pythagoras theorem

What do Euclid, 12-year-old Einstein, and American President James Garfield have in common? They all came up with elegant proofs for the famous Pythagorean theorem, one of the most fundamental rules of geometry and the basis for practical applications like constructing stable buildings and triangulating GPS coordinates. Betty Fei details these three famous proofs.

Here is an elegant visual proof of the Pythagorean Theorem (check the links 1, 2, 3 ) developed by the 12th century Indian mathematician

In this note we discuss the conditions that must be satisfied by the sides of an arbitrary integer-sided triangle if its medians can serve as the sides of a right-angled triangle.
In Part I of this article we had showcased the triple (3, 4, 5) by highlighting some of its properties and some configurations where it occurred naturally. We now attempt to extend this to other triples of consecutive integers.
A “proof without words” sounds like a contradiction in terms! How can you prove something if you are not permitted the use of any words? In spite of the seeming absurdity of the idea, the notion of a proof without words — generally shortened to PWW — has acquired great popularity in mathematics in recent decades, and every now and then we come across new, elegant PWWs for old, familiar propositions. In this short article the seemingly contradictory nature of a PWW is discussed, and some examples of PWWs are presented.
Can unfolding a paper boat reveal a proof of Pythagoras’ theorem? Does making a square within a square be anything more than an exercise in geometry at best? Art and math come together in delightful mathematical exercises described in this article by Sivasankara Sastry.
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