Draw a circle with a radius of 1.
The distance half way around the edge of the circle
Or you could draw a circle with a diameter of 1.
Then the circumference (the distance all the way
Pi (the symbol is the Greek letter π) is:
The ratio of the Circumference
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
82 cm / 26 cm = 3.1538...
That is pretty close to π. Maybe if I measured more accurately?
In fact π is approximately equal to:
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
Example: You walk around a circle which has a diameter of 100m, how far have you walked?
Distance walked = Circumference = π × 100m = 314.159...m
= 314m (to the nearest m)
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 better approximation (but stll not exact) is:
355/113 = 3.1415929...
(think "113355", then divide the "355" by the "113")
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:
|Term||Result (to 12 decimals)|
|...||... etc! ...|
Get a calculator (or use a spreadsheet) and see if you can get better results.