Funny maths?

I popped into town to buy a card and and birthday present for my sister. Not many of the ‘joke’ cards were that funny. Take this example:

What is the difference between a man and a calculator? You can count on a calculator.

Well, it is a pun, but how easy is it to actually count on a calculator? On my Casio scientific calculator, you need to think a little bit, it’s not like there is a [count] key. In fact it is quite simple – hit [Ans] [+] [1] [=] and then keep hitting [=]. Of course, calculators generally work in similar ways whereas men generally don’t – you can count (rely) on some but not on others.
So, although the joke might not be that funny, it is probably quite true.

I also saw a mug with the following formula on it:

Love = Passion / Patience

There are no definitions of the variables on the mug, but this seems patently incorrect to me. As Patience tends to zero, Love tends to infinity? Surely this can’t be right?
I also saw a mug bearing this formula:

Dad = (Football + Barbeque) / Helping with homework

I wonder if there are any more in the collection….

Napoleon’s march on Moscow

Tidying up today I found a photocopy of a photocopy of the above map.
Beginning on the left at the Polish-Russian border, the grey band shows the size of the army as it invaded Russia in June 1812. It started with 422, 000 men and finally reached Moscow with 100, 000 men. The black band shows the army’s retreat from Moscow, finally making it back to Poland with 10,000 men. It is this black band that is linked to the temperatures and dates at the bottom of the chart. Altogether there are six variables plotted – can you see them all?

There is a large and detailed version of this map on the Napoleonic Literature website. Some interesting versions of this map can also be found here.

Quadratic Equations

Another situation cropped up last night when a basic knowedge of quadratic equations proved very useful.
Richard Bacon posed a problem on Radio Five Live:

There is a round robin football tournament, where each team plays every other team once and once only. If there are 91 matches in total, how many teams take part?

If there are n teams, then they have to play the other n – 1 teams, making a total of n(n – 1), but each game is counted twice, so the total number of matches must be n(n – 1)/2.*

So: n(n – 1)/2 = 91

=> n(n – 1) = 182

=> n² – n = 182

=> n² – n – 182 = 0

=> (n – 14) (n + 13) = 0

So there must be 14 teams in the tournament, since a tournament with -13 teams does not make much sense.

*The number of matches can also be viewed as a simple arithmetic series:

Team 1 plays n-1 games
Team 2 plays n-2 games (not counting the game with team 1)
Team 3 plays n-3 games (not counting the games with teams 1 and 2)
.
.
Team n-1 plays 1 game with team n (not including the games counted before).

So the total number of games is:
1 + 2 + 3 + … + (n-2) + (n-1) = n(n-1)/2

The number 51

I just read a webpage listing 51 ideas for plenaries. Immediately I thought, 51: that sounds like an interesting number. Naturally, I flicked through The Penguin Dictionary of Curious and Interesting Numbers and discovered I was wrong (and right):

51
This appears to be the first uninteresting number, which of course makes it an especially interesting number, because it is the smallest number having the property of being uninteresting.
It is therefore also the first number to be simultaneously interesting and uninteresting.

Quizzes

Some quizzes that I have written using Hot Potatoes:

ICT quizzes
Speadsheets
The internet
Javascript

Maths quizzes
Brackets
Linear Sequences
Decimal Division
Decimal Multiplication

Christmas Formulae

Last Christmas I found a formula to help with wrapping presents .

This year the BBC reports a fomula for fun derived by toy expert Barry Eldridge. The formula is:

0.22a + 0.17f + 0.153n + (0.12c – 0.1g) + 0.1s + 0.09e + 0.06d + 0.054l + 0.05m + 0.011c = pfg

Where pfg equals “perfect family game”.
a = age range
f = fun factor
n = number of people
c = competitive factor
g – argumentative factor
s = stimulation
e = engagement
d = duration
l = longevity
m = mobility
c = complexity

So – when all the numbers have been crunched, the factors weighed and the wind speed taken into account – which game comes out on top?

“A pack of cards,” says Mr Eldridge, with a pfg rating of 98%.

Largest Prime Number…

2^20996011 – 1, a number with over 6 million digits, has been identified as a Mersenne prime number. It is the largest discovered so far.

Report at the BBC.

You can download free software and join the search for a ten million digit prime number. Click here.

Harry Potter and the Mathematics of Doom

Some people are very sad.

The Secret Lives of Numbers

The Secret Lives of Numbers. I stumbled across this webpage earlier this year: an interesting idea, beautifully executed. Background information on the data can be found here.

(2L+2H+X)(B+2H) cm2

New research has found the perfect formula for wrapping a Christmas present. Read the press release from Dundee University – where Professor Chaplain solved this problem with sponsorship from Woolworths! I shall try out the formula when I wrap my presents next week.