Pythagorean triple facts for kids

In Mathematics, a Pythagorean triple is a set of three positive integers which satisfy the equation (make the equation work):

x^2 + y^2 = z^2

This equation is known as the Diophantine equation, and is related to Pythagoras' theorem. The lowest Pythagorean triple is [3, 4, 5] because:

3^2 + 4^2 = 9 + 16 = 25 = 5^2

So,

3^2 + 4^2 = 5^2

The next highest triple is [5, 12, 13] then [7, 24, 25], and so on. There is an infinite number of Pythagorean triples.

A Pythagorean Triple always consists of:

• all even numbers, or

• two odd numbers and an even number.

A Pythagorean Triple can never be made up of all odd numbers or two even numbers and one odd number.

Images for kids

Animation demonstrating the simplest Pythagorean triple, $32 + 4 2 = 5 2$ .
Scatter plot of the legs ( $a$ , $b$ ) of the first Pythagorean triples with $a$ and $b$ less than 6000. Negative values are included to illustrate the parabolic patterns. The "rays" are a result of the fact that if $(a, b, c)$ is a Pythagorean triple, then so is $(2 a, 2 b, 2 c)$ , $(3 a, 3 b, 3 c)$ and, more generally, $(ka, kb, kc)$ for any positive integer $k$ .
A plot of triples generated by Euclid's formula maps out part of the $z 2 = x 2 + y 2$ cone. A constant $m$ or $n$ traces out part of a parabola on the cone.