Simple circle problem involving area and circumference

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The discussion revolves around a mathematical problem involving the area and circumference of a circle formed by ripples in water. The key question is how to express the area as a function of the circumference without using differentiation, focusing instead on a limiting process. Participants explore the relationship between area and circumference, eventually arriving at the formula A = C^2/(4π). The conversation highlights the challenge of adhering to the problem's constraints while seeking to understand the underlying calculus concepts. The discussion concludes with a plan to derive the rate of change of area using limits, emphasizing the educational aspect of the problem.
  • #31
SteamKing said:
What's the formula for the circumference of a circle?
c=2*##\pi##*r
 
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  • #32
astrololo said:
c=2*##\pi##*r
Sigh... and what happens when you divide C by 2π ?
 
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  • #33
SteamKing said:
Sigh... and what happens when you divide C by 2π ?
You obtian the radius. Btw why are you desesperate lol
 
  • #34
I was hoping you would start working this problem using the method I was leading you to in post #25. This method involves using limits (which is the main requirement for your teacher). If you do what I suggested in post #25 (which is the first step in the derivation), I can lead you through, step by step, to the final result. But I need you to start.

Chet
 
  • #35
$$A(t)=\frac{C^2(t)}{4\pi}$$
$$A(t+Δt)=\frac{C^2(t+Δt)}{4\pi}$$
$$A(t+Δt)-A(t)=\frac{C^2(t+Δt)-C^2(t)}{4\pi}$$
Do you know how to factor the numerator of the right hand side?
 

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