# Mat 126 Week 4 - Pythagorean Triples

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Pythagorean Triples MAT126 : Survey of Mathematical Methods Pythagorean Triples A Pythagorean triple is any 3 numbers that can be represented by a^2 + b^2 = c^2. There are many different methods for obtaining a Pythagorean triple and there are also an infinite amount of Pythagorean triples. There are four popular formulas for generating a Pythagorean triple such as Euclid’s method, Pythagoras’, Plato’s and Fibonacci’s. In order to generate a Pythagorean triple, choose two positive integers, square them, and the outcome would give you the squared total of the sum. One example of a Pythagorean triple would be (8, 15, 17) or 8^2 + 15^2 = 17^2 or 8^2=64, 15^2=225 and 17^2=289. This method results in 64+225=289, thus meaning 8, 15, and 17 is a Pythagorean triple. As I stated before, there are an infinite amount of Pythagorean triples than can be generated. Another Pythagorean triple would be 12, 35, and 37. When using the formula to create Pythagorean triples, 144 + 1,225 = 1,369. One can see that 12^2 + 35^2 = 37^2, resulting in a Pythagorean triple. Another Pythagorean triple would be 36, 77, and 85 and can be double checked by stating 36^2=1,296, 77^2=5,929, and 85^2=7,225. By adding 1,296+5,929 the sum is equal to 7,225 which the square root is equal to 85 or 36^2 + 77^2 = 85^2. As I stated earlier, there are an infinite number of Pythagorean triples so the numbers can of course be very high numbers and not only small, or single/double digit numbers. Another example would be 39, 760 and 761. When using the formula for Pythagorean triples you will see 39^2=1,521, 760^2=577,600, 761^2=579,121 or 1,521+577,600=579,121. For the fifth and final example of a Pythagorean triple I will use the combination of 44, 483, and 485. By writing these out in the formula, one will get 44^2=1,936, 483^2=233,289, 485^2=235,225 or 1,936+233,289=235,225 (44^2 + 482^2 =