What is the Pythagorean Theorem?

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  • Anonymous
    8 years ago
    Best Answer

    In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas, it states:

    In any right angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

    The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation:

    a² + b² = c²

    where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.

    The Pythagorean theorem is named after the Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof,[2][3] although it is often argued that knowledge of the theorem predates him. There is evidence that Babylonian mathematicians understood the formula, although there is little surviving evidence that they fitted it into a mathematical framework.[4][5]

    The theorem has numerous proofs, possibly the most of any mathematical theorem. These are very diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. The theorem can be generalized in various ways, including higher-dimensional spaces, to spaces that are not Euclidean, to objects that are not right triangles, and indeed, to objects that are not triangles at all, but n-dimensional solids. 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.

    Good luck!

  • 3 years ago

    The fact of the thought became into got here across on a Babylonian pill circa 1900-1600 B.C. whether Pythagoras (c.560-c.480 B.C.) or somebody else from his college became into the 1st to discover its information can't be claimed with any degree of credibility. Euclid's (c 3 hundred B.C.) aspects furnish the 1st and, later, the popular reference in Geometry.

  • 8 years ago

    a^2+b^2=c^2

    the two sides of the right triangle equals the side of the hypotenuse

    example one side is 8 in the second side is 6 in. and the hypotenuse would be a^2+b^2

    8^2+6^2=c^2

    64+36=c^2

    100=c^2

    10=c 100=100

  • Anonymous
    6 years ago

    given the length of any two sides, you can measure the distance of their edge by square rooting the sum of the square of the length of the two sides, in other word, c^2 = a^2 + b^2

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  • 8 years ago

    If you have a triangle with a right angle(90 degrees) in it then

    if side opposite the right angle is h and the other two sides are r and s

    then Pythagoras proved h^2=r^2+h^2

  • 8 years ago

    it states that in atriange, the sum of the squares of the adjacent and opposite sides is equal to the square of the hypotenus........best answer.

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