PI number. When do we use it and what are its properties?

Pi number is the ratio of the circumference of a circle to its diameter. We denote it with the symbol π, this is approximately 3.14. This constant appears in many areas of physics and mathematics, it is needed, among other things, to calculate the area of ​​a circle or the volume of a sphere. What are the properties?

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1. What is Pi number?

Pi (π), also known as the Archimedes constant or ludolfine, is the ratio of the circumference of a circle - the length of the circle to the length of its diameter. This ratio does not depend on the type of wheel, since they are all similar to each other.

We use the number Pi in geometry, when calculating the formulas for the area of ​​a circle, the volume of a cylinder, the volume of a sphere or the area of ​​an ellipse, but we can also use it in mathematical analysis, number theory or probability calculus, and even in Einstein's theory of gravity.

It is sometimes called the Archimedes constant because of the merits of Archimedes of Syracuse, who was one of the first researchers of the properties and the importance of Pi in mathematics.Ludolfina is sometimes called in recognition of Ludolph van Ceulen, who became famous for presenting this number with an accuracy of 35 decimal places.


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2. Which formulas contain Pi?

The pi number is used in many different activities in mathematics and physics. Below are the most commonly used formulas in mathematics (geometry) and physics.

  • πr² - formula for the area of ​​a circle with radius r;
  • 2πr - formula for the circumference of a circle with radius r;
  • abπ - formula for the area of ​​an ellipse with semi-axes a and b;
  • 4πr² - formula for the surface of the sphere with radius r;
  • 4 / 3πr² - formula for the volume of a sphere with radius r;
  • πr² H - formula for the volume of a cylinder with height H and radius r;
  • The arc measure of a semi-double angle is π radians;
  • ∆x∆p ≥ h / 4π, ∆E∆t ≥ h / 4π - Heisenberg quantum uncertainty principle;

3. Properties of Pi number

Pi is an irrational number, which means that Pi has no periodic or finite decimal expansion.

Decimal expansion of Pi to the tenth decimal place:

π ≈ 3,14159 26535 89793 23846 26433 83279...

As you can see, this expansion is infinite, therefore only some approximations are used in the calculations.

Rounding the number Pi:

  • in simplified tasks - π ≈ 3;
  • the most commonly used decimal expansion - π ≈ 3.14;
  • π ≈ 22/7;
  • π ≈ 355/113.

Pi cannot be expressed by a finite number of operations such as addition, subtraction, multiplication, division, and square root, all involving integers. The Pi number is therefore a leap number like the vast majority of numbers.

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4. Day of Pi

Pi number has its admirers. Pi Day was established for March 14 (this date in America is written as "3.14"), and Pi Approximation Day is set for July 22 (the European way of writing it is 7/22 ≈ 3.1428).

On this occasion, stories and poems are created in which the length of each word is equal to the next digit in the decimal expansion of Pi.

Here are a few such poems:

"Once in May, on the second Sunday

Mr. Felek counted the numbers.

He multiplied, summed up,

He noted the numbers,

But he has few of them ... "

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"Hansel discusses vigorously

because this topic feels good

replaced ludolfine with the words of a rhyme

Have you already guessed where this change comes from?

Who and researches and counts,

The thinker is great.

He used to be wrong, however

Any mathematician.

Here and I know and remember perfectly ...

Whoever wants Pi to write down the numbers by will and thought, will be able to "

"Forge and plow furiously during the day,

Because the harvest is not easy!

The golden happiness of the ship,

You rock ...

Forge! We do not wait for a miracle.

Robot is the power of the people! "

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