The mentor advised me, "To learn a new language, try to find the pi using the Monte Carlo method!", So I decided to try it blindly.

What are you saying? (Lol)

However, I didn't understand the meaning of the Japanese word "calculating the circumference ratio by the Monte Carlo method" at all, and I started by understanding it (laughs).

Organize words

-** Monte Carlo method : Observe and analyze using random numbers. Monte Carlo seems to be the name of the district where the Principality of Monaco is located in Monte Carlo. - Random number : A number that is randomly output with equal probability within a fixed range of numbers. - Finding the circumference ratio : What I understood is to find the area of the unit circle from the conclusion. - Unit circle **: A circle with a radius of 1

In summary, I understood that ** finding the circumference ratio by the Monte Carlo method ** means ** generating numbers randomly and analyzing them to find the area of a circle with a radius of 1.

I still don't understand the meaning (laughs)

How to find pi

So, here is a summary of the ideas of the smart people who were on the net.

(1) First, to find the area of a circle with a radius of 1, divide the circle into four parts. (2) Then put it in a square with one side. (3) Take the square as coordinates and imagine it as shown in the figure below. tansu（仮） (2).png (4) The bottom is a state with 1/4 yen. (Ignore the dots for a moment) tansu（仮） (1).png (5) Randomly make dots in the upper square (see the dots). In other words, we will randomly type an array of (x, y). (6) Do this n times (many times). (7) Count the points (colored in pink) inside the circle and use it as p. (8) How to determine that a point is in a circle? Calculate the length of a random point (x, y) from the start point (0, 0), and if this is 1 or less, judge it as inside a circle. tansu（仮）.png (9) The length from (0, 0) to (x, y) can be calculated as the hypotenuse of a right triangle. Do you remember the three-square theorem? (I forgot) (10) After n times, divide p by n (p/n), which is an approximation of the area of a 1/4 circle. (11) Multiply p/n by 4 to find the value of the circle.

When you program

As for the code, I wrote it like this. (Please also refer to the advice of @scivola and @ kojix2 in the comments section)

`main.ruby`


n = 1000000
count = 0

for i in 0 .. n
    z = Math.sqrt((rand ** 2) + (rand ** 2))
    if z < 1
        count += 1
    end
end

#Circumference
cir = count / n . to_f * 4 #to_The decimal point is not displayed unless it is set to float with f.

p cir

Math is a built-in module that groups mathematical methods.
. Specify the receiver message (in this case, the message issqrt ())
Sqrt () is an abbreviation for square root. Similar to PHP.

Afterword

I was 36 years old and changed jobs as an IoT engineer. Since that position is Ruby main, I put the familiar PHP and started studying Ruby.

If you have any suggestions, please do not hesitate to contact us.

The note shows the experience of changing jobs ↓ 36-year-old inexperienced person has been appointed as an IoT engineer (1/3) Programming learning itinerary 36-year-old inexperienced person has been appointed as an IoT engineer (2/3) Job change hesitation

Finding pi with the Monte Carlo method? (Ruby)