User talk:Рајко Велимировић

There are many forms of PI and you can see them http://mathworld.wolfram.com/PiFormulas.html However the number of Pi is not just a circle but a series of geometric images such as an equilateral triangle, square, pentagon, etc. unique pattern that I found 2004. Pi for all numbers is:
 * $$ \pi_n=\frac{n}{2}. sin(\frac{360}{n})$$

sinus in degrees
 * n= {3,4,5,6........., \infinity}
 * n=3 it is the equilateral triangle
 * $$\pi_3=\frac{3}{2}\sin(\frac{360}{3})$$
 * $$\pi_3=1.2990381056766579701455847561294.......$$

Area of an equilateral triangle will be
 * $$ R^2\pi_3$$

R -radius of the circle described about an equilateral triangle
 * n=4 it is a square
 * $$\pi_4=2$$

Area of squares will be
 * $$ R^2\pi_4$$

R -radius of the circle described around the square so on pentagon, hexagon .......
 * evidence
 * $$\pi=\frac{n}{2}. sin(\frac{360}{n})$$
 * $$lim_{n \to \infty}\frac{n}{2}. sin(\frac{360}{n})$$
 * $$\frac{1}{2} lim_{n \to \infty}n. sin(\frac{360}{n})$$
 * $$\frac{1}{2} lim_{n \to \infty}\frac{ sin(\frac{360}{n})}{\frac{1}{n}}$$
 * $$\frac{1}{2} lim_{n \to \infty}\frac{ sin(\frac{360}{n})}{\frac{1}{n}}.\frac{360}{360}$$
 * $$\frac{360}{2} lim_{n \to \infty}\frac{ sin(\frac{360}{n})}{\frac{360}{n}}$$
 * $$\frac{360}{n}=t$$
 * $$t \rightarrow \ 0$$
 * $$180\lim_{t \to \mathbf{0}} \frac{sin t}{t}=180^0$$
 * $$180^0=\pi (rad)$$