Pythagoras was born around 582 BC in Samos. He was a Greek philosopher and a mathematician. The theorem was discovered earlier in Egypt and Mesopotamia a 100 years before. For this reasons some people disagree with it being called Pythagoras’ Theorem.
Still Pythagoras was a respected mathematician and is known as the “father of mathematics.” The theorem compliments some religious beliefs that the state of the universe is split into ratios. Pythagoras proved that for any right angle triangle, the square of the length of the longest side is equal to the sum of the length on the other two sides. Set of three numbers that satisfy the rules of Pythagoras Theorem are called Pythagorean triple. e. g. The set 3, 4, 5 because 3 = 4 + 5 angled triangle.
Pythagoras’ Theorem can be stated as A B “In the right angled triangle the area of the square on the hypotenuse = the sum of the areas of the square on the other two sides” (smallest number^2) + (middle number^2) = (largest number^2) A^2 + B^2 = C^2 Aim: To investigate the family of Pythagorean triples where the shortest side is an odd number and all three sides are positive integers. (Proving The Formula Works a^2 + b^2 = c^2 a = 3, b = 4, c = 5 a^2 + b^2 = c^2 3^2 + 4 ^2 = c^2 9 + 16 = c^2 25 = c^2 5 = c 3, 4, 5 is a Pythagorean triple The perimeter = a + b + c Perimeter = 3 + 4 + 5 Perimeter = 12 units Area = 1/2 b h Area = 1/2 4 3 Area = 6 units^2 a = 5, b = 12, c = 13 a^2 + b^2 = c^2 5^2 + 12^2 = c^2 25 + 144 = c^2 169 = c^2 13 = c 5, 12, 13 is a Pythagorean triple The perimeter = a + b + c Perimeter = 5 + 12+13 Perimeter = 30 units Area = 1/2 b h Area = 1/2 12 5 Area = 30 units^2 a = 7, b = 24, c = 25 a^2 + b^2 = c^2 7^2 + 24^2 = c^2 49 + 576 = c^2 625 = c^2 25 = c The perimeter = a + b + c Perimeter = 7 + 25+26 Perimeter = 58 units Area = 1/2 b h Area = 1/2 25 7 Area = 87. 5 units^2 7, 24, 25 is a Pythagorean triple a = 9, b = 40, c = 41 a^2 + b^2 = c^2 9^2 + 40^2 = c^2 81 + 1600 = c^2 1681 = c^2 41 = c The perimeter = a + b + c Perimeter = 9 + 40 + 41 Perimeter = 90 units Area = 1/2 b h Area = 1/2 40 9 Area = 180 units^2 Below is a table of the information I have gathered so far Shortest Side B Middle Side C Longest side Perimeter Area 3 4 5 12 6 5 12 13 30 30 7 24 25 58 87.
The Essay on The Dark Side Of Kfc
The Dark Side of KFC The fastfood industry has globally conquered the market of fast-paced people who want instant service the moment they need it, wherever they are. Food primed and ready for cooking the moment a customer orders it has become the sustenance of most of the worlds workforce. Fastfood eating has spread from the United States to Europe and Australia up to the Africa including the ...
5 9 40 41 90 180 Finding The Shortest Side To find out the shortest term we have to look at the pattern from the table Number of term (n) 1 2 3 4 Shortest side Sequence 3 5 7 9 I have discovered that the first difference (2) is the same between each term. The formula would be 2 (the difference) multiplied by its term plus 1. Shortest side = 2 n + 1 If the term is 1 then the length is 3 2 n + 1 2 1 + 1 = 3 If the term is 2 then the length is 5 2 n + 1 2 2 + 1 = 5 If the term is 3 then the length is 7 2 n + 1 2 3 + 1 = 7 If the term is 4 then the length is 9 2 n + 1 2 4 + 1 = 9 If the term is 5 then the length is 11 2 n + 1 2 5 + 1 10 + 1 = 11 If the term is 6 then the length is 13 2 n + 1 2 6 + 1 12 + 1 = 13 If the term is 7 then the length is 15 2 n + 1 2 7 + 1 14 + 1 = 15.
