|
||||||||||||||||
|
||||||||||||||||
|
|
|
|
PYTHAGOREAN TRIPLETS |
||||||||||||||||||||||
|
The sides of a right triangle follows the Pythagorean Theorem, a2 + b2 = c2 where a and b are the lengths of the legs of the right triangle while c is the length of the hypothenuse. A right triangle with sides of lengths 3, 4 and 5 is a special right triangle in that all the sides have whole number lengths. The three numbers 3, 4 and 5 forms a Pythagorean triplet or Pythagorean triple. A Pythagorean triplet is a set of three whole numbers where the sum of the squares of the first two is equal to the square of the third number. Below are examples of Pythagorean triplets:
One equation satisfying a Pythagorean Triplet A, B, C is Given A is odd, then B = (A2 - 1)/2 C = (A2 + 1)/2 Another equation derived by Plato was (m2+1)2 = (m2-1)2 + (2m)2 where m is a natural number. The above equation is called Plato's Formula. Euclid has also another method, namely: Given integers x and y, A = x2 - y2 B = 2xy C = x2 + y2
|
||||||||||||||||||||||
|
|
