Pi (π)

 

Pi (π)

pi circle diameter

 

Draw a circle with a diameter (all the way across the circle) of 1

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

 

Pi (pronounced like "pie") is often 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 by the diameter of a circle is always π, no matter how large or small the circle is!

pi circle diameter

 

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

Finding Pi Yourself

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

Measure around the edge (the circumference):

plate circumference 82
I got 82 cm

Measure across the circle (the diameter):

plate diameter
I got 26 cm

Divide:

82 cm / 26 cm = 3.1538...

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

Using Pi

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

Circumference = π × Diameter

Example: You walk around a circle which has a diameter of 100 m, how far have you walked?

pi circle 100m diameter

Distance walked= Circumference
 = π × 100 m
 = 314.159... m
 = 314 m (to the nearest m)

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

Diameter = Circumference / π

annulus pipe

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

Diameter= Circumference / π
 = 94 mm / π
 = 29.92... mm
 = 30 mm (to the nearest mm)

Radius

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

circle radius=1, half circumference=pi

 

For a circle with a radius of 1

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

Digits

π is approximately equal to:

3.14159265358979323846…

The digits go on and on with no pattern.

π has been calculated to over sixty trillion decimal places and still there is no pattern to the digits

Approximation

A quick and easy approximation for π is 22/7

22/7 = 3.1428571...

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.

 

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

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

Summary:

22/7=3.1428571...
355/113=3.1415929...
π=3.14159265...

Remembering The Digits

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

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

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 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).

It goes on for ever and has this pattern:

3 + 42×3×4 − 44×5×6 + 46×7×8 − 48×9×10 + ...

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

It gives these results:

TermResult (to 12 decimals)
13
23.166666666667
33.133333333333
43.145238095238
...... etc! ...

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

 

ballons

Pi Day

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

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