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Can the area of a circle be derived without calculus or Archimedes approach? The area is given as$\pi R^2$, where $\pi$ is defined by circumference=$2\pi R$. It is easy to derive it as an integral or by using the limit as a sequence of polygons (Archimedes). Is there a more elementary geometry derivation?

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  • $\begingroup$ What geometry exists to calculate area at all? For curves.... no, nothing exist that isn't essentially calculus. $\endgroup$ – fleablood Apr 11 '18 at 1:05
  • $\begingroup$ Here is an intuitive approach to motivate the conclusion that the area of a circle equals half the product of the radius and circumference: quora.com/… $\endgroup$ – John Wayland Bales Apr 11 '18 at 1:09
  • $\begingroup$ This question has a number of proofs including my own. math.stackexchange.com/questions/2593324/… $\endgroup$ – Rene Schipperus Apr 11 '18 at 1:10

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