How can I accurately calculate pi using polygons and the concept of infinity?

[Xforce]

Since the ratio of perimeter and diagonal in a polygon( with a side number can be divided whole by 2) is a×sin(180° /a),and a is the side number of the polygon. And if we want the number of sides are always a double number we can say that there are 2a sides, and the equation can be 2a×sin(180°/2a). As a gets greater,where the side number of the polygon approaches infinity, then it becomes a circle, the perimeter becomes circumference and the diagonal becomes diameter, and the ratio becomes π. So the accurate π can be calculated by the equation lim a→∞ (2a×sin(180°/2a)). Happy π day!

 

[mfb]

In rad, this is $\lim_{a\to\infty} 2a \sin(\pi/(2a))$. As $\sin(x) \approx x$ for small x, we get $\lim_{a\to\infty} 2a \sin(\pi/(2a)) = 2a\frac{\pi}{2 a}=\pi$.

 

[Xforce]

Why haven’t I noticed that! My school math teachers usually teach me to calculate angles in degrees, not radiants.