## Abaci, Pi and Mathematical Ink

There are a few things that have been at the forefront of my mind recently, and I thought I would write a post about them here and see if anyone can add anything.

The first is the question of Abacuses (or Abaci? I don’t know the correct pluralisation). Having a 9 month old daughter has meant that invariably I have spent rather a lot of time in toy shops/mothercare/the early learning centre etc since she was born. During one such visit recently I spied an abacus. I think they are fantastic instruments. Although I don’t know too much about them. I figured that, as we live in a base ten world, each wire should have nine beads on it. That was 1-9 would be on wire a then ten would be the first one on wire b. However, all the Abaci I have been able to find have ten beads on each wire. Have I misunderstood the use? (Having read up a little it would seem the Romans used them in line with their numeral system, so currently a 9 bead approach would be the natural successor.) I suspect the ten bead per wire has been introduced at somepoint by someone who didn’t realise why there was only 9. If this (9 per wire) isn’t how they were meant to be, then someone’s missed a trick. I want one (9 per wire) for my daughter, and one for school, as I think it could be a really useful tool for teaching place value!

The next thing that has been on my mind recently is Pi. (Not pie!) this has been prompted by a friend of mine called Steve who is planning to get Pi to 39 digits (so 38 dp) tattooed on his arm. (If you aren’t aware of the significance of 38 dp, this video explains it well http://www.numberphile.com/videos/pi_universe.html ). He asked me whether I thought he should round to 38 dp or put it as is and dot dot dot, my answer was simple: “we’re mathematicians, not physicists nor engineers, don’t round!” he found it a persuasive argument!

This conversation led to me wondering out loud, how many dp do calculators hold Pi to? I assumed it is more than the display, but how much more? This prompted a few trials: His Casio silver holds it to 12dp, His Phone (can’t remember the model) to 8 dp, my phone (Iphone4) to 16dp. Calculators we had at school: Sharp 13dp and texet 11dp. I’d be interested to hear if your phone/calculator hold it any further!

We discussed maths tattoos for a while, he knew someone with e^ipi + 1 = 0. We agreed phi = 1 + root 5 all over two would be cool. Graham’s number would be cool. A colleague of mine has a Casio calculator circuit board tattooed on him, which is awesome. Navier-stokes, Euler’s Formula, de Moivre’s theorem were all suggested as possibles maths tattoos! Have you got any? If so I’d love to hear about them, or even just ideas of them would be cool.

A modern soroban, still a commonly used and very fast calculation tool, has 4 earth beads and 1 heaven bead for each place. The heaven bead is worth 5, for a total of 9. Older soroban had 5 and 1 or 5 and 2.

Speaking of base 10, before Steve gets a tattoo of base 10 digits of π, ask him to have a glance at: http://ccssimath.blogspot.com/2013/03/the-life-of-pi.html

I only know of abaci that look like this… http://www.computerworld.com/common/images/site/features/2011/01/abacus.jpg although a 10-bead one makes no sense…

Tatto wise I don’t just have a calculator circuit board (Casio FX85-ES, since you ask…), I also have Heisenberg’s uncertainty principle – a big favourite of mine.

I new there was an inequality, but couldn’t remember which one!

Someone should get a tattoo with as many digits of Pi as they can. I think that could turn into a bit of a thing!