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# What is a pythagorean triple

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What is a pythagorean triple

Apr 21, 2015

#2
+20842
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What is a pythagorean triple

https://commons.wikimedia.org/wiki/File:Pythagorean.svg#/media/File:Pythagorean.svg

A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k.

Generating a triple:

A fundamental formula for generating Pythagorean triples given an arbitrary pair of positive integers m and n with m > n. The formula states that the integers

$$a = m^2 - n^2 ,\ \, b = 2mn ,\ \, c = m^2 + n^2$$

or

$$a = k\cdot(m^2 - n^2) ,\ \, b = k\cdot(2mn) ,\ \, c = k\cdot(m^2 + n^2)$$

form a Pythagorean triple.

Example:

$$\\ \text{If } m=2 \text{ and } n = 1:\\ a= 2^2-1^2 =4 - 1 = 3 \\ b = 2\cdot 2 \cdot 1 = 4 \\ c = 2^2 + 1^2 = 4+1=5$$

Pythagorean triple (3, 4, 5), because $$\small{\text{3^2+4^2=5^2}}$$

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Apr 22, 2015

#1
+1191
+5

A Pythagorean Triple is a group of three numbers that satisfy the Pythagorean Theorem, a^2+b^2=c^2.

Examples would be 3-4-5,6-8-10,7-24-25,8-15-17,16-30-34... you get the idea.

There's an infinite amount of Pythagorean Triples, though.

Apr 21, 2015
#2
+20842
+5

What is a pythagorean triple

https://commons.wikimedia.org/wiki/File:Pythagorean.svg#/media/File:Pythagorean.svg

A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k.

Generating a triple:

A fundamental formula for generating Pythagorean triples given an arbitrary pair of positive integers m and n with m > n. The formula states that the integers

$$a = m^2 - n^2 ,\ \, b = 2mn ,\ \, c = m^2 + n^2$$

or

$$a = k\cdot(m^2 - n^2) ,\ \, b = k\cdot(2mn) ,\ \, c = k\cdot(m^2 + n^2)$$

form a Pythagorean triple.

Example:

$$\\ \text{If } m=2 \text{ and } n = 1:\\ a= 2^2-1^2 =4 - 1 = 3 \\ b = 2\cdot 2 \cdot 1 = 4 \\ c = 2^2 + 1^2 = 4+1=5$$

Pythagorean triple (3, 4, 5), because $$\small{\text{3^2+4^2=5^2}}$$

heureka Apr 22, 2015