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# The Pythagorean Theorem

School Project

by

Tweet## Momo Sohma

on 19 March 2013#### Transcript of The Pythagorean Theorem

Pre-Algebra 7

Period 1 The Pythagorean Theorem Fact 2 Fact 4 Why We Chose This Topic The theorem can be represented by an equation and solved with algebra.

a^2 + b^2 = c^2

For example: a is 3, b is 4, c is 5. The equation would be

3^2 + 4^2 = 5^2. Fact 3 The Pythagorean Theorem is Pythagoras' most famous contribution to math. Pythagoras had an influence on the work of Plato, who had a great influence on Western philosophy. We chose to do our project on the Pythagorean Theorem because we recognized it as something our friend talks about sometimes. We thought it would be interesting to learn about it. References How This Relates To The Real World Today Fact 5 A Pythagorean triple is three positive integers (a,b,c) that are the triangle's sides. A Pythagorean triangle is a triangle whose sides form a Pythagorean triple. Fact 1 The Pythagorean Theorem is a theory stating that the length of the hypotenuse of a right triangle is equal to the sum of the lengths of the squares of the other sides. It can be used to find the length of a right triangle's hypotenuse. The Pythagorean Theorem can be used in a situation when trying to determine the minimum distance from where you are to where you to be. "...if you watch a baseball outfielder make a catch, or a football player make a tackle, they have in effect used the Pythagorean Theorem to judge the minimum distance between where they started, and where they needed to be," (PUzzled). Fact 6 http://jwilson.coe.uga.edu/emt669/student.folders/morris.stephanie/emt.669/essay.1/pythagorean.html http://www.herenow4u.net/index.php?id=76960 http://en.wikipedia.org/wiki/Pythagoras http://www.mnsu.edu/its/started/website/krypton/ The Pythagorean theory can be proved by an algebraically by four right triangles that are the same size and arrange them with sides a, b and c, arranged inside a square with side c as in the top half. "The triangles are similar with area , while the small square has side b − a and area (b − a)^2. The area of the large square is therefore

(b − a)^2 + 4 x a/b = a^2 +b^2.

But this is a square with side c and area c^2, so

c^2 = a^2 + b^2," (Wikipedia contributors). http://en.wikipedia.org/wiki/Pythagorean_triples http://www.mathsisfun.com/pythagoras.html http://www.mathsisfun.com/pythagoras.html http://www.mathsisfun.com/pythagoras.html http://en.wikipedia.org/wiki/Pythagoras’_theorem http://en.wikipedia.org/wiki/Pythagoras’_theorem http://mathandmultimedia.com/2010/02/03/pythagorean-theorem/ http://ncalculators.com/number-conversion/pythagoras-theorem.htm Calcutta University, . "Pythagoras: The Vegetarian." HereNow4U. N.p., 21 Feb 2011. Web. 15 Mar 2013. <http://www.herenow4u.net/index.php?id=76960>.

"Pythagoras Theorem." Math is Fun. N.p., n.d. Web. 15 Mar 2013. <http://www.mathsisfun.com/pythagoras.html>.

"Pythagorean Theorem Calculator." Calculators. N.p., n.d. Web. 15 Mar 2013. <http://ncalculators.com/number-conversion/pythagoras-theorem.htm>.

Morris, Stephanie. "The Pythagorean Theorem." The University of Georgia Department of Mathematics Education. N.p.. Web. 15 Mar 2013. <http://jwilson.coe.uga.edu/emt669/student.folders/morris.stephanie/emt.669/essay.1/pythagorean.html>.

Wikipedia contributors. "Pythagoras." Wikipedia, The Free Encyclopedia. 26 February 2013. <http://en.wikipedia.org/wiki/Pythagoras>.

PUzzled, . "How does Pythagorean Theorem relate to real life?." Yahoo! Answers. N.p., n.d. Web. 19 Mar 2013. <http://answers.yahoo.com/question/index?qid=20090522134955AAfcXDj>.

Wikipedia contributors. "Pythagorean triple." Wikipedia, The Free Encyclopedia. 21 February 2013. <http://en.wikipedia.org/wiki/Pythagorean_triples>.

"Plato’s Metaphysics." . N.p.. Web. 19 Mar 2013. <http://www2.palomar.edu/users/jfmartin/adobe/knowledge/plato_metaphysics.pdf>.

"Pythagorean Triples." Math is Fun. N.p., n.d. Web. 19 Mar 2013. <http://www.mathsisfun.com/pythagorean_triples.html>. (Information and Images) http://site.aace.org/sitevideo/math.cfm http://www.giantitp.com/forums/showthread.php?t=39392 http://answers.yahoo.com/question/index?qid=20090522134955AAfcXDj In all, there are eight ideas of Pythagoras' that influenced Plato. http://www2.palomar.edu/users/jfmartin/adobe/knowledge/plato_metaphysics.pdf Example: a = 5, b = 12, and c = 13. The equation is 5^2 + 12^2 =13^2. Simplified it becomes 25 + 144 = 169 http://www.mathsisfun.com/pythagorean_triples.html http://www.mathsisfun.com/pythagorean_triples.html However, he is also known to have discovered numerical ratios that cause harmony in music. http://www2.palomar.edu/users/jfmartin/adobe/knowledge/plato_metaphysics.pdf

Full transcriptPeriod 1 The Pythagorean Theorem Fact 2 Fact 4 Why We Chose This Topic The theorem can be represented by an equation and solved with algebra.

a^2 + b^2 = c^2

For example: a is 3, b is 4, c is 5. The equation would be

3^2 + 4^2 = 5^2. Fact 3 The Pythagorean Theorem is Pythagoras' most famous contribution to math. Pythagoras had an influence on the work of Plato, who had a great influence on Western philosophy. We chose to do our project on the Pythagorean Theorem because we recognized it as something our friend talks about sometimes. We thought it would be interesting to learn about it. References How This Relates To The Real World Today Fact 5 A Pythagorean triple is three positive integers (a,b,c) that are the triangle's sides. A Pythagorean triangle is a triangle whose sides form a Pythagorean triple. Fact 1 The Pythagorean Theorem is a theory stating that the length of the hypotenuse of a right triangle is equal to the sum of the lengths of the squares of the other sides. It can be used to find the length of a right triangle's hypotenuse. The Pythagorean Theorem can be used in a situation when trying to determine the minimum distance from where you are to where you to be. "...if you watch a baseball outfielder make a catch, or a football player make a tackle, they have in effect used the Pythagorean Theorem to judge the minimum distance between where they started, and where they needed to be," (PUzzled). Fact 6 http://jwilson.coe.uga.edu/emt669/student.folders/morris.stephanie/emt.669/essay.1/pythagorean.html http://www.herenow4u.net/index.php?id=76960 http://en.wikipedia.org/wiki/Pythagoras http://www.mnsu.edu/its/started/website/krypton/ The Pythagorean theory can be proved by an algebraically by four right triangles that are the same size and arrange them with sides a, b and c, arranged inside a square with side c as in the top half. "The triangles are similar with area , while the small square has side b − a and area (b − a)^2. The area of the large square is therefore

(b − a)^2 + 4 x a/b = a^2 +b^2.

But this is a square with side c and area c^2, so

c^2 = a^2 + b^2," (Wikipedia contributors). http://en.wikipedia.org/wiki/Pythagorean_triples http://www.mathsisfun.com/pythagoras.html http://www.mathsisfun.com/pythagoras.html http://www.mathsisfun.com/pythagoras.html http://en.wikipedia.org/wiki/Pythagoras’_theorem http://en.wikipedia.org/wiki/Pythagoras’_theorem http://mathandmultimedia.com/2010/02/03/pythagorean-theorem/ http://ncalculators.com/number-conversion/pythagoras-theorem.htm Calcutta University, . "Pythagoras: The Vegetarian." HereNow4U. N.p., 21 Feb 2011. Web. 15 Mar 2013. <http://www.herenow4u.net/index.php?id=76960>.

"Pythagoras Theorem." Math is Fun. N.p., n.d. Web. 15 Mar 2013. <http://www.mathsisfun.com/pythagoras.html>.

"Pythagorean Theorem Calculator." Calculators. N.p., n.d. Web. 15 Mar 2013. <http://ncalculators.com/number-conversion/pythagoras-theorem.htm>.

Morris, Stephanie. "The Pythagorean Theorem." The University of Georgia Department of Mathematics Education. N.p.. Web. 15 Mar 2013. <http://jwilson.coe.uga.edu/emt669/student.folders/morris.stephanie/emt.669/essay.1/pythagorean.html>.

Wikipedia contributors. "Pythagoras." Wikipedia, The Free Encyclopedia. 26 February 2013. <http://en.wikipedia.org/wiki/Pythagoras>.

PUzzled, . "How does Pythagorean Theorem relate to real life?." Yahoo! Answers. N.p., n.d. Web. 19 Mar 2013. <http://answers.yahoo.com/question/index?qid=20090522134955AAfcXDj>.

Wikipedia contributors. "Pythagorean triple." Wikipedia, The Free Encyclopedia. 21 February 2013. <http://en.wikipedia.org/wiki/Pythagorean_triples>.

"Plato’s Metaphysics." . N.p.. Web. 19 Mar 2013. <http://www2.palomar.edu/users/jfmartin/adobe/knowledge/plato_metaphysics.pdf>.

"Pythagorean Triples." Math is Fun. N.p., n.d. Web. 19 Mar 2013. <http://www.mathsisfun.com/pythagorean_triples.html>. (Information and Images) http://site.aace.org/sitevideo/math.cfm http://www.giantitp.com/forums/showthread.php?t=39392 http://answers.yahoo.com/question/index?qid=20090522134955AAfcXDj In all, there are eight ideas of Pythagoras' that influenced Plato. http://www2.palomar.edu/users/jfmartin/adobe/knowledge/plato_metaphysics.pdf Example: a = 5, b = 12, and c = 13. The equation is 5^2 + 12^2 =13^2. Simplified it becomes 25 + 144 = 169 http://www.mathsisfun.com/pythagorean_triples.html http://www.mathsisfun.com/pythagorean_triples.html However, he is also known to have discovered numerical ratios that cause harmony in music. http://www2.palomar.edu/users/jfmartin/adobe/knowledge/plato_metaphysics.pdf