How python represents pi

python representationPiMethod:

Use the "import" statement to import the math package. "The function can get pi, then you can use the function to represent pi."

The following is an example: The following is the result:

There are two methods for calculating pi, namely the mathematical formula method and the Monte Carlo method in engineering.

1.Formula method.

**:Running Effect:

Note: Because the upper limit of k in the formula is positive infinity, here for the sake of simple calculation, take k=10000.

If you increase the k value, you will find that the value of pi is more accurate, at the cost of a longer running time. When I set n to 10000000, the computer fan started whirring for a long time.

2.Monte Carlo method.

The core idea: the value of pi ( ) is indirectly equal to the ratio of the number of points falling into the circle to the total number of points in the square.

To make it easier to calculate, let's first calculate the PI value of 1 4 circles, and then multiply by 4 to get the PI value of the whole circle.

1 4 Circular dot simulation.

** As follows: Notes:

dots is the total number of random dots scattered within a 1 4 square.

Hits are used to record the number of points that fall within 1 4 circles.

The random() function is used to generate a random number between 0 and 1, which is a unit circle, exactly If you don't set the seed, it will automatically be seeded according to the current time of the operating system (accurate to milliseconds). Therefore, the randomly generated 1000*1000 points must be different, and there will be no overlap of points.

pow(x**2+y**2, which is used to calculate the Euclidean distance from the random point (x,y) to the center of the circle o(0,0). Namely.

When the distance is 1, it means that the random point is within 1 4 circles, and the Hits variable is increased by 1.

The result is as follows:

It can be seen that the value of pi is not accurate enough, and this problem can be solved by increasing the number of dots.

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4. Below, let's take a look at the first way to retrieve the QQ password: verify the password problem. Correctly answer the 3 security questions, click "OK" - enter the new password reset and confirm, confirm the submission - QQ password modification is successful.

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Note: Sending SMS will be charged for the Yanqi fee: yuan).

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Enter the QQ account and verification code, click "Confirm and agree to the following agreement" -- verify the contact email phone -- fill in the historical information to verify the identity -- notify your friends to complete the assistance to retrieve the QQ password -- check the email text message after four hours, set a new QQ password, and protect the password.

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