterloo.ca/navigation/ideas/grains/pythagoras-key.shtml

Use Menus The key to the proof of the theorem of Pythagoras The theorem states that the area of the large white square (square of the hypoteneuse) in the following diagram is equal to the sum of the areas of the two squares (of the two sides) in the next diagram It's important to notice that the orange triangle in both pictures is the same one, just rotated to better show the squares (and to match the animation). The proof begins by changing the solid white square to a blue one outlined in white. Then the same orange triangle is placed at each side of the square. The inside edges of the four triangles form the hypoteneus square. The outside edges of these four triangles form a large outer square. The outer square has fixed area equal to the area of the blue hypoteneuse square plus the areas of all four orange triangles. As the orange triangles move about in the animation, the outer square is preserved and consequently, the area of the outer square does not change. Because the orange triangles never overlap in the animation, the total area of the four triangles does not change either.

12. Pythagoras Detailed biography, including pictures, from the MacTutor History of Mathematics archive.Category Kids and Teens School Time Math Mathematicians Pythagoras...... (ii) The theorem of pythagoras for a right angled triangle the square onthe hypotenuse is equal to the sum of the squares on the other two sides. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Pythagoras.html

13. PinkMonkey.com Geometry Study Guide - 6.2 The Theorem Of Pythagoras 6.2 The theorem of pythagoras. Figure 6.3. D ABC is a right triangle. Index. 6.1The Right Triangle 6.2 The theorem of pythagoras 6.3 Special Right Triangles. http://www.pinkmonkey.com/studyguides/subjects/geometry/chap6/g0606201.asp

Support the Monkey! Tell All your Friends and Teachers Get Cash for Giving Your Opinions! Free College Cash 4U Advertise Here See What's New on the Message Boards today! Favorite Link of the Week. Your house from the sky! ... Tell a Friend Win a $1000 or more Scholarship to college! Place your Banner Ads or Text Links on PinkMonkey for $0.50 CPM or less! Pay by credit card. Same day setup. Please Take our User Survey 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

14. PinkMonkey.com Geometry Study Guide - CHAPTER 6 : THEOREM OF PYTHAGORAS AND THE CHAPTER 6 theorem of pythagoras AND THE RIGHT TRIANGLE. Index. 6.1 The RightTriangle 6.2 The theorem of pythagoras 6.3 Special Right Triangles. Chapter 7. http://www.pinkmonkey.com/studyguides/subjects/geometry/chap6/g0606101.asp

Support the Monkey! Tell All your Friends and Teachers Get Cash for Giving Your Opinions! Free College Cash 4U Advertise Here See What's New on the Message Boards today! Favorite Link of the Week. Your house from the sky! ... Tell a Friend Win a $1000 or more Scholarship to college! Place your Banner Ads or Text Links on PinkMonkey for $0.50 CPM or less! Pay by credit card. Same day setup. Please Take our User Survey 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.

15. About "The Theorem Of Pythagoras" The theorem of pythagoras. Library Home Full Table of Contents Suggesta Link Library Help Visit this site http//www.projectmathematics 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 Suggestion Box Home ... Search http://mathforum.org/ webmaster@mathforum.org

16. Math Forum - Mathematics Teacher Bibliography: Right Triangles, Pythagorean Theo Mathematics Teacher. Geometry Bibliography Right Triangles and the Theoremof Pythagoras. The questions are related to 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/ Suggestion Box Home The Math Library ... Search http://mathforum.org/

17. The Theorem Of Pythagoras - Anagrams Rearranging the letters of the theorem of pythagoras gives 'He has that geometryproof.'! See this page for other points concerning the theorem of pythagoras. http://www.anagramgenius.com/archive/thethe.html

Rearranging the letters of 'The theorem of Pythagoras' (Embodies basic spatial relationship) gives: He has that geometry proof. (by V.Rabin) See also: Pythagoras Pythagoras' Theorem. (FREE!) Download FREE anagram-generating software for your Windows computer Instructions for linking to this page! Learn about the Anagram Genius software (Windows/MacOS) Search the Archive Add YOUR anagrams to the Archive! League table of top contributors Find anagram aliases of the theorem of pythagoras (or any other text)! Find gold service anagrams of the theorem of pythagoras (or any other text)! Anagram Genius Archive Main Index Anagram Gems Mailing List www.anagramgenius.com home page Crossword Maestro for Windows . The world's first expert system for solving crossword clues! Click here for more information or to download. William Tunstall-Pedoe . See this page for other points concerning the theorem of pythagoras.

18. Pythagoras' Theorem. - Anagrams Rearranging the letters of pythagoras' theorem. gives 'Geometry? Geometry? (Sharpoath!), (by V.Rabin) (2002). See also Pythagoras The theorem of pythagoras http://www.anagramgenius.com/archive/pythag2.html

Rearranging the letters of 'Pythagoras' Theorem.' (Basic property of right-angled triangles) gives: Geometry? (Sharp oath!) (by V.Rabin) See also: Pythagoras The theorem of Pythagoras (FREE!) Download FREE anagram-generating software for your Windows computer Instructions for linking to this page! Learn about the Anagram Genius software (Windows/MacOS) Search the Archive Add YOUR anagrams to the Archive! League table of top contributors Find anagram aliases of pythagoras' theorem. (or any other text)! Find gold service anagrams of pythagoras' theorem. (or any other text)! Anagram Genius Archive Main Index Anagram Gems Mailing List www.anagramgenius.com home page Crossword Maestro for Windows . The world's first expert system for solving crossword clues! Click here for more information or to download. William Tunstall-Pedoe . See this page for other points concerning pythagoras' theorem..

19. 1300 A.C.: Theorem Of Pythagoras 1300 bC. theorem of pythagoras. In the tablet, of which the translationis reported, it seems 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.

20. The Theorem Of Pythagoras Pythagoras. Letters. The theorem of pythagoras is wellknown. Downloadthe latest version of The theorem of pythagoras. Pythag.exe (113k), http://www.coster.demon.nl/e_pythag.htm

Dutch Mathematics Flippo Games ... Letters The Theorem of Pythagoras is wellknown. If you don't believe it, well probably this programm will convince you. Download the latest version of The Theorem of Pythagoras. Pythag.exe (113k)

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