B A pi day calculation

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

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