Could you please tell me what pythagoria triad is.I am a year 10 student.

thank you
Bob Ross

Hi Bob,

The usual terminology is PYTHAGOREAN TRIPLE. A Pythagorean triple is a set of three counting numbers (a, b, c) that satisfy the equation

a2 + b2 = c2

The name comes from the relationship of these numbers to the sides of right triangles -- the theorem of Pythagoras says that the sum of the squares on the sides of a right triangle equals the square on the hypotenuse. In other words, a Pythagorean triple gives the side lengths of a right triangle when those lengths are all integers. Familiar examples are (3, 4, 5), (6, 8, 10) and (5, 12, 13). Note that the numbers in the middle triple have a common divisor greater than 1 (namely 2), while the first and last have 1 as their greatest common divisor. Such Pythagorean triples are called "primitive." There is a simple way to list all primitive Pythagorean triples:

Choose two counting numbers r and s that satisfy

  1. 0 < r < s,

  2. r and s have no common divisor except 1, and

  3. one of them is odd, the other even.

If you set a = 2rs, b = s2 - r2, and c = s2 + r2, then (a, b, c) is a Pythagorean triple. Moreover, for every primitive Pythagorean triple you can work backwards and find such an r and s.

To test your understanding, you might want to make a complete list of all Pythagorean triples having a < b < c < 26. There are 8 triples in the list, four of which are primitive.

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