SampleWritingAssignment

SampleWritingAssignment - For example, 3, 4, 5 6, 8, 10...

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Sample Writing Assignment: Pythagorean Theorem by Gwen Fisher Write about the Pythagorean Theorem. First, we start with a statement of the theorem: Let ABC be a right triangle with sides of lengths a , b , and c . Let the sides with lengths a and b be the legs, and let c be the hypotenuse. Then a ^2 + b ^2 = c ^2. Also, if a ^2 + b ^2 = c ^2, then ABC is a right triangle. c A a b C B An illustration of the theorem is shown with the picture below. c A a b C B The theorem tells us that if the angle at C is a right angle then the sum of the areas of the squares with sides a and b is equal to the area of the square with sides c . We can give some examples of the theorem. 3^2 + 4^2 = 5^2, so a square with sides of length 3, 4, and 5 is a right triangle. Similarly 5, 12, 13 is the side lengths of a right triangle. These sets of numbers are called Pythagorean Triples. Also, all multiples of Pythagorean Triples are Pythagorean triples.
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Unformatted text preview: For example, 3, 4, 5 6, 8, 10 (times 2) 9, 12, 15 (times 3) 1.5, 2, 2.5 (times 0.5) These are all Pythagorean Triples. Lets see what happens if we have a triangle that is not a right triangle. I know that equilateral triangles are not right. So if I take a triangle with sides all 1 and I try to use the Pythagorean Theorem, I get 1^2 + 1^2 = 1^2 or 2 = 1, which is nonsense. So I have shown that if a triangle does not have a right angle, then we do not always get a ^2 + b ^2 = c ^2. If I know any two sides of a right triangle, then I can always find the third. Lets see what happens if we fix a = 1 b x 0 1 2 3 4 5 6 7 8 c ( x ^2 + 1) 1 2 3 2 5 6 7 8 3 So if a = 1, then we can think of c as a function of b , namely c is f ( x ) = ( x ^2 + 1). b or x c or f ( x ) (Note that this is about 350 words.)...
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This note was uploaded on 01/12/2010 for the course MATH 247 taught by Professor F,newberger during the Spring '03 term at Stanford.

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SampleWritingAssignment - For example, 3, 4, 5 6, 8, 10...

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