Circumference and Area
Can someone please help me??? While it is easy for me to tell my middle school daughter that Circumference=2*pi*radius, and Area=pi*radius squared, how do I simply and clearly explain to her where these came from? I have tried searching online, but have not come across anything helpful.
I don't think there is any easy way to explain these. There is a proof of the area formula, given the circumference formula, using Calculus but I suspect that's far too advanced for what you are going now.
Originally Posted by 3fireman8
You are probably just going to have to take these formulas as the Truth and go from there. (You might find the odd physical demonstration of these formulas, such as measuring the circumference and radius and finding a value for pi, that sort of thing.)
Euler defined as the ratio of circumference to diameter, you can do this because all circles are the same shape as all other circles! What this meant is that whatever factor you increase the diameter (to get different circles) you increase the circumference by the same amount (in order for it to stay a circle, i.e. so everything is in proportion ) so in the ratio they always cancel and you always get .
There is a lot of fascinating maths behind and around but I agree with topsquark that most of it's probably not appropriate for your daughter! (at the moment...)