__Theorem 1__
Area of circle = ∏/4 x area of square
When I was in bed one night I started thinking about circles and squares, and then I suddenly
thought that circles are about 3/4 the size of squares. In the morning I asked Mummy and she helped
me work out that it was ∏/4.
__Theorem 2__
1/n - 1/(n+1) = 1/(n^{2} + n)
One day I was in the car and Mummy was asking me a question about fractions when I realised that
when you start with 1 over a number and take away 1 over the number + 1, the denominator on the
answer is the denominator of the two fractions times-ed together, and that helped me work out the
theorem. |