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Home > Pythagorean trigonometric identity

1 Proof

Or:

Note

The reason for:

is that any number, when divided by itself, is equal to one.

2 See also

• Trigonometric identity

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Topics: Pythagorean Trigonometric Identity Number Equal Angle Reason...

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Pythagorean theoremIn mathematics, the Pythagorean theorem or Pythagoras's theorem is a relation in Euclidean geometry between the three sides of a right triangle. The theorem is named after and commonly attributed to the 6th century BC Greek philosopher and mathematician P Pythagorean tripleA Pythagorean triple consists of three positive integers a b c such that a''2 + b''2 c''2. The name comes from the Pythagorean theorem, which states that any right triangle with integer side lengths yields a Pythagorean triple. The converse is also true: Pythagorean tuningPythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. Its discovery is generally credited to Pythagoras. It is the oldest way of tuning the 12-note chromatic scale and, as such, Pythagorean commaWhen you ascend by a cycle of justly tuned perfect fifths (ratio 3:2), leapfrogging 12 times, you eventually reach a note around seven octaves above the note you started on, which, when lowered to the same octave as your starting point, is 23. 46 cents hi PythagoreansThe Pythagoreans were an Hellenic organization of astronomers, musicians, mathematicians, and philosophers; who believed that all things are, essentially, numeric. The group strove to keep the discovery of irrational numbers a secret; and legends tell of PythagoreanismPythagoreanism is a term used for the religious and metaphysical beliefs held by Pythagoras and his followers the Pythagoreans, much influenced by mathematics and probably a main inspiration source to Plato and platonism. Later resurgence of the same idea Pythagorean expectation Pythagorean trigonometric identity