A Practical Demonstration of the Pythagorean Theorem

The Pythagorean Theorem is probably the most popular theorem in school mathematics. Surely, you have heard or read about it at least once from elementary school to high school. The Pythagorean Theorem states that given a right triangle with shorter sides a, b, and hypotenuse c, the following equation holds

c^2 = a^2 + b^2.

The Pythagorean Theorem

 

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Using Similarity to Prove the Pythagorean Theorem

The Pythagorean Theorem is one of the most interesting theorems for two reasons: First, it’s very elementary; even high school students know it by heart. Second, it has hundreds of proofs. The proof below uses triangle similarity.

Pythagorean Theorem

In a right triangle with side lengths a and b and hypotenuse c,  the following equation always holds:

c^2 = a^2 + b^2. » Read more

A US President’s Proof of the Pythagorean Theorem

James Garfield, the 20th president of the United States, came up with an original proof of the Pythagorean Theorem in 1876 when he was still a Congressman. His proof was published in New England Journal of Education.

Pythagorean Theorem proof by President Garfield

Recall that the Pythagorean Theorem states that given a right triangle with sides a, b, and hypotenuse c, the following equation is always satisified:

a^2 + b^2 = c^2.

President Garfield’s proof is quite simple. We can do this in three steps:

  1. Find the area of figure above using the trapezoid
  2. Find the area of the same figure using the three triangles
  3. Equate the results in 1 and 2. » Read more
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