There are plenty of ways of defining Pi but this is probably the most intuitive one:
If a circle has a diameter d then its circumference will be πd.
In other words, it is π times as far to walk all the way around the outside of a circle and back to your starting point than to walk straight across from one side to the other.
π is roughly equal to 3.14159… but the decimal expansion of π carries on forever!
You can do lots of fun things with the decimal expansion of π!
You could memorise it to 70,000 decimal places like Guinness world record holder Rajveer Meena! Are you up to the challenge? Here’s a catchy Pi Song to help you learn the first 100 digits!
Alternatively, if memorising digits isn’t really your thing, you could write a poem in Pilish, a language where the length of each word corresponds to the digits of π – the first word is three letters, the second one letter and so on (if you encounter a 0 in the decimal expansion, use a ten letter word).
Here’s a short extract from a very impressive example by Mike Keith:
Midnights so dreary, tired and weary,
Silently pondering volumes extolling all by-now obsolete lore.
During my rather long nap – the weirdest tap!
An ominous vibrating sound disturbing my chamber’s antedoor.
“This”, I whispered quietly, “I ignore”.
Perfectly, the intellect remembers: the ghostly fires, a glittering ember.
Inflamed by lightning’s outbursts, windows cast penumbras upon this floor.
Sorrowful, as one mistreated, unhappy thoughts I heeded:
That inimitable lesson in elegance – Lenore –
Is delighting, exciting…nevermore.
You can read the full poem here!
Pi is used absolutely everywhere in maths and physics!
Here’s Pi making an appearance in the Einstein field equations of general relativity:
And here it is again popping up in the time-dependent Schrödinger equation of quantum mechanics:
Here’s a Pi Related Question!
One of my favourite maths puzzles involving Pi is “The Chicken from Minsk” from The Chicken from Minsk: And 99 Other Infuriating Brainteasers by Yuri Chernyak and Robert Rose. The puzzle goes something like this:
Just outside Minsk in Belarus, there is a chicken farm.
Unfortunately, there is an electric cable that runs all the way around the world, along a circumference (for over 40,000 kilometres), that passes straight through the middle of the chicken farm. The cable is just 30 centimetres above the ground and very poorly insulated, meaning that the chickens on the farm keep getting electrocuted.
The chicken farmer is getting a little tired of this so he writes to the electricity company to ask if they can move the cable half a metre higher off the ground so his chickens can walk under it safely.
The electricity company writes back to say that they’d be very happy to raise the cable if the farmer is willing to pay for the extra length of cable required to lift it by half a metre all the way around the world. The farmer is disappointed. He’s not a wealthy man and it seems to him that buying that much cable will be more expensive than he can possibly afford.
How much extra cable do you think he’ll need to buy?
Let’s think about what we know about circles. The circumference of a circle is 2πr where r is the radius of the circle (in this case the radius of the earth plus an extra 30cm). The farmer wants the cable raised by half a metre which means that he wants the radius of the circle increased by 0.5m. The amount of extra cable required to do this is:
Which can also be represented as:
[As the radius of the Earth is equal to 6371000m and Pi is equal to 3.14]
So the farmer only needs to buy π metres of cable (so a little bit more than 3 metres). In fact the answer has nothing to do with how big the sphere he lived on was. If the farmer lived on the sun or a marble he’d still need to buy π metres of cable!