How many right-angled triangles are there with sides that are all
integers less than 100 units?
A tennis ball is served from directly above the baseline (assume
the ball travels in a straight line). What is the minimum height
that the ball can be hit at to ensure it lands in the service area?
Which is a better fit, a square peg in a round hole or a round peg
in a square hole?
Pythagoras (say "pie-thag-or-as") of Samos was a Greek
philosopher who lived from about 580 BC to about 500 BC. He made
important developments in mathematics, astronomy, and the theory of
Pythagoras spent much of his life studying mathematics and
formed a special school where members followed strict rules, such
as never eating meat. Pythagoras believed that everything in the
world could be explained by numbers and his school worked hard to
try to learn enough about numbers to be able to understand the
someone's idea of what Pythagorus might have looked like
Some of the things they believed about numbers seem odd to us
now. For example, numbers were thought to have their own special
nature. Pythagoreans thought numbers were male or female, ugly or
beautiful, or had a special meaning.
Other ideas they worked on are things you
still learn about in school and that mathematicians still use. Some
of these are:
The sum of the angles of a
triangle is equal to two right angles .
The theorem is: for a
right-angled triangle the square on the hypotenuse is equal to the
sum of the squares on the other two sides.