Generating Pythagorean Triples from Square Numbers

A figurate number is a number that can be represented by a regular geometrical arrangement of equally spaced points (or circles as shown in the first figure). If the arrangement forms a regular polygon, the number is called a polygonal number. Examples of polygonal numbers are square numbers. The first  four square numbers are 1, 4, 9, and […]
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The Infinitude of Pythagorean Triples

In the Understanding the Fermat’s Last Theorem post, I have mentioned about Pythagorean Triples.  In this post, we will show that there are infinitely many of them. We will use intuitive reasoning to prove the theorem. For the 100th time (kidding), recall that the Pythagorean Theorem states that in a right triangle with side lengths […]
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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 its hypotenuse. Putting it in equation form, we have: . For example, if a right triangle has […]
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