Пи 2

The number pi

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We can use π to find a Circumference when we know the Diameter

A quick and easy approximation for π is 22/7

To help you remember what π is . just draw this diagram.

Pi is the ratio of the circumference of a circle to its diameter:

Draw a circle, or use something circular like a plate.

Equations using pi

Pi (π) is the ratio of the circumference of a circle to its diameter. The value of pi is 3.14159. an irrational number.

Also we can use π to find a Diameter when we know the Circumference

But as you can see, 22/7 is not exactly right. In fact π is not equal to the ratio of any two numbers, which makes it an irrational number.

The circumference divided by the diameter of a circle is always π , no matter how large or small the circle is!

Using this relationship, we can determine equation for the circumference of a circle by solving for C:

Measure around the edge (the circumference):

Circumference of a circle

Possible causes are:

Diameter = Circumference / π

A really good approximation, better than 1 part in 10 million, is:

I got 82 cm

C = πd or C = 2πr

Measure across the circle (the diameter):

To 100 Decimal Places

3 + 4 2×3×4 − 4 4×5×6 + 4 6×7×8 − 4 8×9×10 + .

It gives these results:

For a sphere that has a radius of r,

The distance half way around the circle is π = 3.14159265.

(Notice the + and − pattern, and also the pattern of numbers below the lines.)

That is pretty close to π . Maybe if I measured more accurately?

«May I have a large container of butter today»
3 1 4 1 5 9 2 6 5

Pi is an irrational number. An irrational number does not have a repeating pattern and does not end, so it can only be approximated. Calculated to one hundred places after the decimal:

Remembering The Digits

There are many special methods used to calculate π and here is one you can try yourself: it is called the Nilakantha series (after an Indian mathematician who lived in the years 1444–1544).

Get a calculator (or use a spreadsheet) and see if you can get better results.

where A is the area and r is the radius of the circle.

For a circle with a radius of 1

Here is π with the first 100 decimal places:

I got 26 cm

22/7 = 3.1428571.

Pi is a constant value. That is, the ratio of the circumference to the diameter is the same for all circles. The drawing below shows the circumference of a circle that has been «straightened out.» It is a little more than three diameters in length:

Approximation

I usually just remember «3.14159», but you can also count the letters of:

It goes on for ever and has this pattern:

Another well-known formula that uses pi is the area of a circle. The area of a circle is the region that is bounded by the circumference of a circle.

Circumference = π × Diameter

355/113 = 3.1415929.
(think «113355», slash the middle «113/355», then flip «355/113»)

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The digits go on and on with no pattern.

3.14 and (or ) are often used as approximate values for pi.

Digits

π has been calculated to over 100 trillion decimal places and still there is no pattern to the digits, see Pi Normal.

Pi Day is celebrated on March 14. March is the 3rd month, so it looks like 3/14

where C is the circumference, d is the diameter, and r is the radius of the circle.

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3.14159265358979323846…

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The radius is half of the diameter, so we can also say:

For a right circular cylinder that has a radius of r and height h,

Right circular cylinder

Lateral surface area = 2πrh

82 cm / 26 cm = 3.1538.

A right circular cone that has a radius of r and height h,

Pi is used widely in equations in geometry, trigonometry, and other branches of mathematics:

Possible causes are:

π is approximately equal to:

Right circular cone

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Источники:

https://mathworld.wolfram.com/Pi.html&rut=b16f31b07d2c917d4df22a7e483356b45a77b51857d8cc7f30b7d6d3808cc3f9
https://simple.wikipedia.org/wiki/Pi&rut=833bd38717dd0dc035af34dc8e288209ce9f156d4367213398c7c6c7548f4bc9
https://en.wikipedia.org/wiki/Pi&rut=0eb66ad73bceaa26e408dbf732a70c7ff0fef7c87035f0caca9de05e6d122ad9
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https://www.math.net/pi&rut=68c6f6277741cea6377c036b96d83ceb351da2eac159dcdd4f896f8d3336c4d8
https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80&rut=7ea4698b30f6fd1261a51e80cebdc37dcc0b60a8fb59936287547e9febb33189
https://www.piday.org/learn-about-pi/&rut=2564afb82085547eab59c458c7ecb5808ef16378f34bb2d1f767451234f2913f
https://www.mathsisfun.com/numbers/pi.html&rut=f157d7b739ce2cd326781d322c7cdaf7f67102801b6970c196ab5f575495d457
https://www.britannica.com/science/pi-mathematics&rut=e5898871fc39049548febbdfc797920cea7ca5291af7372b4275464dbbf24f52