Pythagorean Triple And Its Formula

The Pythagorean triple is derived from the Pythagorean theorem. The theorem states that the sides of the right angle triangle must satisfy the formula “a^2 + b^2 = c^2”. However, with the help of the Pythagorean triple the three sides of the triangle can be easily determined. This theorem is famous from the ancient times and the oldest record can be received from the Plimpton 322.

The Plimpton 322 which is a Babylon tablet made up of clay and it is present from 1800 BC. The number system which is used to write upon it is known as the sexagesimal number system. This number system was discovered by Edgar James Banks after the year of 1900 and it was sold out to the George Arthur Plimpton in the year of 1922. There is a primitive Pythagorean triple where there are three sides a, b and c which are coprime. the triangle whose sides takes the formation of Pythagorean triple is known as Pythagorean triangle. the triangle is compulsorily a right angled triangle. There is various formula that is used for generating the Pythagorean triples. The primitive triples which is present arises with the help or rather exchange of a and b, in case where ‘a’ is even. Since the time of Euclid there are different formulas which are developed and introduced to generate the triples. The three variables a, b and c, there is exactly one variable which is odd, divisible by 3,4 and 5. The largest number that can divide the triples that is ‘abc’ is 60. The acute angles present in the Pythagorean theorem can be w a rational number of degrees. This is related with the Niven’s theorem.

The formula for the Pythagorean theorem is a^2 + b^2 = c^2.  The three variables are the positive integers. For example, suppose there is a smallest Pythagorean triple which is 3,4 and 5.

According to the theorem a^2 + b^2 = c^2

Therefore, 3^2+4^2=5^2

     9+16=25

Yes, the above triples is a Pythagorean triples. it can be stated that when the triples are Pythagorean triples that the triangle is a right angled triangle. In order to create the Pythagorean triples all the set of triples need to scaled up. There are different formulas which is used to describe the Pythagorean triples. The formulas are the Plato’s and Euclid formulas. There are certain special cases related with the Pythagorean triples. Each and every integer greater than 2 is a part of the primitive or the non- primitive Pythagorean triples. If there is natural number, then there is presence of k Pythagorean triples all of them having different hypotenuse with the same area. There are different types of Pythagorean triangles. There are no such non- primitive Pythagorean triangles where there is an integer altitude from the hypotenuse. This type of Pythagorean triangle is known as the decomposable as they can be easily separated and form two separate Pythagorean triangles. The altitude of the two triangles are the same. However, the Pythagorean triple is one of the oldest formula

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