Pythagorean Triples
There is an infinity amount of Pythagorean Triples. A Pythagorean Triple is any three whole numbers that satisfy the equation a² + b²= c², also known as the Pythagorean theorem. In this equation a and b are the legs of a right triangle, and c is the hypotenuse. An example of a Pythagorean Triple 3,4,5 since 3² is 9 and 4² is 16. So the sum is 25 and 5² is also 25, and that satisfies the equation. This is also the smallest Pythagorean Triple. This triple can be found with the converse of Pythagorean theorem, but most Pythagorean Triples can be found with other equations. Most Pythagorean Triples are relatively prime or redu
The ancient Babylonians had found a formula to generate Pythagorean triples on this since they recorded some systematic tables involving huge triples on clay tablets, which have been unearthed and deciphered this century. One given by both Pythagoras and the Babylonians is (2m, (m²-1) , (m² +1)). ced triples, and only have 1 as a common factor since other triples can be made from the primitives. This equation does not necessarily pertain to primitive triples. This equation is like the one given by Pythagoras, but it is different since each term is squared. One of the sides must also be divisible by 3, and another side must also be divisible by 5. Attempts to find formulas for Pythagorean Triples have been dated back thousands of years ago. An example that follows all of these rules for a Pythagorean triple is the triple 5, 12, 13. Another rule is that the legs of the right triangle must also be divisible by 12, and the product of all three sides must also by divisible by 60. C, also known as the hypotenuse must always be odd. There have also been many equations that have been given by different people to generate Pythagorean Triples. This equation can get coprime triples like ka, kb, and kc. Another equation given by Plato is (2m²,(m²-1)²,(m²+1)²). There are many formulas to generate triples, one of the more famous ones is by Pythagoras.
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