Difference between revisions of "Pythagorean Theorem"

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The Pythagorean Theorem states that for all right triangles, a^2+b^2=c^2, where c is the long hypotenuse, and a and b are the legs of the right triangle. This theorem is a classic to prove, and hundreds of proofs have been published. The Pythagorean Theorem is the most frequently used theorem in geometry, and is one of the many tools in a good geometer's arsenal.
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The '''Pythagorean Theorem''' states that for all [[right triangle|right triangles]], <math>{a}^{2}+{b}^{2}={c}^{2}</math>, where c is the [[hypotenuse]], and a and b are the legs of the right triangle. This theorem is a classic to prove, and hundreds of proofs have been published. The Pythagorean Theorem is one of the most frequently used theorem in geometry, and is one of the many tools in a good geometer's arsenal.
  
This is generalized by the Pythagorean Inequality (See [[Geometric inequalities]]) and the [[Law of cosines]].
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This is generalized by the [[Pythagorean Inequality]] (See [[Geometric inequalities]]) and the [[Law of cosines]].

Revision as of 18:10, 18 June 2006

The Pythagorean Theorem states that for all right triangles, ${a}^{2}+{b}^{2}={c}^{2}$, where c is the hypotenuse, and a and b are the legs of the right triangle. This theorem is a classic to prove, and hundreds of proofs have been published. The Pythagorean Theorem is one of the most frequently used theorem in geometry, and is one of the many tools in a good geometer's arsenal.

This is generalized by the Pythagorean Inequality (See Geometric inequalities) and the Law of cosines.

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