28 March 2014

Welcome the duodecimal currency so says Mr Osborne

Well not quite. This by the way is not Mr Osborne the Green Goblin although he probably has been called worse. It's Mr George Osborne Chancellor of the exchequer.

Also he hasn't announced a new base for the currency, what he has done instead is announced that the humble £1 coin will have a different design. It will have 12 sides. Yes, this is where I have deceived you, I apologise.

What does 12 sides mean anyway? Does it look better?
Well have you ever wondered how machines recognise coins? They have holes which is just big enough for the coin to go through. 20p and 50p are 5 sided which means thanks to rotation and objects of constant width, they are easy to say what the width is. The issue with the 12 sided coin is it does not have that property, it's a bit of an issue, I'm not sure what the solution is. I personally find object of perfect symmetry ghastly but it depends on who you ask. The dozenal society in the UK would probably be quite pleased.

Who are the dozenal society?
They believe that changing the base of currency and counting to 12 will make things simpler, and they are right. Also there is a dozenal society in the UK and in America.
First of all counting. Every number you get in base 10 can easily be converted over to base 12. Take 2014 as a number, the first thing we have to do is work out the highest powers of 12 (power of 12 e.g. 12^0=1, 12^1=12, 12^2=144, ...) that is less than 2014. Which is 3 (12^4=20736 and 12^3=1728).

(12^3)*1=1728. 2014-1728=286.
(12^2)*1=144. 286-144=142.
12*11=132. 142-132=10.

Convert 11 and 10 into base 12 numbers i.e. 10=a and 11=b

There is other methods, this is just one of them.

If anyone does implement the base 12 system they need a symbol for 10 and for 11 and also a name. This I believe is where the fun comes in, for naming anyway. We already have a number which is in alphabetic order (forty) so can we have reverse alphabetic name like trone for example. The other thing we haven't got is a Palindrome (something that reads the same forwards or backwards e.g. racecar, hannah, 123321). For 11 we could have caac or ette. It probably should be only 1 syllable.

With base 10 we count on our fingers and thumbs, thats fine. In base 12 we only use the knuckles of our fingers of 1 hand (see already much more efficient) and the thumb can count along. If you count on one finger you can get to 3, do that on all 4 fingers we can get to 12. Now if use both hands we can get to 143 or 12^2-1, good lots of big numbers, but now you ask about learning the times tables.

Lets count this in base 10. Up to 10 times table there is 100 digits but thanks to patterns we don't need to learn them all, only 77 digits. Times tables 5 and 2 and 10 we can reduce. In the 5 times table, a number ends with a 5 or a 0. We only 2 numbers we need to know. In the 2 times table after 5 numbers it repeats 2, 4, 6, 8, 10. The 10 times table is the same as the 1 times table but with a 0, so we don't need to learn them.
In base 12 however there is a total of 144 digits but we only need to learn 85 numbers. This is more than base 10 but less overall. As a percentage you needed to know 77% of the 100 numbers. In base 12 we need to only know 60%(bit less) of 144 numbers. Why? In base 10 it has prime factors 2 and 5. In base 12 it has 2, 3, 4 and 6. More prime factors means less to remember.

Also base 12 means there is some interesting things you can do with symmetry, but that's a subject for another day.

23 August 2013

Pick Up: there is no uming and O.R.ing in MY queue part 2


Panel 1:

Ryan and Michael are walking to the front of the queue to see what the problem is.
1st Security Guard: Good evening ladies. Have you got ID on you?

Panel 2:

1st security guard checks the ID

Panel 3:

Then he check her chest

Panel 4:

Finally he check out her legs
1st security Guard: Okay, go on through

Panel 4:

Ryan turns to Michael Ryan: Michael, I think we have found the problem.
1st Security Guard: NEXT.

Well there are several problems here, where the hell did the 2nd security guy slide off to?

I apologise for the long long absence, I'm still not satisfied with my drawing ability, hopefully practise makes perfect. Anyway how to you solve a problem of a wandering eye?

3 May 2013

Pick Up: there is no uming and O.R.ing in MY queue part 1


Panel 1:


Panel 2:

Ryan:What are we going to do?
Michael:Nothing. I'm British, I know how to queue.

Panel 3:

Ryan:But what if we could speed it up?
Ryan is rubbing his hands together and looking mischievous. Michael on the over hand looks intrigued and curious.

Okay quite a bigger gap than I said, my delay was due to nervousness over drawing panel 2, as it turns out wasn't that hard and it's okay my art sucks. I'm annoyed I can't draw someone rubbing his hands together.

Since this is part 1 I written part 2 and 3 already. You can guess in the comments what you think Ryan is going to do next.

3 February 2013

Pick Up: Pulling the guys


Panel 1:


Panel 2:

Ryan:hmm <eyes closed, head tilted to one side>

Panel 3:

Ryan:and then... <smooch face>
Michael:What in all-the-numbers-that-have-2-in-it are you doing?

Panel 4:

Ryan:playing a scenario where I team up and apply the Nash equilibrium.
Michael:you want to "score" the blonde girl from the film "A beautiful mind"

Panel 5:

Ryan:<sigh>No, the other girls.
Michael:okay good, what am i here for then?

Panel 6:

Ryan: To help me pull guys to help pull girls

Panel 7:

blank look

Panel 8:

side on, Michael is serious.
Michael:okay, let's do this.

the comic

The proof for all numbers contain 2 was done on numberphile youtube for the proof we just consider positive integer numbers and count the numbers that contain 2 under 10, then numbers that contain 2 under 100 and the percentage of numbers that contain 2 goes up and you can keep on doing this and there is an equation to work it out. Watch the youtube video they do it for 3 but the same rules apply.

I assume most people in the maths area have watch "A beautiful mind". If you haven't I will try not to spoil it for you. A group of women enter a bar, there is one that stands apart from the rest (the blonde) and the guys are saying "best man gets the prize" Nash then saw what the outcome would be and came up with a different method where every guy wins and the blonde lady is left alone.

A guy who is a pick up trainer suggested looking for guys to help find and pick up women. Sounds strange but watch the video.

In the comic Michael the driver is not looking on the road on panels 2, 3, 5 and 7(purely coincidental). The seat belt was added after, if your driving you should always wear a seatbelt. The position of Michaels hands on the steering wheel is at the 10 and 2 position (on a clock) always good practise. The driver is in the left which means he's driving on the left hand side of the road (like they do in Britain).

I have wrote the script for the next one already so it should be up soonish.

21 December 2012

Pick Up: It's a golden car

Ryan: So whose car are we going in?
Michael: mine
Ryan: What? I thought it would be mine because mines cool
Michael: It is cool but my car has dimensions which are closer to the "Golden Ratio"
Ryan: Does this mean what I think it means?
Michael: I don't know
Ryan: It's a real lady puller
Michael: Not exactly... the gears are spaced to make it more fuel efficient. It has a go fast stripe though!

The golden ratio value is irrational so to 5 decimal places it is 1.61803. A while ago someone did a experiment putting different rectangle on a sheet of paper and they asked volunteers to select the most beautiful rectangle and would you have guessed it, it was the one that had a ratio of 1:1.61803... among other reason like Fibonacci numbers this is why this number may be considered beautiful. Sorry it has been so long, had to have the script tweaked, the car is meant to be based on the old volvo cars, nice and boxy. They have hat and scarves because it's winter and cold, sorry about facial expressions. Like I said before if you are a better artist or you know someone who would do this for FUN, get in touch.

Also it's the time of year for presents (Yay!) the giving and receiving of presents. For some people just staying warm is hard enough. The reason I'm saying this is as mathematicians we don't really believe in luck we believe in chaos and probability. Some people have everything going for them then that small chance of probability hits and things gets worse. Someone's situation may be their fault but some of it could be down to the pesky "no-way-is-that-going-to-happen" probability. Maybe this Christmas think of others. Merry Christmas and a happy new year.

15 November 2012

Maths Events in the London area

A while ago I was asked to publicise maths events in the London area, that might be of interest to London based university mathematics students. I was asked on behalf of the IMA (the Institute of Mathematics and its Applications.).
I am not a member of the IMA and all the views in this blog are my own and no way are representative of the IMA.
The Facebook page had been already set up so all I had to do is populate it with events. Harder than you can imagine and also I do need an audience so they can read it (current time of writing it has 190 fans) so I brought it over to twitter, since this is where I was getting any events from.
On Facebook I did run an advert campaign for 2 days trying to aim for London universities i.e.:
  • Birkbeck University
  • City University London
  • University of Greenwich
  • Imperial College London
  • Kingston University
  • Kings College London
  • London Metropolitan University
  • London School of Economics
  • The Open University???
  • Queen Mary, University of London
  • Royal Holloway, University of London
  • UCL, University College London
The main twitter accounts I got my maths event information is these: There is others so I put them in a twitter list not all talk about events, but most of the links are of some interest. If you know of any events please tweet @IMALonEvents or write on the facebook page please.

17 October 2012

Three word guessing game

This I heard from Alistair from Out of the Norm at one of the MathJams a couple of people wondered if you could put this online, well I believe I have done it. The rules are simple, someone puts in a valid three letter word, then the other person guesses using valid three letter words. If you guess one letter or 3 letters correct you will get the result of "odd", if you get 2 letters correct the result is even, if all the letters are correct and in the right order result is "finish".

A couple of things I haven't done, CAN'T play against the computer it is a 2 player game, also can't verify if the word is a proper three letter word apart from that it's all good

Pick a three letter word