# Investigating Pythagoras

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Investigating Pythagoras Introduction ============ [IMAGE]For this piece of work I am investigating Pythagoras. Pythagoras was a Greek mathematician. Pythagoras lived on the island of Samos and was born around 569BC. He did not write anything but he is regarded as one of the world's most important characters in maths. His most famous theorem is named after him and is called the Pythagoras Theorem. It is basically aÂ²+bÂ²=cÂ². This is what the coursework is based on. I am going to look at the patterns, which surround this theorem and look at the different sequences that can be formed. The coursework The numbers 3, 4 and 5 satisfy the condition 3Â²+4Â²=5Â² because 3Â²=3x3=9 4Â²=4x4=16 5Â²=5x5=25 And so 3Â²+4Â²=9+16=25=5Â² I will now check that the following sets of numbers also satisfy the similar condition of (smallest number) Â²+(middle number) Â²=(largest number) Â² a) 5, 12, 13 5Â²=5x5=25 12Â²=12x12=144 25+144=169 âˆš169 = 13 This satisfies the condition as 5Â²+12Â²=25+144=169=13Â² b) 7, 24, 25 7Â²=7x7=49 24Â²=24x24=576 49+576=625 âˆš625=25 This satisfies the condition as 7Â²+24Â²=49+576=625=25Â² The numbers 3,4 and 5 can be the lengths - in appropriate units - of the side of a right-angled triangle. [IMAGE] 5 3 [IMAGE] The perimeter and area of this triangle are: Perimeter = 3+4+5=12 units Area = Â½x3x4=6 units Â² [IMAGE] The numbers 5,12,13 can also be the lengths - in appropriate units - of a right-angled triangle. [IMAGE] Perimeter = 5+12+13=30 Area=Â½x5x12=30 [IMAGE] This is also true for the numbers 7,24,25 [IMAGE] Perimeter = 7+24+25=56 Area=Â½x7x24=84 I have put these results into a table to see if I can work out any patterns. Length of shortest side Length of middle side Length of longest side Perimeter