Pi (π)

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 is often written using the greek symbol π

The definition of π is:

''TheCircumference divided by theDiameter of a Circle.''

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):

I got 82 cm

Measure across the circle (the 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?
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

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:

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 two quadrillion 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")

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:

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

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

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

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