Pythagorean triple facts for kids

A Pythagorean triple is a special group of three positive integers (whole numbers) that work together in a specific equation. This equation is:

This means if you take the first number, multiply it by itself (square it), and add it to the second number multiplied by itself, you will get the third number multiplied by itself. This idea is closely connected to Pythagoras' theorem, which you might learn about in geometry!

The smallest and most famous Pythagorean triple is [3, 4, 5]. Let's see why:

Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): 3^2 + 4^2 = 9 + 16 = 25

And Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): 5^2 = 25 . So, is true!

Other examples of Pythagorean triples include [5, 12, 13] and [7, 24, 25]. There are actually an endless number of these triples!

What Makes a Pythagorean Triple?

Pythagorean triples always follow certain patterns with odd and even numbers:

• They can have all even numbers.
• They can have two odd numbers and one even number.

What they can never be is:

• All odd numbers.
• Two even numbers and one odd number.

Images for kids

• 

  Animation demonstrating the simplest Pythagorean triple, 3² + 4² = 5².

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  This Scatter plot shows many Pythagorean triples. The lines you see are because if (a, b, c) is a triple, then (2a, 2b, 2c) or (3a, 3b, 3c) are also triples!

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  This image shows how triples look when plotted on a 3D graph, forming part of a cone shape.

See also

In Spanish: Terna pitagórica para niños