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If we know any two sides of a right-angle triangle, we can easily work out the
unknown side. The method is called the Theorem of Pythagoras.

Pythagoras of Samos (570-495BC) was an ancient Ionian Greek philosopher and
the eponymous founder of Pythagoreanism. His political and religious teachings
were well known in Magna Graecia and influenced the philosophies of Plato,
Aristotle, and, through them, Western philosophy. Knowledge of his life is clouded
by legend, but he appears to have been the son of Mnesarchus, a gem-engraver on
the island of Samos. Modern scholars disagree regarding Pythagoras's education
and influences, but they do agree that, around 530 BC, he travelled to Craton, where
he founded a school in which initiates were sworn to secrecy and lived a communal
ascetic lifestyle. This lifestyle entailed several dietary prohibitions, traditionally said
to have included vegetarianism, although modern scholars doubt that he ever
advocated for complete vegetarianism.

Now Pythagoras is attributed with the theorem of solving right angle triangles. He
allegedly said that the "square on the Hypotenuse is equal to the sum of the squares
on the other two sides".

I am sceptical that Pythagoras was the first to discover this. I am sure the Egyptians
and many other civilisations before 530 BC knew about right angle triangles. I
remember when I first heard this in school. I had no idea what it meant. So what
does it mean?

2
To square something means to multiply it by itself - 2 squared (written 2 ) = 4. Let us
see what this would look like if we squared all sides of a right-angle triangle.

Figure 41-2 The area of H equals the area of O + A
To square a side means just to make a square out of it. So we have made three
squares out of the three sides of the triangle in Figure 41-2.
The area of the Opposite Square plus the area of the Adjacent Square equals the
area of the Hypotenuse Square.
For example, if these were paddocks with the maximum number of sheep in them,
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