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Topic: Pythagorean theorem

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Pythagorean triangle

Isoceles triangle

List of theorems

List of mathematical theorems

Pythagorean triple

Triangle

List of fundamental theorems

Law of cosines

Triangle

Euclidean geometry

Parallelogram law

Orthogonal

Theorem

	Pythagorean theorem - Wikipedia, the free encyclopedia
		A generalization of this theorem is the law of cosines, which allows the computation of the length of the third side of any triangle, given the lengths of two sides and the size of the angle between them.
		Another generalization of the Pythagorean theorem to three dimensions is de Gua's theorem: If a tetrahedron has a right angle corner (a corner like a cube), then the square of the area of the face opposite the right angle corner is the sum of the squares of the areas of the other three faces.
		The theorem is referenced in an episode of The Simpsons.
	en.wikipedia.org /wiki/Pythagorean_theorem (3053 words)

	Pythagorean Theorems - Some 'Not So Familiar' Implications
		Still, the Pythagorean relationship holds, the sum of the areas of the rectangles drawn on the two legs is equal to the area of the rhombus drawn on the hypotenuse of the right triangle.
		In these figures the Pythagorean relationship still holds, the sum of the areas of the parallelograms drawn on the two sides is equal to the area of the parallelogram drawn on the third side of the triangle.
		Similar to Pythagorean Triples, quadruples are sets of 4 integers, such that the sum of the squares of the smaller three equals the square of the fourth larger integer.
	contracosta.edu /math/pythagoras.htm (1637 words)

	Math Forum: A Proof of the Pythagorean Theorem
		The Pythagorean theorem is one of the most famous in all of mathematics.
		Theorem: The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the legs.
		There are many different proofs of the theorem (even one supplied by President Garfield in 1876!), and we know that the Babylonians knew about the Pythagorean theorem about 1000 years before the time of Pythagoras (born in 572 B.C.).
	mathforum.org /isaac/problems/pythagthm.html (156 words)

	Math Forum: Ask Dr. Math FAQ: Pythagorean Theorem
		The Pythagorean theorem is used any time we have a right triangle, we know the length of two sides, and we want to find the third side.
		The applications that use the Pythagorean theorem include computing the distance between points on a plane; converting between polar and rectangular coordinates; computing perimeters, surface areas and volumes of various geometric shapes; and calculating maxima and minima of perimeters, or surface areas and volumes of various geometric shapes.
		One of the most common applications of the Pythagorean theorem is in the distance formula.
	mathforum.org /dr.math/faq/faq.pythagorean.html (657 words)

	Pythagorean Theorem
		To begin, the Pythagorean theorem states that the square on the hypotenuse of a right triangle has an area equal to the combined areas of the squares on the other two sides.
		The Pythagorean theorem was a mathematical fact that the Babylonians knew and used.
		With the Pythagorean theorem being such a popular topic, it is no wonder high school students study the theorem.
	www.ms.uky.edu /~lee/ma502/pythag/pythag.htm (488 words)

	Pythagorean theorem - Gurupedia
		In mathematics, the Pythagorean theorem or Pythagoras' theorem, is a relation in Euclidean geometry between the three sides of a right triangle.
		Pythagoras, although the facts of the theorem were known by Indian and Greek mathematicians well before he lived.
		Perhaps this theorem has a greater variety of different known proofs than any other (the law of quadratic reciprocity may also be a contender for that distinction).
	www.gurupedia.com /p/py/pythagorean_theorem.htm (989 words)

	MathSteps: Grade 7: Pythagorean Theorem: What Is It?
		The Pythagorean (puh thag or ee un) Theorem, also called the Pythagorean Property, says that the sum of the squares of the lengths of the legs of any right triangle is equal to the square of the length of the hypotenuse,
		Another way of looking at the Pythagorean Theorem is to think about actual squares of the lengths of the sides of a right triangle.
		Pythagorean Triples are groups of three whole numbers that make the Pythagorean Theorem true (and therefore define a true right triangle).
	www.eduplace.com /math/mathsteps/7/c (545 words)

	Pythagorean Theorem and its many proofs (Site not responding. Last check: 2007-10-22)
		The theorem is of fundamental importance in the Euclidean Geometry where it serves as a basis for the definition of distance between two points.
		It is known that the Pythagorean Theorem is Equivalent to Parallel Postulate.
		It generalizes the Pythagorean Theorem in two ways: the triangle ABC is not required to be right-angled and the shapes built on its sides are arbitrary parallelograms instead of squares.
	www.cut-the-knot.org /pythagoras/index.shtml (8093 words)

	Proofs of the Pythagorean Theorem (Site not responding. Last check: 2007-10-22)
		The theorem bears his name although we have evidence that the Babylonians knew this relationship some 1000 years earlier.
		The Pythagorean School was more than a school; it was "a closely knit brotherhood with secret rites and observances" (Eves 75).
		This theorem is talking about the area of the squares that are built on each side of the right triangle.
	jwilson.coe.uga.edu /EMT668/EMT668.Student.Folders/HeadAngela/essay1/Pythagorean.html (1106 words)

	PlanetMath: Pythagorean theorem
		Cosines law is a generalization of Pythagorean theorem for any triangle.
		It implies that the converse of Pythagorean theorem also holds: if the sides of a triangle satisfy
		This is version 15 of Pythagorean theorem, born on 2001-10-06, modified 2005-05-15.
	planetmath.org /encyclopedia/PythagorasTheorem.html (146 words)

	The Pythagorean Theorem
		Thus, implicit in this particular constructivist approach to the Pythagorean theorem is the notion that the student should build his or her own knowledge by "eyeballing" right angles.
		Another problem arising in this constructivist approach to the Pythagorean theorem is that of calculating the areas of the squares built on the sides and hypotenuse of a geoboard triangle.
		Experiments with the geoboard correspond to a cumbersome verification of the Pythagorean theorem in rather special circumstances (the geoboard's discrete structure is well suited to experimentation, but it fails to represent the more general structure of the Euclidean plane).
	mathematicallycorrect.com /pythag.htm (980 words)

	Pythagorean Theorem
		The Pythagorean Theorem is a statement relating the lengths of the sides of any right triangle.
		Pythagoras, for whom the theorem is named, lived in ancient Greece, 2500 years ago.
		So the Pythagorean theorem states the area h^2 of the square drawn on the hypotenuse is equal to the area a^2 of the square drawn on side a plus the area b^2 of the square drawn on side b.
	www.grc.nasa.gov /WWW/K-12/airplane/pythag.html (946 words)

	Pythagorean History
		The Pythagoreans wrote many geometric proofs, but it is difficult to ascertain who proved what, as the group wanted to keep their findings secret.
		It is thought that the Babylonians saw this pattern of tiles to be a proof of the Pythagorean Theorem.
		We know that the Pythagorean theorem is a case of this equation when n = 2, and that integral solutions exist.
	www.geom.uiuc.edu /~demo5337/Group3/hist.html (688 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		The Pythagorean Theorem is one of Euclidean Geometry's most beautiful theorems.
		The legend has it that he was so excited by its proof that he sacrificed a bull for the occasion, even though Pythagoreans were against animal sacrifice.
		This first method is one of the ways the Pythagoreans would have proved the theorem.
	www.perseus.tufts.edu /GreekScience/Students/Tim/Pythag'sTheorem.html (340 words)

	Pythagoras' Theorem (Site not responding. Last check: 2007-10-22)
		Use Pythagoras' theorem to show that, in a right-angled triangle, the area of the semicircle on the hypotenuse is the sum of the areas of the semicircles on the other two sides.
		The converse of Pythagoras' theorem is the statement:
		A Pythagorean triple is a set of three integers which can be lengths of the sides of a right-angled triangle.
	thejuniverse.org /Mathdesign/widgets/Pythagoras (516 words)

	Pythagorean Theorem (Site not responding. Last check: 2007-10-22)
		Pythagoras, for whom the famous theorem is named, lived during the 6th century B.C. on the island of Samos in the Aegean Sea, in Egypt, in Babylon and in southern Italy.
		The Pythagorean Theorem asserts that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides:
		The figure at the left contains a proof of the theorem, because the area of the big, outer, green square is equal to the sum of the areas of the four red triangles and the little, inner white square:
	scidiv.bcc.ctc.edu /Math/Pythagoras.html (191 words)

	Finding Unknown Sides
		You may already have learned to calculate the third side when the other two sides of a right triangle are known using the Pythagorean Theorem.
		To use this theorem, label the sides of the right triangle a, b, c.
		Pythagorean triples are integer length sides of right triangles.
	argyll.epsb.ca /jreed/math9/strand3/3102.htm (547 words)

	A Hotlist to Explore The Pythagorean Theorem (Site not responding. Last check: 2007-10-22)
		Animated Proof of the Pythagorean Theorem - This is another wonderful animation of the proof of the Pythagorean Theorem.
		Pythagorean Explorer Exploration Questions - Be sure to answer the thought provoking exploration questions listed on this website to turn in to Ms.
		Pythagorean Theorem - This wonderful site will help you understand the Pythagorean theorem and understand how to apply it to triangles.
	www.kn.pacbell.com /wired/fil/pages/listpythagorms.html (501 words)

	Pythagorean Theorem
		Not only do these numbers satisfy the Pythagorean Theorem, but any multiples of these numbers also satisfy the Pythagorean Theorem.
		If you multiply all three numbers by 2 (6, 8, and 10), these new numbers ALSO satisfy the Pythagorean theorem.
		This problem could also be solved using the Pythagorean Triple 3, 4, 5.
	regentsprep.org /Regents/math/fpyth/Pythag.htm (295 words)

	Relations and sizes - Right triangle facts - In Depth (Site not responding. Last check: 2007-10-22)
		It is usually written as the equation below, where a and b are the measures of the legs of the triangle and c is the measure of the hypotenuse.
		Let's try out the Pythagorean Theorem using this right triangle with sides of 5 and 12 cm, and a hypotenuse of 13 cm.
		We can verify that the Pythagorean Theorem is true by substituting in the values.
	www.math.com /school/subject3/lessons/S3U3L4DP.html (505 words)

	Pythagorean Theorem/ Science in Ancient Artwork
		Various essays deal with the possible extension of the Pythagorean Theorem to the third power (to the cube) in relation to the mathematical and geometrical appearance of the maya long count fractals within progressive series of right triangles.
		With the extension of the Pythagorean Theorem, not only is one able to achieve a translation between right triangles on a series of progression, but this is achieved through the maya long count numbers/fractals.
		This proposition has become known as the Pythagorean Theorem: the square of the hypotenuse of a right triangle equals the sum of the squares of the legs.
	www.earthmatrix.com /Pitagor3.htm (638 words)

	Pythagorean Theorem
		The Pythagorean Theorem is one of the most important facts learned in Geometry.
		Common pythagorean triple are: 3, 4, 5; 5, 12, 13; 7, 24, 25; 9, 40, 41; and 6, 8, 10. All but this last triple are primitive.
		This is a characteristic of a general class of primitive pythagorean triples involving squares and two consecutive integers and was illustrated in homework 3, problem 6.
	www.andrews.edu /~calkins/math/webtexts/numb11.htm (1601 words)

	Pythagorean Theorem Problems
		In this last section we present a few problems that require the use of the Pythagorean Theorem.
		This is a hands-on exercise for you to convince yourself that the Pythagorean theorem works.
		The Pythagorean Triples were described with Tip number 1.
	www.arcytech.org /java/pythagoras/problems.html (479 words)

	Pythagorean Theorem Lesson
		Students know the Pythagorean Theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures:
		Know and understand the Pythagorean Theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean Theorem by direct measurement.
		Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles.
	score.kings.k12.ca.us /lessons/pytha.html (668 words)

	Session 6, Part B: Proving the Pythagorean Theorem
		A theorem about right triangles must be true for every right triangle; there can be no exceptions.
		The Pythagorean theorem has been proven to work for every possible right triangle.
		The proof that follows is probably from China, about 200 B.C.E. Rather than learning of it from the Pythagoreans, though, the author of the proof most likely developed the theorem independently.
	www.learner.org /channel/courses/learningmath/geometry/session6/part_b (147 words)

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