Pythagorean triangle

1 6.1

Triangle with a right angle whose sides are whole numbers and follow a^2 + b^2 = c^2

noun
/ˌpaɪθəˈɡɔriən ˈtraɪæŋɡəl/

Specialized

: triángulo pitagórico

A Pythagorean triangle has integer side lengths that follow the equation a² + b² = c².

Examples

Mathematicians study the properties of Pythagorean triangles for number theory research.
The (3, 4, 5) triangle is a classic example of a Pythagorean triangle.
She showed how to construct a new Pythagorean triangle with different integer side lengths.
A Pythagorean triangle has sides of integer lengths.
The lengths of the sides in a Pythagorean triangle must satisfy a² + b² = c².
In mathematics, a Pythagorean triangle is formed when the lengths of the sides correspond to the Pythagorean theorem.
To construct a Pythagorean triangle, you can use the side lengths 3, 4, and 5.

Surface Forms

Pythagorean triangle singular

Pythagorean triangles plural

Morphology

Pythagorean + triangle

The headword 'triangle' gives the basic shape, and 'Pythagorean' signals a relation to Pythagoras/the Pythagorean theorem, so a learner could infer this is a special kind of triangle (likely a right triangle). However, the precise mathematical constraint (integer side lengths satisfying a² + b² = c²) is specialized and not fully predictable from the constituents, making the expression only partially transparent to a B1 learner.

Etymology

Pythagorean triangle is named after the Greek mathematician Pythagoras, who showed that in a 'right triangle' the square of the long side equals the sum of the squares of the two short sides. That's why a Pythagorean triangle is a 'right triangle' whose side lengths are 'whole numbers' that fit that rule, and the simple 3, 4, 5 triangle gives a clear image to remember it.