MathsNet: Interactive Pythagoras's Theorem

Pythagoras's Theorem The Egyptians measure their fields with lengths of knotted rope. The size of the farmer's field is used to work out how big his harvest will be, and how much tax he should pay. This knotted rope indicates a triangle with sides of length 3, 4 and 5 units.
Pythagoras's Theorem is all about right-angled triangles. If squares are constructed on the three sides of a right-angled triangle, then these three squares have a very simply but important connection. Can you see what it is?

The areas of the two smaller squares add up to the area of the largest one. Check it out here:

To sum up: another way of stating the theorem is

The square on the hypotenuse is equal to the sum of the squares on the other two sides.
if the three sides of the right angled triangle are labelled a, b and c (with c the longest side or hypotenuse), then Pythagoras's theorem says that:

c² = a²+b²

Returning to the knotted rope triangle with sides of length 3, 4 and 5 units, we can see that

5² = 3²+4².

Triples like these (ie., 3,4,5) are called Pythagorean triples.

There remains one small problem. The Egyptians used knotted ropes to measure the dimensions of their fields. Further evidence from the The Rhind papyrus confirms this. The papyrus, a scroll about 6 metres long and 1/3 of a metre wide, was written around 1650 BC by the scribe Ahmes who is copying a document which is 200 years older. This makes the original papyrus date from about 1850BC.

One of the Babylonian tablets (Plimpton 322) which is dated from between 1900 and 1600 BC contains answers to a problem containing Pythagorean triples, i.e. numbers a, b, c with a² + b² = c². It is said to be the oldest number theory document in existence.

BUT Pythagoras was not born until about 1200 years later! He could not, therefore, have discovered the theorem that bears his name. There is a theory that many great inventions were not invented by the people they are named after. This is Dye's Theory. For example, On June 15th, 2002, the US Congress officially recognized that the italian inventor Antonio Meucci is to be credited for the invention of the telephone, and not Alexander G. Bell, as previously claimed.