A triangle with sides of lengths 3, 4 and 5. Note that no units are mentioned here -- so pick your favourite units, and any similar triangles will also be 3-4-5 triangles.

Due to the pythagorean theorem, this is a right triangle. So if you need to construct a right angle in the field, use the power of 3-4-5! (Egyptian surveyors apparently did just that.)

It is the right triangle with smallest integer sides, and as so is (justly) famous! This marriage of geometry (a right triangle) and arithmetic (a requirement for integer solutions) is the first Diophantine equation.

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