How are the formulas for the circumference of a circle and area of a circle derived?

Question

anonymous · Answer

@.Sam. ?

anonymous · Answer

integration

anonymous · Answer

By Definite integration

accessdenied · Answer

The circumference is relatively easy; we determined by experiment that the ratio between circumference (distance around) and diameter (distance through) is roughly a constant.  So we have:
  $ \dfrac{C}{d} = k $

  $ C = kd $

That constant of proportionality has been given a name, $ \pi $, which we have estimated to great accuracies.
Place that in for k, and we have the formula:
  $ C = \pi d = 2 \pi r $       $d = 2r $

Then yes, integration would get you from circumference to area.  :)

anonymous · Answer

" http://www.mathopenref.com/circumferencederive.html "

dumbcow · Answer

http://en.wikipedia.org/wiki/Area_of_a_disk#Onion_proof