The Wizard of Oz
Scarecrow’s Speech on Pythagorean Theorem

The Pythagorean theorem is one of the earliest theorems known to ancient civilization. The well-known theorem is named after the Greek mathematician and philosopher, Pythagoras. In the Wizard of Oz, after the Scarecrow gets a brain, he states the Pythagorean theorem. However, he mistakenly says it applies to an isosceles triangle when it applies to a right triangle. He not only says the wrong triangle, he also gets the equation wrong. The Scarecrow says, “The sum of the square root of two sides of an isosceles triangle is equal to the square root of the third side.” The correct equation for the Pythagorean theorem is, “The sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.” The isosceles triangle is a triangle with at least two equal sides; it also has two equal angles. The Pythagorean theorem is a statement about triangles containing a right angle. A right triangle is a triangle with a ninety-degree angle. With the Pythagorean theorem, you take a triangle with a right angle and make a square on each of the three sides; the biggest square has the exact same area as the two other squares put together. A square root of a number is a value that can be multiplied by itself to give the original number. Here is an example of a square root; the square root of nine is three because when three is multiplied by itself you get nine. To square a number, you just THE WIZARD OF OZ3

multiply it by itself, as in the Pythagorean theorem. You can also square negative numbers, when you square a negative number you get a positive answer.
Although the Scarecrow got a brain from the wizard, he didn’t necessarily get the knowledge of having a brain. He messed up the Pythagorean theorem multiple times. He said that it had to do with square roots and isosceles triangles when the correct equation has to do with right...

...In mathematics, the Pythagoreantheorem — or Pythagoras' theorem — is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas, it states:
In any right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
The...

...Farhrenheit = 1.8 x (Celsius) + 32
8. The PythagoreanTheorem states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse. For example, if two sides of a right triangle have lengths 3 and 4, then the hypotenuse must have a length of 5. The integers 3, 4, and 5 together form a Pythagorean triple. There is an infinite number of such triples. Given two positive integers, m and n, where m > n, a...

...triangles have special properties which make it easier to conceptualize and calculate their parameters in many cases.
The side opposite of the right angle is called the hypotenuse. The sides adjacent to the right angle are the legs. When using the PythagoreanTheorem, the hypotenuse or its length is often labeled with a lower case c. The legs (or their lengths) are often labeled a and b.
Either of the legs can be considered a base and the other leg would be...

...Pythagorean Triples
Tammie Strohl
MAT 126
David Gualco
November 9, 2009
Pythagorean Triples
PythagoreanTheorem states that the sum of the areas of the two squares formed along the two small sides of a right angled triangle equals the area of the square formed along the longest.
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If a, b, and c are positive integers, they are together called Pythagorean Triples.
The smallest such Pythagorean...

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PythagoreanTheorem
In mathematics, the Pythagoreantheorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas, it states:
In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares...

...PythagoreanTheorem
Diana Lorance
MAT126
Dan Urbanski
March 3, 2013
PythagoreanTheorem
In this paper we are going to look at a problem that can be seen in the “Projects” section on page 620 of the Math in our World text. The problem discusses Pythagorean triples and asks if you can find more Pythagorean triples than the two that are listed which are (3,4, and 5) and (5,12, and 13) (Bluman, 2012). The...

...PYTHAGOREANTHEOREM
More than 4000 years ago, the Babyloneans and the Chinese already knew that a triangle with the sides of 3, 4 and 5 must be a right triangle. They used this knowledge to construct right angles. By dividing a string into twelve equal pieces and then laying it into a triangle so that one side is three, the second side four and the last side five sections long, they could easily construct a right angle.
A Greek scholar named Pythagoras, who...

...ancient Greek mathematician and philosopher. Pythagoras was responsible for important developments in the history of mathematics, astronomy, and the theory of music.
The thing that Pythagoras is probably the most famous for is the PythagoreanTheorem. The PythagoreanTheorem is used in the field of mathematics and it states the following: the square of the hypotenuse of a right triangle is equal to the sum of the squares of the two...