Triples

Pythagorean triads

Pythagorean Triples
Pythagorean triples are made up of three positive integers a, b, c verbal expressionted as: a2 + b2 = c2. agree to the Pythagorean Theorem a right trilateral having human face a and b and hypotenuse c, satisfies a2 + b2 = c2. The Pythagorean Theorem states for any right trilateral, the sum of the squares of the continuance of the legs of a right triangle is equal to the squares of the length of the hypotenuse (the side opposite the right angle) (Bluman 2008).  A simplified explanation that I found easy to follow is that 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.  apply a set of positive integers, the smallest example, 32 + 42 = 52, when mensural becomes: 9 + 16 = 25, which we know to be true.



By intimate that smallest equation and building on it by doubling or tripling the number values we can create spare triples; the results produce endless possibilities:
62 + 82 = 102 or: 36 + 64 = 100
122 + 162 = 202 or 144 + 256 = 400
242 + 362 = 402 or 576 + 1296 = 1600
One way to create Pythagorean Triples is by using the following formula derived by Euclid (Ross 2009):
A = 2mn B = m2 n2 C = m2 + n2
Substituting 5 for m and 2 for n:
A= 2x5x2
A = 20
B= 52 - 22
B = 25 4
B = 21
C = 52 + 22
C = 25 + 4
C = 29
Thus, {20, 21, 29} is a Pythagorean Triple. Proof of this equation by using the Pythagorean Theorem is as follows:
a2 + b2 = 202 + 212 = 841
c2 = 292 = 841
Substituting 6 for m and 2 for n:
A= 2x6x2
A =24
B= 62 - 22
B = 36 4
B = 32
C = 62 + 22
C = 36 + 4
C = 40
{24, 32, 40} is a Pythagorean Triple and proof of this equation by using the Pythagorean Theorem is as follows:
a2 + b2 = 242 + 322 = 1600
c2 = 402 = 1600

Substituting 4 for m and 1 for n:
A= 4x1x2
A = 8
B= 42 - 12
B = 16 - 1
B =15
C = 42 + 12
C = 16 + 1
C = 17
{8, 15, 17} is a Pythagorean Triple....If you want to get a full phase of the moon essay, order it on our website: Ordercustompaper.com



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