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What is a pythagorean triple 

 Apr 21, 2015

Best Answer 

 #2
avatar+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 $$\small{\text{$3^2+4^2=5^2$}}$$

.
 Apr 22, 2015
 #1
avatar+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
avatar+20842 
+5
Best Answer

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

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