I am indebted to Jen for drawing my attention to a truly great offer from Sainsbury’s.
You can currently take out a subscription to 12 monthly editions of their excellent magazine for just £20. The usual cover price is £1.60.
That’s a yearly saving of −80p.
Fact: Bad mathematics can get you chatted-up. Well, sort of. Bad mathematics certainly got me chatted-up once; I don’t know if it works that way for everyone. Well, when I say chatted-up, I mean spoken to unexpectedly by a member of the opposite sex—which pretty much counted, back in the early 1980s. Or it might even have been the late 1970s.
Irish Mick and I were on our way home from school. For some reason, we were on the top floor of a bus. There must have been something wrong with the trains. Anyway, it had been raining heavily, and the windows were all steamed up, so I explained to Irish Mick (who wasn’t even Irish Mick back then) how I could prove mathematically that two equals one. I wrote my proof in the condensation on the window. It went like this:
Let a = b
∴ a² = ab
∴ a² – b² = ab – b²
Factorise…
(a + b)(a – b) = b(a – b)
∴ (a + b)(a – b)= b(a – b)
∴ a + b = b
But remember, a = b, so…
b + b = b
∴ 2b = b
∴ 2 = 1
Q.E.D
Irish Mick looked on bemused, then went back to reading The Lord of the Rings. After about ten minutes, however, this cute girl on the seat behind us leant forward and said, “Excuse me, I’ve been staring at that proof for ten minutes, and I can’t work out what’s wrong with it. Can you explain, please?”
So I did.
I never saw her again.
Lesson: Never explain anything: it totally destroys the air of mystery.
(Yes, I could easily get to 953 as well.)
(via OpenCulture)
BBC: Complaints over Clarkson strike comments reach 23,000
The BBC has received more than 23,000 complaints over Top Gear presenter Jeremy Clarkson’s remarks that striking public sector workers should be shot
To put this figure into some sort of perspective, Mr Clarkson’s original complaint was about what their unions claim were two-million public sector workers on strike this Wednesday.
That’s 23,000 complaints versus Clarkson’s two-million.
Remember that video of the Miss USA contestants’ trying to justify why evolution either should or should not be taught in schools? Well, now there’s a rather wonderful piss-take parody:
God Bless America! (Even though they don’t know how to spell Maths.)
BBC: Councils lobby government to raise parking fines
… The British Parking Association argues that the differential between the cost of parking all day and the penalty charge for not paying it must increase in order for there to be a deterrent.
For one point, children, can you think of any other way of increasing the difference between the cost of parking all day and the penalty charge for not paying, other than by increasing the penalty charge?
I went to buy a book in Waterstones this week. Its recommended retail price was £25, but there was a sticker on the front saying there was £9 off. Woo-hoo!
The girl on the checkout zapped the book. “Oh, the computer hasn’t taken the £9 off!” she said, and she walked away.
I watched open-mouthed as the girl returned a minute later with a pocket calculator and began to punch in a calculation.
“It’s £16,” I said: “twenty-five minus nine is sixteen.”
“You’re right!” the girl said, clearly impressed. “I’m hopeless at maths.” I didn’t say that I could tell.
“The trick is to take off ten and add one,” I said. The girl looked at me as if I was from another planet. “Taking off ten and adding one is the same as taking off nine, but it’s easier,” I tried to explain. The girl looked back at me blankly.
So I paid my money and left.
Thinking about it afterwards, I should have pointed out that 9, 16 and 25 represent the squares on the sides on a classic Pythagorean 3, 4, 5 triangle.
That should have made it a lot easier.
That’s how many plastic bags were reused by the customers of the Prestwich branch of Tesco last week. Someone had hung a sign up telling us so. Every little helps, they couldn’t help adding, without a hint of irony.
I know for a fact that seven of those bags were mine. That’s 2.18%.
It seems to me that, at this rate, it’s going to take an awful lot of time to save the planet.
Having said that, if and when we do finally save the planet, it seems only fair that 2.18% of it should be mine. That’s 11,119,430 km2.
What’s the missing number?
Admit it, you think it’s 5, don’t you? Occam’s Razor and all that.
Stop thinking so linearly. I’m all for keeping things simple, but you need to let your hair down once in a while.
The answer I’m looking for is 17.
Why? I’d have thought that much was obvious: 1, 2, 3, 4 and 17 are the five solutions to the polynomial equation:
x5 – 27x4 + 205x3 – 645x2 +874x – 408 = 0
Like all good puzzles, it’s obvious when you know the answer.
Good job that didn’t come up in an IQ test, eh?
New Scientist (21-Jul-2007): Interview: Why mathematics is beautiful
Christopher Zeeman is a British mathematician who inspired generations of young people, built a world-class maths department from scratch and still manages to find time to correct theorems developed by Euclid in ancient Greece…
You built a world-class mathematics department from scratch at the University of Warwick when it was founded in the 1960s. How?
I wrote to the six best topologists in the world asking them to join me. They all said no. So I wrote again saying the other five had agreed, and all replied to say yes.
That’s the way to do it.
See also: Here’s looking at Euclid
BBC: UK adults fail child’s maths test
One in 14 adults cannot answer a maths question aimed at eight-year-old children, a survey suggests.
One in 14… That’s almost 23%!
Here’s a (pretty simple) maths problem for you: a rectangle has an area of 15cm2 and a perimeter of 16cm. What are the lengths of its sides? The answer, if you can’t work it out (or even if you can) is 3cm and 5cm. Here’s how you might work it out:
But hang on a second… Look at the sixth line:
n2 – 8n + 15 = 0
Just think about what that’s saying (bearing in mind that we now know n = 3cm): that’s saying that 9cm2 (an two-dimensional area) take away 24cm (a one-dimensional length) and add 15 (a no-dimensional integer) equals nothing.
HOW THE HELL CAN YOU TAKE AWAY A LENGTH FROM AN AREA? THEY’RE TWO ENTIRELY DIFFERENT THINGS. IT’S LIKE TAKING AWAY CREAM CAKES FROM THE COLOUR BLUE!
Maths is crazy.
I fully appreciate this is hardly the right time of year to be worrying about this sort of thing, but you’ll be thanking me in December, mark my words.
Have you ever noticed how the year number changes at the end of each year? Damned confusing. Well, I’ve been doing some reverse-engineering, and I’ve come up with a handy, little formula for working out what next year’s number will be:
(Where yn = next year’s number, and y = the current year’s number. Works for all years after 1 A.D.)
I await the call of the Nobel Committee.
Ever since I first encountered it at school, I’ve always admired the elegant simplicity of the reductio ad absurdum proof of the irrationality of the square-root of two. I know, I know: I really should get out more.
This week’s New Scientist includes a description of Euclid‘s equally elegant and simple, 2,300-year-old, reductio ad absurdum proof that there is an infinite number of prime numbers. I hadn’t seen it before. It’s really neat. The description goes as follows:
Suppose a mathematician comes with a finite list of primes and claims there are no more. Euclid showed that there must be a prime missing from the list. Multiply all the primes on the list together and then add one to this number. This new number is not divisible by any of the primes on the list because you always get remainder one. So Euclid’s new number is either another prime itself or divisible by a prime that is missing from the list. If you add this new prime to the list, repeating Euclid’s trick will always show that any finite list is missing a prime.
Sorry to bore you with maths. The real reason I’m doing it is because I just thought of the here’s looking at Euclid pun, and I really didn’t want to let it to go to waste.
New Scientist letters: Not so Fibonacci
From Ian Stewart Coventry, Warwickshire, UK:
Gael Mariani and Martin Scott perpetuate a series of myths in their letter about Fibonacci numbers in nature (3 September, p 19). It is true that the Fibonacci numbers are associated with a particular kind of spiral – the logarithmic spiral – and they are also closely associated with the “golden number”, which is roughly 1.6. And the nautilus shell does have the form of a logarithmic spiral.
Unfortunately the correlation ends there, because there are many different logarithmic spirals. In such spirals the space between consecutive windings grows exponentially at a fixed rate, and this rate can be any positive number. The usual “Fibonacci” spiral has a growth rate of about 6.8 – the fourth power of the golden number – whereas that of the nautilus is about 3, meaning it is too tightly wound to be related to Fibonacci. This growth rate is different in different gastropod species.
The spirals in horns have even less to do with Fibonacci. The connection with elephant tusks is pretty much non-existent. The spirals of galaxies are not even logarithmic. In particular, most have two arms winding from the centre, whereas the logarithmic spiral has a single arm.
The connection between Fibonacci numbers, certain spirals, the golden number and the structure of many plants is genuine and increasingly well understood. Most other alleged occurrences of Fibonacci in nature are bogus.
A great example of people getting carried away by an interesting phenomenon.
Fitz did a great cartoon about Fibonacci spirals in snail shells many years ago. I must ask him if he still has a copy—but only maths anoraks will appreciate it.
Talking of obscure mathematical cartoons, see also: Challenge
Conversation with someone you don’t know earlier this week:
R: Did you know that, if you write each of the first three odd numbers down twice like this, 113355, and then move the second three above the first three to get a fraction, you get 355÷113?
X: So what?
R: Work it out on your calculator. What do you get?
X: 3
R: No, don’t round it down. Read it out in full.
X: 3.1415929
R: Isn’t that cool?
X: What the hell are you talking about?
R: Doesn’t that number ring a bell?
X: Nope. Should it?
R: It’s a very close approximation to the number pi. It’s miles better than 22÷7.
X: What the hell is pi?
R: WHAT?! You must have heard of pi, it’s one of the most important numbers in mathematics!
X: Oh, I’ve heard of it all right, but I don’t know what it means. I was never any good at maths at school. Why is pi so important, then?
R: It’s the number you get when you divide the circumference of a circle by its diameter.
X: Why the HELL would I need to know that?
R: Well, it’s really important. Suppose you were going to paint a circular door, for example…
X: Where would I get a circular door?
R: It doesn’t matter. Just suppose you were going to paint one. How would you know how much paint to buy?
X: I’d just buy five litres. That would be plenty.
R: …Ok, bad example, forget about the door. Imagine that teapot over there was a perfect sphere two feet across…
X: Can’t I imagine a cube instead? They’re easier.
R: But you don’t need pi for cubes. Pi is for circular stuff.
X: Oh, I see, pi doesn’t work on cubes—IT’S JUST A BIG CHEAT!
R: No it isn’t. Pi makes it easier to do calculations with circles. That’s the whole point! So imagine you’ve got this sphere two feet across and you wanted to fill it with water. How much water would you need?
X: I wouldn’t need to work it out. I’d just fill it from the tap.
R: Yes, but if you did need to work it out, how many cubic feet of water would you need?
X: I suppose you’re going to say pi.
R: Well, almost. You’d actually need four-thirds pi cubic feet.
X: ARE YOU HAVING ME ON?
R: NO! That’s the volume of a sphere: four-thirds pi times the cube of its radius.
X: YOU SAID IT DOESN’T WORK ON CUBES!
X is right of course. I have never needed to use pi outside my school maths homework—even though I can still recite it to 22 decimal places (nerdish schoolboy’s trick).
Mind you, did you hear about that Japanese bloke the other week who recited pi to 83,431 decimal places?
WHAT THE HELL WAS THAT ABOUT?
Postscript:
HOLY CRAP!!! I PROMISE I didn’t fix this… I just read on Wikipedia that today (22/7 in British date format, geddit?) is Pi Approximation Day.
Of course, you realise this proves that the paranormal is real, and there really is a god.
[Actually, there are two Pi Approximation Days (see Wikipedia article), so the odds of my publishing this particular item on one of them is 2 in 365 (or 1 in 182½). Hardly amazing, if you think about it—but still rather pleasing.]