One of the most difficult proof strategies in mathematics is proof by contradiction. If P, for example, is a statement or a conjecture, one strategy to prove that P is true is to assume that P is not true and find a contradiction so that the statement not P does not hold. If not P […]

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# Posts tagged with 'pure mathematics'

## The Algebraic and Geometric Proofs of Pythagorean Theorem

The Pythagorean Theorem states that if a right triangle has side lengths and , where is the hypotenuse, then the sum of the squares of the two shorter lengths is equal to the square of the length of the hypotenuse. Putting it in equation form, we have . For example, if a right triangle has […]

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