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Topic: Pythagorean triangle

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Pythagorean theorem

Triangle

Pythagorean triple

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Parallelogram law

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	Triangle
		A central theorem is the Pythagorean theorem stating that in any right triangle, the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
		A perpendicular bisector of a triangle is a straight line passing through the midpoint of a side and being perpendicular to it, i.e.
		The area S of a triangle is S = ½bh, where b is the length of any side of the triangle (the base) and h (the altitude) is the perpendicular distance between the base and the vertex not on the base.
	www.brainyencyclopedia.com /encyclopedia/t/tr/triangle.html (1791 words)

	Encyclopedia: Triangle
		In geometry, a simplex or n-simplex is an n-dimensional analogue of a triangle.
		The Pythagorean theorem can be generalized to the law of cosines: In trigonometry, the law of cosines is a statement about arbitrary triangles which generalizes the Pythagorean theorem by correcting it with a term proportional to the cosine of the opposing angle.
		The area S of a triangle is S = Â½bh, where b is the length of any side of the triangle (the base) and h (the altitude) is the perpendicular distance between the base and the vertex not on the base.
	www.nationmaster.com /encyclopedia/triangle (4215 words)

	Triangle - LearnThis.Info Enclyclopedia (Site not responding. Last check: 2007-11-02)
		That is, if the longest side of a triangle is twice that of the longest side of a similar triangle, say, then the shortest side will also be twice that of the shortest side of the other triangle, and the median side will be twice that of the other triangle.
		The crucial fact is that two triangles are similar if and only if their corresponding angles are equal, and this occurs for example when two triangles share an angle and the sides opposite to that angle are parallel.
		This is also the triangle's center of gravity: if the triangle were made out of wood, say, you could balance it on its centroid, or on any line through the centroid.
	encyclopedia.learnthis.info /t/tr/triangle.html (1754 words)

	Search Tuna Report for Pythagorean (Site not responding. Last check: 2007-11-02)
		Pythagorean Theorem -- From MathWorld Theorem, Peacock's Tail, Pythagoras's Theorem, Windmill...
		Pythagorean Theorem Proof Starting with a right triangle and squares on each side, the middle size square is cut into congruent quadrilaterals (the cuts through the center and parallel to the sides of the biggest square)....
		Pythagorean Triplets It is part of the demonstration formulated by the Pythagoreans that the square root of 2 is an irrational number....
	searchtuna.com /ftlive/746.html (2842 words)

	Read This: Pythagorean Triangles
		Chapter 5: We find that at least one of the arms of a Pythagorean triangle is a multiple of 3, while at least one of the three sides (arms or hypotenuse) must be a multiple of 5.
		We are also given the exact number of primitive Pythagorean triangles with a given integer as the radius of the inscribed circle.
		It is dedicated to proving Fermat's assertion that the smallest Pythagorean triangle in which the hypotenuse and the sum of the arms are squares is the triangle (456548602761, 1061652293520, 4687298610289).
	www.maa.org /reviews/pythtriangles.html (1089 words)

	lessonone
		Students need to see how the angles and sides of a right triangle relate to each other in order to understand the trigonometric ratios; these ratios must be mastered because they are the basis of this course and are necessary for further study in mathematics.
		In addition, students must understand the Pythagorean theorem because it is a fundamental theorem that instructs students how to relate the sides of a right triangle so that they are able to solve mathematical problems.
		Next, define what the Pythagorean theorem states; that is, the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse (c2 = a2 + b2).
	home.moravian.edu /students/p/stdap01/lessonone.htm (862 words)

	Pythagorean Square Triangle (Site not responding. Last check: 2007-11-02)
		Prove that the area of a right triangle with integer sides is not a perfect square.
		Let a, b, and c be the lengths of the sides of a right triangle with integer sides.
		The primitive Pythagorean triple (a,b,c) becomes (2z,b,c), and zb is a square.
	mcraeclan.com /MathHelp/GeometryPythagoreanTriangleAreaNotSquare.htm (928 words)

	Pythagorean_triangle (Site not responding. Last check: 2007-11-02)
		In mathematics, the Pythagorean theorem or Pythagoras' theorem, is a relation in Euclidean geometry between the three sides of a right triangle.
		The theorem is named after and commonly attributed to the 6th century BC Greek philosopher and mathematician Pythagoras, although the facts of the theorem were known by Indian (Baudhayana's and Katyayana's Sulbasutras), Greek, Chinese and Babylonian mathematicians well before he lived.
		The Pythagorean Theorem is Equivalent to the Parallel Postulate.
	www.apawn.com /search.php?title=Pythagorean_triangle (1323 words)

	Math Forum - Geometry Problem of the Week (Site not responding. Last check: 2007-11-02)
		Pythagorean Theorem is the hypotenuse squared equal to sum of the squares of the another sides.
		The area of triangle ABE is 30 and the area of triangle FEB is 6.
		Using the Pythagorean Theorm I found side x in triangle DBC to be 5 because the original length of side DB is 6 inits long, but since DE is 1 unit, then I subtracted 1 from 6 and found side x to be 5 units long.
	mathforum.org /geopow/fullsolutions/19980515.fullsolution.html (20575 words)

	Pythagorean Triples
		This is a Pythagorean triple since, as a triangle, is it just 3 times the 3-4-5 triangle (by which we mean that we just triple the lengths of each side of a 3-4-5 triangle, which we already know is right-angled).
		The length of the rope is the perimeter of the triangle.
		However, in any triangle the two shorter sides must add to more than the longest side or else the sides will not meet (think of the longest side as the base and the two shorter sides hinged at the ends of the base).
	www.mcs.surrey.ac.uk /Personal/R.Knott/Pythag/pythag.html (6303 words)

	numcom21 (Site not responding. Last check: 2007-11-02)
		The three numbers 3, 4, and 5 form what is called a Pythagorean set or Pythagorean triple since these three integers can represent (exactly) the sides of a right angled triangle for which Pythagoras' Theorem holds.
		This theorem states that for any right angled triangle the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.
		From your table you should notice that the two primitive triangles 21, 20, 29 and 35, 12, 37 have the same area, namely 210 square units.
	www.eng.um.edu.mt /~andebo/numbers/numcom21.htm (439 words)

	The CTK Exchange Forums (Site not responding. Last check: 2007-11-02)
		·The area of a Pythagorean triangle is always an integral number of units.
		In fact the area of a Pythagorean triangle is always a multiple of 6 units.
		·The area of a Pythagorean triangle cannot be a square number of units.
	www.cut-the-knot.com /htdocs/dcforum/DCForumID4/448.shtml (409 words)

	Mudd Math Fun Facts: Spherical Pythagorean Theorem
		In such a triangle, let C denote the length of the side opposite right angle.
		Verify the formula is true in some simple examples: such a triangle with two right angles formed by the equator and two longitudes.
		This formula is called the "Spherical Pythagorean Theorem" because the regular Pythagorean theorem can be obtained as a special case: as R goes to infinity, expanding the cosines using their Taylor series and manipulating the resulting expression will yield:
	www.math.hmc.edu /funfacts/ffiles/20006.2.shtml (293 words)

	Pythagorean Theorem/ Science in Ancient Artwork
		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.
		PROP.- In a progression of 3-4-5 right triangles, the cube of the shorter leg equals the sum of the cubes of the three sides of the right triangle inmediately preceding it on the progression.
	www.earthmatrix.com /Pitagor3.htm (638 words)

	Pythagorean Theorem
		Over 2,500 years ago, a Greek mathematician named Pythagoras developed a proof that the relationship between the hypotenuse and the legs is true for all right triangles.
		This problem could also be solved using the Pythagorean Triple 3, 4, 5.
		The ramp will allow packages to be loaded into an area of the truck that is too high to be reached from the ground.
	regentsprep.org /Regents/math/fpyth/Pythag.htm (295 words)

	Relations and sizes - Right triangle facts - First Glance (Site not responding. Last check: 2007-11-02)
		The right triangle is one of the most important geometrical figures, used in many applications for thousands of years.
		He treated each side of a right triangle as though it were a square and discovered that the total area of the two smaller squares is equal to the area of the largest square.
		where c is the hypotenuse and a and b are the other two legs of the triangle.
	www.math.com /school/subject3/lessons/S3U3L4GL.html (112 words)

	Lesson: Pythagorean Theorem (Site not responding. Last check: 2007-11-02)
		You might show students several different right triangles and then write the Pythagorean Theorem on the board and label the sides of the triangles according to the theorem.
		Using the Pythagorean Explorer applet, have students write down the measurements of four or five triangles, and then give them time to find the length of the missing angle.
		Have students work in groups of two or three to practice using the Pythagorean Theorem to find areas of triangles in the medium and hard levels of the Triangle Explorer.
	www.shodor.org /interactivate/lessons/pyth.html (963 words)

	THE PYTHAGOREAN TRIANGLE
		The numerical array to the left may be termed the Pythagorean Triangle.
		In the special case where (n) equals there is no diagonal displacement of the sequence, it is included completely in a given row, and the sum of the sequence equals the mid-sequence number times it self, it's square.
		As seen here to the right, the rows of beads on the rods of the rectangular array revealed between two triangular arrays, with bases of three beads, corresponds to the row of numbers in the Pythagorean Triangle with the mid-sequence number three.
	www.pythabacus.com /pythagorean_triangle.htm (486 words)

	ipedia.com: Triangle Article (Site not responding. Last check: 2007-11-02)
		For alternate meanings, such as the musical instrument, see triangle.
		A triangle is one of the basic shapes of geometry : a two-dimensional figure with three vertices and three sides which are straigh...
		For alternate meanings, such as the musical instrument, see triangle (disambiguation).
	www.ipedia.com /triangle.html (1799 words)

	Mathematics, Pythagorean Triangle (Site not responding. Last check: 2007-11-02)
		A device for automatically working out the length of the hypotenuse of a triangle after the length of the two legs has been set.
		The Pythagorean theorem states that the length of the hypotenuse of a right triangle is equal to the square root of the sum of the squares of the other two legs.
		This is a place holder for work, coming soon.
	www.hineslab.com /MathPythagoreanTriangle.html (120 words)

	Riverdeep \| Destination Math \| MSC V \| Exploring the Pythagorean Theorem
		Leo is putting the finishing touches to the weather satellite at the Rockridge Weather Research Center.
		Identify the hypotenuse of each of 3 right triangles.
		Identify the hypotenuse in a right triangle and apply the Pythagorean theorem.
	www.riverdeep.net /math/destination_math/dm_tools/coursev/msc5_3.11.jhtml (135 words)

	HBNweb.de Pythagorean Triples b=(a²/m - m)/2 c=b+m Pythagorean Triplets
		HBNweb.de Pythagorean Triples b=(a²/m - m)/2 c=b+m Pythagorean Triplets
		Only if a is a prime number or the double of them,
		= radius of the incircle of the pythagorean triangle
	www.hbnweb.de /pythagoras/pythagoras.html (119 words)

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