If p and q are integers, then
a = p2 - q2
b = 2pq, and
c = p2 + q2
form a Pythagorean triple.
Furthermore, if p and q are co-prime then the triple is primitive Pythagorean.
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Let's try it out: 152 + 362 = 392 225 + 1296 = 1521 1521 = 1521 That is a pythagorean triple.
If the lengths of the sides of the triangle can be substituted for 'a', 'b', and 'c'in the equationa2 + b2 = c2and maintain the equality, then the lengths of the sides are a Pythagorean triple, and the triangle is a right one.
3,4,5 1,2,3 these are sets of pythagorean triples
The Pythagorean Theorem allows the mathematician to determine the value of the hypotenuse. The converse of the Pythagorean Theorem manipulates the formula so that the mathematician can use the values to determine that if the triangle is a right triangle.
'Pythagorean' is the 'adjective for 'Pythagoras'. {ythagoras was a Classical Greek mathematician who gave us the equation h^2 = a^(2) + b^(2) . In words, 'The square of the hypotenuse(h) is equal to the sum of the other two sides squared'. NB This only applies to 'right-angled' triangles (trigons).