Say we have a regular polygon $s$, with number of sides $n$:
Is there a way to prove that as $n → ∞,\space $then $s → circle$ using integration?
2026-03-29 12:41:19.1774788079
Prove using integration that $polygon → circle\space \text{as}\space number\space of\space sides → infinity$
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The pioneers of the calculus, including Leibniz, thought of a circle as an infinite-sided polygon, as the OP suggests. This turned out to be a fruitful idea, even though today we avoid this viewpoint. See this answer for aditional details.