IT’S THE MATHS

Let me start out this month by bending your brain with the ultimate ate `how long is a piece of string?’ question. I love stuff like this, and I’m doing you a favour, vour, because as any neuro-quack will tell you, making your brain do new things is a great way to maintain aintain and even build new neural pathways and in extreme eme cases, even stave off dementia. Brain plasticity and all that.

Anyway, here’s the pop quiz: The planet Earth is a big ’un (maybe not by Milky Way standards, ndards, but I wouldn’t want to have to vacuum it, right?). t?). With a diameter of (depending on where you’re standing anding or where you look it up) 12,742km, it therefore e has a circumference of 40,035.364km. So far, so third-grade.

But here’s where you get to challenge your own brain. Let’s assume you had a series of little posts measuring just 100mm from the ground to their tip, and you placed them right around the Earth’s equator. Yeah, yeah, I know, you’d need a couple of weeks to do this, but stay with me here. Next, you run a piece of string from the top of the first post, to the top of the second and then the third and finally right around the planet (there goes another couple of weeks). You now have a piece of string encircling the planet, 100mm above the ground.

So the question now becomes, how much longer is that piece of string than the earth’s circumference? If you’re anything like me, you’ll be tempted to say many, many, if not hundreds, of kilometres. I mean, it’s got to be at least a few kilometres, right, based on even a small change to the huge distances we’re working with, right?

Um, wrong. If you do the maths you’ll find that our piece of suspended string is, in fact, just 628mm longer than the circumference of the planet around which it’s strung! And that’s because maths doesn’t lie, nor is it any more flexible than your ex-partner. Circumference is diameter multiplied by Pi (3.142) and if you take the 200mm (that’s the 100mm you’ve raised the string on both sides of the planet) you’ve added to the diameter and multiply that by 3.142, you get 628. That’s millimetres. Yeah, 62.8 centimetres! Amazing?

An old mate tortured me with this a few years back, and it still does my head in. But then you start to mess around with the formula and it starts to look pretty solid. Even, for instance, if you made those posts one kilometre high (to keep the maths simple) you’ve only added two kays to the diameter of the new circle you’re measuring. So let’s crack out the calculator. That original circumference we talked about for the planet was 40,035.364km, based on a diameter of 12,742km. Now add the extra two kliks (12,744km) and multiply that new diameter by Pi. You get 40,041.648km and, therefore, you’ve only added 6.284km to the string’s journey. Makes setting the timing marks on a DOHC engine seem simple, no?

Bottom line? If you can’t win beers with this at the pub, you aint trying. Either that, or I’ve just ruined your headspace for the next week. You’re welcome.