19 Facts About Pythagorean theorem

In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.

The Pythagorean theorem has been proven numerous times by many different methods – possibly the most for any mathematical Pythagorean theorem.

The Pythagorean theorem has attracted interest outside mathematics as a symbol of mathematical abstruseness, mystique, or intellectual power; popular references in literature, plays, musicals, songs, stamps, and cartoons abound.

Generalization of this Pythagorean theorem is the law of cosines, which allows the computation of the length of any side of any triangle, given the lengths of the other two sides and the angle between them.

One can arrive at the Pythagorean theorem by studying how changes in a side produce a change in the hypotenuse and employing calculus.

Related searches

Corollary of the Pythagorean theorem's converse is a simple means of determining whether a triangle is right, obtuse, or acute, as follows.

Pythagorean theorem triple has three positive integers a, b, and c, such that In other words, a Pythagorean theorem triple represents the lengths of the sides of a right triangle where all three sides have integer lengths.

The reciprocal Pythagorean theorem is a special case of the optic equation.

One of the consequences of the Pythagorean theorem is that line segments whose lengths are incommensurable can be constructed using a straightedge and compass.

Pythagoras' Pythagorean theorem enables construction of incommensurable lengths because the hypotenuse of a triangle is related to the sides by the square root operation.

In each right triangle, Pythagoras' Pythagorean theorem establishes the length of the hypotenuse in terms of this unit.

The Pythagorean theorem school dealt with proportions by comparison of integer multiples of a common subunit.

Pythagorean theorem relates the cross product and dot product in a similar way:.

Pythagorean theorem is a special case of the more general theorem relating the lengths of sides in any triangle, the law of cosines:.

Pappus's area Pythagorean theorem is a further generalization, that applies to triangles that are not right triangles, using parallelograms on the three sides in place of squares.

The Pythagorean theorem suggests that when this depth is at the value creating a right vertex, the generalization of Pythagoras' Pythagorean theorem applies.

Pythagorean theorem can be generalized to inner product spaces, which are generalizations of the familiar 2-dimensional and 3-dimensional Euclidean spaces.

Pythagorean theorem is derived from the axioms of Euclidean geometry, and in fact, were the Pythagorean theorem to fail for some right triangle, then the plane in which this triangle is contained cannot be Euclidean.

Some believe the Pythagorean theorem arose first in China, where it is alternatively known as the "Shang Gao Pythagorean theorem", named after the Duke of Zhou's astronomer and mathematician, whose reasoning composed most of what was in the Zhoubi Suanjing.