The method of making a circle inscribed with a regular polygon and multiplying it by the number of sides of the circle inscribed with a regular polygon to find pi is very cumbersome. Using a ruler as a circle inscribed with a regular polygon has many limitations, resulting in low accuracy.

Second, Buffon threw the needle.

1777, French scientist buffon made a needle throwing experiment at a banquet:

Needle injection steps:

1) Take a piece of white paper and draw many parallel lines with an interval of a on it.

2) Take a needle with a length of 0.5 a, throw it randomly on the paper with parallel straight lines for n times, and observe the number of times the needle intersects the straight line, and record it as m..

3) Calculate the ratio of n to m 。

The guests didn't know what Mr. Buffon was going to play, so they joined the experiment one by one. After throwing a small needle, they picked it up and threw it again, while Mr. Buffon himself kept counting and remembering, so he was busy for nearly an hour. Finally, Mr. Buffon announced loudly: "Gentlemen, I have recorded the result of your throwing the needle just now, * * *. Among them, 704 times intersect with parallel lines, and the ratio of the total number of intersections of 22 12 to 704 times is 3. 142. " Speaking of this, Mr. Buffon deliberately stopped, gave everyone a mysterious smile, and then deliberately raised his voice and said, "Gentlemen, this is the approximate value of pi!"

He later gave a proof, which was recorded in Buffon's book published by 1777: "Draw a set of parallel lines with an interval of A on the plane and put a length of L (L

Third, the calculation method of trigonometric function

The larger n is, the closer it is to π.

Fourth, randomness and π

Say three positive numbers at random, and the probability p that these three positive numbers can form an obtuse triangle is also related to π, which is (π-2)/4.

Five, Taylor expansion

At first glance, this seems incredible. ...