h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Entry: Mathematics in the Arts - A2756180
Author: Cyzaki - Join the (un)official F1 supporters' club A1918244 - U223973

This is an essay I wrote for one of my university modules this last year. Please review, comment, and pull it to pieces!

Interesting one, this.

Given that it's a Latin word, I suspect the Pythagoreans didn't actually use the word 'Quadrivium'. If you're taking the term from the Trivium/Quadrivium distinction in mediaeval universities, you'd probably better say so, even if there's a direct link.

Since the title refers to 'the arts', I recommend saying something like 'the visual arts' instead of 'art' at least once. I know what you mean by 'art', but the terminology still looks inconsistent.

Regarding literature -- Flatland! Plus Ian Stewart's Flatterland.

I don't suppose DNA's '6 x 9 = 42' qualifies...

Cyzaki, this is a very involved piece that you've covered well.

It seems to me that there are arts missing from the outline. Perhaps you would want to include dance? Especially in that it is closely related to tempo, and uses additional mathematics that describe how one counters gravity to sustain movement.

If anyone wants to write a paragraph or two about any of the arts they think I have missed, I can include them and credit them. I would find it hard to do that myself as I'm at home now, not uni, and so don't have access to my uni library where I did much of the research for this.

I'll have a look at changing 'art' to 'visual arts'.

His work isn't exactly high culture, but it's music/lyrics and it's great: besides 'That's Mathematics', which is more about what maths does than about how it des it, and 'Lobachevsky', which uses maths to frame a song about plagiarism, Tom Lehrer's (A907517) 'New Math' actually works maths into lyrics, based on the changes in U.S. maths teaching that were going on when the song was written.

'And so you've got thirteen tens,
And you take away seven,
And that leaves five...

Well, six actually,
But the idea is the important thing!

Now go back to the hundreds place,
And you're left with two...'

(That it works written down and out of context I actually doubt, but I assure you it works in the song.)

Oooh what fun. One of my favourite topics. Some comments in no particular order.

You could say more about Escher. Not only did he play with perspective but he did a lot of other interesting stuff mathematically. For example, his tiling pictures, as well as being amazingly clever, illustrate some serious mathematics. He did spherical, Euclidean and hyperbolic tilings (which are all the 2 dimensional mathematical possibilities). He worked closely with the mathematician Coxeter in coming up with some of these ideas, read papers by mathematicians, etc. There's probably loads more one could say about him. Have a read of this fantastic page:

http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Escher.html

Given that there's already an edited entry on Escher, you don't want to go in to too much detail but I think you could probably say a little more.

My personal feeling is that the stuff about the golden ratio is a load of nonsense. Not what you've written, which is good, but the idea that there is anything important about the golden ratio. IT'S JUST A NUMBER! I suppose it has to be included though, to satisfy the numerologists.

I kind of feel the same about fractals.

More importantly, I think you've missed something out. The thing is that mathematics has an aesthetic element to it. Some mathematical ideas are just so pleasing and just feel 'right' that they can give you a sense of pleasure which is very much like listening to a fantastic piece of music or looking at a wonderful painting. Perhaps you missed this out because your subject is 'mathematics IN the arts' and not 'mathematics AND the arts' but you do say 'this essay aims to show that there are many more, deeper, links between the mathematics and the arts' (incidentally, that should be just 'mathematics' not 'the mathematics' I think). You're doing maths at university right? So, think about something like the proof that sqrt(2) is irrational, or Cantor's diagonalisation method.

Also, mathematical research is a creative activity. Research mathematicians work with their intuition, their aesthetic sensibilities, their feelings about what is right. I imagine that artists are in a similar situation. Just as a mathematician has to learn the 'rules' of mathematics, so a painter has to learn techniques, or a composer the theory, etc. Just as mathematicians spend a lot of time working out the nitty gritty details of things, so do many artists (the painter actually has to paint the thing, not just come up with the idea), the writer has to craft each sentence, etc. In both the arts and in mathematics, you have short bursts of creativity followed by a long hard slog turning it into the finished thing.

Oh, and I want to second RFJS' suggestion to include Tom Lehrer. I love the Lobachevsky song, it's a real lesson in the history of maths (as well as including the title of Lehrer's own maths PhD thesis). :D

Having studied mathematics, and being a bit of an artist, I never thought that I am sometimes combining the two, although very aware of perspective when scaling drawings up for scenery. Thanks.

The 'golden ratio' was also considered in 3D - being a component often considered in architecture - though I can't quote any examples!

English bell-ringing peals are also purely mathematical being a series of all possible orders of the bells.

One 'typo'- missing quotes for title

his On Perspective for Painting was the most mathematical. >
his 'On Perspective for Painting' was the most mathematical.


Watermusic

Nice entry.

A couple of ideas for further poins should you want to include them:

The dance link that FT mentioned - there's always folk dancing, which is very mathematical (eg going through the permutations of positions when lined up and moving around each other)
And the architecture part - maybe add a mention to the Acropolis (I think that's the one, anyway), which was built 'wonky' so that when seen from the bottom of the hill, where everyone lived, it looked right.

And there were a couple of typos I noticed - give me a minute and I'll find them again.

Ah yes, in the "Mathematics in the Visual Arts" section, end of the second paragraph, you might want to change the last sentence to split it into two or something. Putting a full stop before the "However" might work.
Also, another idea: possibly name the greek symbol that is used for the Golden Ratio? I tend to read aloud in my head, so if I don't know what it's called it rather throws me.

You could even link to A216073 if you really wanted to.

Is 'A Beautiful Mind' worth mentioning? I haven't seen it, so I don't know how mathematical it actually is.

Oh, 'New Math' definitely works both within the song and without. Mr. Lehrer would even use what he termed 'primitive visual aids' in order to go through the problem three times.

The first time, spoken, he would use good, old-fashioned subtraction; but, after going through the new math version in song, he'd declare that the answer was 'wrong' because the book from which he gleaned the problem wanted the computation done in base 8.

And so, verse 2, the same problem in base 8.

Thanks for the comments, guys. One problem with the essay I wrote was the word count - I couldn't fit *everything* in as I had a word limit to keep to. However, there's no such thing as a word limit here so keep on suggesting things!

I'll have a look at all the suggestions already made and try to fit them in

I *think* I've addressed all your comments, yell if I haven't, and also yell if you want to be credited for bits of your stuff I've added

Even if you don't think it strictly qualifies as literature, I still think Flatland deserves at least a brief mention.

http://www.alcyone.com/max/lit/flatland/

Great entry.

You could also mention Bridget Riley. Her 'op art' can also be seen as mathematical in the ratios of line thickness and frequencies of neighbouring colours.

Along with perspective other aspects of mathematics like trigonometry and symetry could also be covered.

However, it's always difficult to know where to draw the line (pun not intended); perhaps it could split it into different entries one covering visual arts one covering music/dance and another for literature (I think there is a lot more that could be put into that Lewis Carroll's maths could probably be an entry in itself).

Having said all that it seems like I'm saying that you entry isn't good enough - but that's not the case. I'm trying to do a couple myself at the moment and quickly realising how much work it involves! But you could possibly concentrate this entry on one area and put other sections into the Collaborative Writing Workshop? Anyway it's your (prime) number.

I think if people want to go more in-depth on particular areas, they could write their own entries which could be linked to from this one. There's already a 'mathematics in music' entry in PR somewhere, but it doesn't seem to be getting anywhere. If I write much more in this entry, I think I run the risk of making it too long and involved, so nobody who isn't already interested would read it.

Oh, and my main problem with including Flatland is I've never heard of it before, so wouldn't know what to say about it

I take it you haven't time to read it, then.

I'll see whether I can dig up some general information somewhere.

http://www.geom.uiuc.edu/~banchoff/ISR/ISR.html

http://mathforum.org/mam/00/master/people/abbott/satire.html

http://www.fortunecity.com/emachines/e11/86/tourist4a.html (Warning: this page will try to get you to install something.)

http://www.sciencenews.org/articles/20000101/mathtrek.asp

Any good?

Interesting entry.

Perhaps a sentence or two in the 'Literature' section could be added on the mathematical nature of poetry. Dante's 'Divine Comedy' has, I'm told, a number of complex mathematical patterns running through it.