Geometry.Net - Theorems_And_Conjectures: Theorem Of Pythagoras

The Theorem Of Pythagoras
Brief description and proof of the Pythagorean theorem by dissection, based onsquares of sum and difference.
http://www-spof.gsfc.nasa.gov/stargaze/Spyth.htm

Extractions: Site Map 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
Theorem Of Pythagoras
Gives a geometric proof of the rule for measuring the sides of a right triangle.
http://www.alphaquark.com/Traduction/Pythagore.htm

Extractions: 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 A 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 sides by the following letters: One has four right-angled triangles of which :
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

Extractions: 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. The Theorem of Pythagoras
The Pythagorean Theorem
Theorem is Pythagoras' most famous mathematical contribution. According to legend, Pythagoras was so happy when he discovered the theorem that
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Pythagorean Theorem -- From MathWorld
Dixon, R. The theorem of pythagoras. §4.1 in Mathographics. Talbot,RF Generalizations of Pythagoras Theorem in n Dimensions. Math.
http://mathworld.wolfram.com/PythagoreanTheorem.html

Extractions: MATHWORLD - IN PRINT Order book from Amazon Geometry Plane Geometry Triangles ... Triangle Properties Pythagorean Theorem For a right triangle with legs and and hypotenuse 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.
Pythagoras' Theorem - By Seth Y-Maxwell
Pythagoras was a great Mathematician who was the first to create the music scale NEW ! Pythagorean Theorem Proof Calculator Pythagorean
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An Interactive Proof Of Pythagoras' Theorem
An Interactive Proof of Pythagoras' theorem This Java applet was written by Jim Morey.
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Pythagorean Theorem
move Drag the central red point. Reference "Pythagoras Theorem" OYA, Shinichi, 1975, Tokai University Press.
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Pythagoras [Internet Encyclopedia Of Philosophy]
Pythagoras (fl. 530 BCE.) problem at this date was the duplication of the square, a problem which gave rise to the theorem of the square on the
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Pythagoras' Playground (by The Event Inventor)
site, we will use the amazing properties of the Pythagorean Theorem to explore the world around us. 2500 years ago, Pythagoras of Samos and his
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NOVA Online The Proof Pythagorean Puzzle Theorem
Demonstrate the Pythagorean Theorem. Think of each side of a right triangle as also being a side of a square that's attached to the triangle.
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Pythagorean Theorem
The Pythagorean Theorem. Pythagoras, for whom the famous theorem is named, lived during the 6th century B.C. on the island of Samos in the Aegean
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Coordinates--lesson Plan #9
The theorem of pythagoras, for instance, was proved by a method using not numbersbut triangles, rectangles and squares. Even today students in schools
http://www-spof.gsfc.nasa.gov/stargaze/Lcelcoor.htm

Extractions: Goals : The student will Optional items below are for students familiar with trigonometry and with the theorem of Pythagoras (areas of math also covered by web files linked to httm://www.phy6.org/stargaze/Smath Terms: Cartesian coordinates, axes, origin (of coordinates) [polar coordinates] Theodolite, azimuth, elevation, zenith, [nadir]. Stories and extras: Guiding questions and additional tidbits
Project MATHEMATICS!Theorem Of Pythagoras
The theorem of pythagoras
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Theorem Of Pythagoras
Proof of Pythagoras Theorem.
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Project MATHEMATICS!--Theorem Of Pythagoras
Discovering the theorem of pythagoras. 3. Geometric interpretation. 4. Pythagoras.5. Applying the theorem of pythagoras. 6. Pythagorean triples
http://www.projectmathematics.com/pythag.htm

Extractions: 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 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.
The Theorem Of Pythagoras
The theorem of pythagoras is one of the earliest and most important results theorem of pythagoras. Given any right angle triangle, if one forms a square
http://www.math.uwaterloo.ca/navigation/ideas/grains/pythagoras.shtml

Extractions: UWdir Math Google Search Math Index Search Skip to the content of the web site. 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 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! 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.
The Theorem Of Pythagoras ... Key To Proof
The key to the proof of the theorem of pythagoras. The theorem states that thearea of the large white square (square of the hypoteneuse) in the following
http://www.math.uwaterloo.ca/navigation/ideas/grains/pythagoras-key.shtml

Extractions: 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.
NTNU JAVA :: View Topic - Theorem Of Pythagoras A*a + B*b = C*c
How ancient Chinese people discovers the same theorem. (much earlier than Pythagoras).You can change the interval delta T (in second, default value = 2
http://www.phy.ntnu.edu.tw/~hwang/abc/Pythagoras.html

Extractions: When you reach the last step, Press reset button to restart Registed user can get files related to this applet for offline access. Back to top Display posts from previous: All Posts 1 Day 7 Days 2 Weeks 1 Month 3 Months 6 Months 1 Year Oldest First Newest First NTNU JAVA Physics simulations Misc All times are GMT Jump to: Select a forum Physics simulations kinematics Dynamics Wave Thermodynamics Electromagnetics Optics Misc Comment about NTNUJAVA Mirror sites Molecular Workbench Easy java simulations Information and Download Optics Kinematics Dynamics Wave Thermodynamics Modern Physics misc You cannot post new topics in this forum
Keymath.com : Discovering Geometry : JavaSketchpad Activities : The Theorem Of
The theorem of pythagoras. The Pythagorean Theorem relates the lengths of thethree sides of a right triangle. In the investigation on this web page,
http://www.keymath.com/DG/dynamic/pythagorean_theorem.html

Extractions: Home Discovering Geometry Dynamic Geometry Explorations : The Theorem of Pythagoras The Pythagorean Theorem relates the lengths of the three sides of a right triangle. In the investigation on this web page, you will learn more about the Pythagorean Theorem and see whether or not it works for triangles that are not right triangles. This investigation will help you understand Lesson 9.1 on pages 462-464 of Discovering Geometry: An Investigative Approach. Sketch The sketch below shows a right triangle with squares constructed on its three sides. You can drag vertex A to change the size and shape, but it will remain a right triangle. Sorry, this page requires a Java-compatible web browser. Investigate Click "Construct Center of Square" to show center O of the square on the longer leg. The center of a square is located at the intersection of the diagonals. Click "Construct j and k" to show two lines through O : line j perpendicular to the hypotenuse and line k perpendicular to line j . Lines j and k divide the square on the longer leg into four quadrilaterals. Click "Construct Quadrilaterals" to show the quadrilaterals and the square on the shorter leg.

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