Pi (π)
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
Divide:
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: 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 |
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) |
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 better approximation (but stll not exact) is:
355/113 = 3.1415929...
(think "113355", then divide the "355" by the "113")
Remembering
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 + \frac{4}{2×3×4} − \frac{4}{4×5×6} + \frac{4}{6×7×8} − \frac{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) |
---|---|
1 | 3 |
2 | 3.166666666667 |
3 | 3.133333333333 |
4 | 3.145238095238 |
... | ... etc! ... |
Get a calculator (or use a spreadsheet) and see if you can get better results.