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The Pythagorean Theorem. Spyros Karoris Wayne State University TED 6020 11/05/05. It is my great pleasure to bring to you the Pythagorean Theorem, this famous theorem is named for the philosopher and mathematician Pythagoras. So in
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The Pythagorean Theorem Spyros Karoris Wayne State University TED 6020 11/05/05 It is my great pleasure to bring to you the Pythagorean Theorem, this famous theorem is named for the philosopher and mathematician Pythagoras. So in the spirit off the Pythagorean Brotherhood, with their oath of autos ephe“he himself said” the secret cult of the Mathematikoi, let us proceed.
Home Page Click on the Text to go to an Area of Interest or click on the Next button • Who was Pythagoras • The Pythagorean Theorem • Proof • Baseball Problem
Pythagoras • Pythagoras was a philosopher and mathematician who lived in Southern Italy in the late 6th century B.C. • He believed that the earth was spherical and that the sun, moon, and planets move in relation to each other. • He is credited with “proving” the Pythagorean Theorem which is a formula that is used to find the lengths of the sides of right triangle. • His discoveries laid the groundwork for subsequent developments in geometry and mathematics.
Pythagorean Theorem • A triangle is called a right triangle if one of its angles is a right angle. In a right triangle, the side opposite the right angle is called the hypotenuse, and the other two sides are called the legs. • The Pythagorean Theorem: In any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. • This relationship can be stated as: c2 = a2 + b2 B c is the hypotenuse (c is opposite the right angle) a,b are the legs a c C A b
Proof To see other proofs of the Pythagorean Theorem, click on the link to go to this website: Pythagorean Theorem and its many proofs http://www.cut-the-knot.org/pythagoras/index.shtml
Baseball Problem The bases are loaded. It’s a long fly ball to center field. The ball bounces from ground and one of your team mates scoops it up and rockets the ball to you at second base. You turn to see the other team’s player rounding third base and headed for home plate! The crowd goes wild. It’s all up to you now at second base. Don’t panic, thanks to the Pythagorean Theorem you know exactly how far to throw the ball to get it from second base to home plate, and throw the runner out. You make the play and save the game!
Baseball Diamond We can use the Pythagorean Theorem to find the distance between second base and home plate. The baseball diamond is really a square, with right angles at each base. Draw a line from second base to home plate. We get a right triangle with the line as the hypotenuse. Use c2 = a2 + b2 to find the length of the hypotenuse. We know the length of the other two sides of the triangle, a = b = 90 ft. So we take the sum of the squares, c2 = (90 ft)2 + (90 ft)2 = 16200 ft2. Now we take the square root c = (16200 ft2)1/2 = 127.3 ft. Thus you need to throw the ball 127.3 ft to get it from second base to home plate.
Credits Pythagoras - Wikipedia, the free encyclopedia. http://en.wikipedia.org/wiki/Pythagoras Pythagoras of Samos Biography http://space.about.com/od/astronomerbiographies/a/pythagorasbio.htm Pythagorean Theorem -- From Mathworld http://mathworld.wolfram.com/PythagoreanTheorem.html Pythagorean Theorem - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Pythagorean_theorem Pythagorean Theorem and its many proofs http://www.cut-the-knot.org/pythagoras/index.shtml Baseball and the Pythagorean Theorem http://www.geom.uiuc.edu/~demo5337/Group3/bball.html This is a list of the sources I used in the presentation, click on a link to go to any of these websites. Here is another interesting link, click on it to go to this website: The Math Forum Home Page http://mathforum.org
