Pi (π)

pi circle diameter

Draw a circumvolve with a diameter (all the mode across the circle) of ane

And so the circumference (all the way around the circle) is 3.14159265... a number known as Pi

Pi (pronounced like "pie") is frequently written using the greek symbol π

circumference, diameter, radius

The definition of π is:

The Circumference
divided by the Diameter
of a Circle.

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

pi circle diameter

To help you retrieve what π is ... just depict this diagram.

Finding Pi Yourself

Draw a circle, or use something round similar a plate.

Measure out around the border (the circumference):

plate circumference 82
I got 82 cm

Measure out across the circle (the diameter):

plate diameter
I got 26 cm

Separate:

82 cm / 26 cm = 3.1538...

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

Using Pi

We tin can apply π to find a Circumference when we know the Bore

Circumference = π × Bore

Example: Y'all walk around a circle which has a diameter of 100 g, how far take yous walked?

pi circle 100m diameter

Distance walked = Circumference

= π × 100 m

= 314.159... m

= 314 k (to the nearest m)

Also nosotros tin can utilise π to observe a Diameter when nosotros know the Circumference

Bore = Circumference / π

annulus pipe

Example: Sam measured 94 mm around the exterior of a piping ... what is its Diameter?

Bore = Circumference / π

= 94 mm / π

= 29.92... mm

= 30 mm (to the nearest mm)

Radius

The radius is one-half of the diameter, and then we can also say:

circle radius=1, half circumference=pi

For a circle with a radius of ane

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

Digits

π is approximately equal to:

iii.14159265358979323846…

The digits proceed and on with no design.

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

Approximation

A quick and easy approximation for π is 22/vii

22/vii = 3.1428571...

But as you can run into, 22/7 is not exactly right. In fact π is not equal to the ratio of whatever 2 numbers, which makes information technology an irrational number.

A actually skilful approximation, ameliorate than 1 part in 10 one thousand thousand, is:

355/113 = iii.1415929...
(recollect "113355", slash the middle "113/355", then flip "355/113")

Summary:

22/7 = three.1428571...
355/113 = 3.1415929...
π = three.14159265...

Remembering The Digits

I usually just retrieve "3.14159", but you tin can also count the letters of:

"May I take a big container of butter today"
3 i 4 1 5 9 2 6 five

To 100 Decimal Places

Here is π with the first 100 decimal places:

3.14159265358979323846264338327950288
4197169399375105820974944592307816
4062862089986280348253421170679...

Calculating Pi Yourself

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

It goes on for ever and has this pattern:

iii + 4 2×3×4 − 4 4×5×six + 4 6×7×8 − iv 8×9×x + ...

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

It gives these results:

Term Result (to 12 decimals)
1 3
2 3.166666666667
3 3.133333333333
iv three.145238095238
... ... etc! ...

Get a calculator (or utilize a spreadsheet) and see if you can go better results.

ballons

Pi Day

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

5839,5050,5052,1745,2106,5473,5477,1744,3236,3237