# 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** (pronounced like "pie") is often written using the greek symbol π

The definition of π is:

*The Circumferencedivided by the Diameterof a Circle.*

The circumference divided by the diameter of a circle is always π, no matter how large or small the circle is!

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?

**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?

**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 fifty 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 + \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.

### Pi Day

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