The Pythagorean Theorem

A Math Forum Project

Table of Contents:

Famous Problems Home

The Bridges of Konigsberg
· Euler's Solution
· Solution, problem 1
· Solution, problem 2
· Solution, problem 4
· Solution, problem 5

The Value of Pi
· A Chronological Table of Values
· Squaring the Circle

Prime Numbers
· Finding Prime Numbers

Famous Paradoxes
· Zeno's Paradox
· Cantor's Infinities
· Cantor's Infinities, Page 2

The Problem of Points
· Pascal's Generalization
· Summary and Problems
· Solution, Problem 1
· Solution, Problem 2

Proof of the Pythagorean Theorem

Proof that e is Irrational

Book Reviews

References

Links

The Pythagorean theorem is one of the most famous in all of mathematics. It states:

Theorem: The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the legs.

There are many different proofs of the theorem (even one supplied by President Garfield in 1876!), and we know that the Babylonians knew about the Pythagorean theorem about 1000 years before the time of Pythagoras (born in 572 B.C.). Nonetheless, a rigorous, general proof of the theorem requires the development of deductive geometry, and thus it is thought that Pythagoras probably supplied the first proof. Most math historians credit him with a proof by dissection, which relies on the use of two squares, one inscribed inside the other. The Indian astronomer Bhaskara (1114-1185) developed this proof:

to Probability: Summary and Problems
to a Proof that e is irrational

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August, 1998