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
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)


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…


π is approximately equal to:
The digits go on and on with no pattern.
π has been calculated to fifty trillion decimal places and still there is no pattern to the digits


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 + 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)
… etc! …
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
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