- #1
John Clement Husain
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- TL;DR Summary
- Does the limit as n approaches infinity of the area of an n-sided polygon equal to the area of a circle?
Hello everyone!
I have been looking for a general equation for any regular polygon and I have arrived at this equation:
$$\frac{nx^{2}}{4}tan(90-\frac{180}{n})$$
Where x is the side length and n the number of sides.
So I thought to myself "if the number of sides is increased as to almost look like a circle, does it result in the area of a circle?"
Is this:
$$\lim_{n\to\infty} \frac{nx^{2}}{4}tan(90-\frac{180}{n}) = \frac{C^{2}}{4\pi}$$
true?
I have been looking for a general equation for any regular polygon and I have arrived at this equation:
$$\frac{nx^{2}}{4}tan(90-\frac{180}{n})$$
Where x is the side length and n the number of sides.
So I thought to myself "if the number of sides is increased as to almost look like a circle, does it result in the area of a circle?"
Is this:
$$\lim_{n\to\infty} \frac{nx^{2}}{4}tan(90-\frac{180}{n}) = \frac{C^{2}}{4\pi}$$
true?
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