A Level

The Weird and Wonderful World of Pi

Pi Day is on its way – the one time a year where 14-year-olds will see it as socially acceptable to pretend they like maths, and tasty deserts decorated with numbers and Greek symbols grace classrooms worldwide. And this year, Pi Day will be extra special. Take a look at the first few digits of pi (3.1415), turn them into a date and you’ve got 3/14/15! Even better, you don’t have to worry if you’re a little too busy to celebrate Pi Day this year, as the digit following 5 is 9, so if we want to be accurate we can round up to make next year’s 3/14/16 an extra special Pi Day too! In celebration of this occasion, we’re bringing you the top 5 facts about pi to brighten up your revision and make Pi Day 2015 that little bit more special. (Title Photo Credit: Wikipedia)

1 – Pi is irrational. We don’t mean that it’s behaving inexplicably – it’s an irrational number, meaning that no fraction accurately describes pi (except perhaps pi/1, but that’s probably cheating). Pi is also an infinite decimal meaning that those significant figures just keep on coming. Although you’ve been taught that the circumference of a circle is pi*diameter, and that the area of a circle is pi*r2, the irritating truth is that because we can never know all of the digits of pi, we can never truly know the circumference or the area of a circle. (This, by the way, is not an excuse to skip any pi related questions in upcoming exams).

2 – Pi has been calculated by computer up to 13 trillion decimal places, although the human record for reciting it correctly is held by Chao Lu, who remains undefeated since 2005 as reciting 67,890 digits. He had planned to make it to 93,000 but went wrong on the 67,891st… ouch! He did do quite a lot better than Ludolph Van Ceulen though, who spent most of his life calculating pi to 35 digits (although we suppose he was probably at a disadvantage for having lived in the 16th Century). In fact, computing pi is so difficult that it’s used as a stress test for modern computers. Those of you who watched Star Trek may remember Spock defeating an evil supercomputer by commanding it to calculate the last digit of pi.

3 – If you’re celebrating Pi Day today, you might do it by baking a pie. Maybe with the pi symbol on top. Maybe throw some pineapple in there? Go crazy. It’s pretty cool how pi and pie sound the same, right? They actually make a better combination than you might think; write 3.14 on a piece of paper and hold it up to a mirror… Spooky.

4 – Pi has a lot to say in terms of practical applications too. Well, sort of practical, probably more strange than practical. Want to convert between seconds and years? An easy rule of thumb is that there are roughly pi*10 million seconds in a year. This also means that pi seconds is roughly one “nano-century” (1 billionth of a century), so we can flip this relationship to work out that if you live to 100 years old, you’ll have lived for roughly pi billion seconds. Better get counting…

5 – This last fact is our favourite – pi is in rivers too. Its is a pretty cool phenomenon, although it does take a bit of explaining. Sinuosity is defined as how bendy a line is, measured as a ratio between total length and length from start to end “as the crow flies”. For an easy analogy, the curlier your hair is, the more sinuosity it has. Here’s the weird part: the average sinuosity of all the lakes and rivers on planet earth is, you guessed it, pi.

This phenomenon actually has a very rational explanation. Those of you who’ve studied chemistry may know that the universe tends towards disorder. The same applies for lakes and rivers; as they flow, the outer banks become eroded and the bendiness of the curves increases. So why doesn’t the sinuosity exponentially increase? Well, as the curves get curvier and curvier (imagine here a horseshoe shape), the river or lake will naturally try to use the quickest path of flow (which in this case would be bridging the top of the horseshoe, rather than travelling all the way around the outer edge), hence reducing the sinuosity.

Okay, so that first bit makes sense, but why pi? The researchers who initially noted this relationship attributed it to the fact that waves in a river are like little semi circles, and so the equation circumference = pi*diameter is responsible. However, this theory hasn’t been directly tested, so, just like pi itself, this phenomenon remains a little bit of a mystery.

What weird and wonderful facts about pi would you like to share with us?

Written by Sophie Valentine

A MyTutor Chemistry Tutor

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