Here’s another reason why you should read xkcd. Awesome stuff.

Happy Valentine’s Day to you all (btw, it’s over rated).

Want more information about the Sierpinski triangle? Try wikipedia.

This was written by the late Stanislaw Lem. This poem is featured in his book the Cyberiad. I recommend it

Happy thanksgiving y’all!

Expect Math-art to be updated on a regular basis now that Australian Uni is out of session. Today’s math-art is again, food. And its a pecan pie. Or, rather, many pecan pies in the shape of an icosahedron.

Now I’m quite sure math-art readers are quite familiar with what icosahedrons are, so no new explanation is needed. But the best thing about this pie is that it’s modularly constructed. Each triangle is its own module. And what’s more, you can make it for yourself! The instructions are here on Instructable.

If anyone managed to make their own, do tell me. I’m interested (since I really suck at baking)

Yes, I know I have a fetish for food pictures and pie. This is an apple pie, baked by my friend one late night. I tried to get him to cut one slice that was 1/2 ? radians for me, but apparently he thought I was getting to large a piece already :(.

So that slightly-smaller-than 1/2 ? radians was all I got. That said, apple pie + ice cream + loads of custard cream = Win for a midnight snack. Gotta get the recipe from him.

p/s: for those who do not know what 1/2 ? radians is, it’s simply 90 degrees - or in the case of this pie, one quarter of it (oh shut it, I know I AM greedy)

Aaaaaaand, we’re back! To all those who applied, I’ll email you guys soon. Thanks for the enthusiasm.

Today’s math art is a sculpture of a rhombic dodecahedron, by Vladimir Bulatov. I’m sure by now, most of you, my beloved readers would know what a dodecahedron is - but in case you forget, its a polyhedron with 12 sides. Aha!

Now, what caught my eye about this sculpture is its rhombic form. I must confess, I’m a sucker for things like celtic knots, and this sculpture is like a celtic knot, only in 3D. The topography from the view posted above is almost a celtic knot.

Though I must say, I am quite confused as to how its actually a dodecahedron. Vladimir mentioned that he models his sculpture virtually before cutting them. So, I suspect he started out with a plain rhombic dodecahedron - that’s how it’s got its rather unimaginative name. If it were me, I’d call it something like the Infinite Celtic Knot In Three Dee or something.

Tell me what you think

p/s: gotta upgrade my wordpress soon.

I’m so sorry for not blogging in a bit. University has just started, and you know at the beginning of semesters, we have plenty of stuff to do. As such, I am looking for contributors who are interested in writing for Math-Art.

You preferably have an interest in mathematics and art. You do not necessarily need either qualification, as just an interest is sufficient.

Please leave a comment below with an email address that I can contact you with. Thanks

You know how some artists have immensely beautiful work, but ridiculous names? Well, today’s math art features one such artist - Kern S. For all his genius in making sculptures, he could have at least named his work less serially.

Reader Francesco from Italy had submitted this to me, thanks to her. Today’s math art is a virtual sculpture, meaning it was made with a program like 3DS Max or Maya. According to the artist, it combines

“the moebius strip transformations with some attractor extraction formula.”

Which of course, yielded this beautiful result. Yes, the focal blur looks a little fake (hey, its a virtual sculpture afterall - I’ll guess its a photoshopped lens blur), but this is one piece of magnificent art nonetheless. Now sit back and relax

Okay, slight detour today, as promised.

Today, I’ll be talking about the Noh performance. I had the privilege to catch an annual performance of the Noh in Kyouto. And while I didn’t really understand the thing, I did notice some mathematical quirk about the Noh performance.

When I came back to Australia (and had internet access), I Wiki’d Noh, and read up about it. And I was kinda right. You see, in Noh performances, there is the three-act structure (here’s something humorous about the three-act if you want to skip this article) - known in Japanese as the jo-ha-kyu. Basically, it means beginning, exposition and climax. I noted that there rarely is a closure kind-of end - in all four of the plays, they were all left hanging, as though as there was more to come - only the last play had somewhat of a half-closure.

But let’s look at the way the Noh is structured. The whole performance consisted of one half-Noh, followed by a speech by the Governor of Kyoto and a firelighting ceremony, which is then followed by three full Nohs. The entire performance is largely based on Genji mono (The Tale of Genji - one of the world’s first novels).

Anyways, if you look at it, the first half-Noh served as an opening theme song-esque type of performance (and it was full of singing too), followed by the intermission (the Governor’s speech, and the awesome firelighting ceremony), then the real story starts. The four Nohs are all separate stories, but strangely, after the entire performance is over, you can’t help but notice they’re actually telling a more sublime, unseen story. The three plays that follows the firelighting ceremony is largely a jo, ha and kyu respectively - i.e. they’re the begining of the story, the exposition, and the climax. Even though the third play was a largely different type of play in the sense that it is a parody play, and occasionally breaks the fourth wall, after the whole performance, you realize that it served really well as an exposition tool.

So, the three stories are jo-ha-kyu respectively. So what? Well, for one, each play has its own jo-ha-kyu sequence as well. Each play has its own beginning, exposition and climax. But wait! There’s more! Within each section of the play, there is jo-ha-kyu as well! For example, in each beginning scene, there is a scene where the music players step out from the stage, and sit down. Then the actors will appear, telling a bit of the story first. Then they will play on till the music hits a climax, and stops, usually quite abruptly. Then you know its time for the ‘ha’ part of the beginning section of the play.

And according to some of my friends, if you watch carefully, even the way the actors start and stop each speech and each song, each step they take, all follows jo-ha-kyu.

Now, if this starts to sound familiar, don’t worry, you’re not lost. Yes, the Noh play, I have concluded personally, is a very self-similar artform (why else do you think you see me talk about a Noh in Math-art?). It is self similar down to the point of each individual speech action of the actors and musicians are part of the math. They all incorporate the jo-ha-kyu in every aspect of the whole performance. Some are so subtle in the big scale and some are so subtle in the small scale, that you don’t really notice till after the performance.

If you’ve got a chance to see a Noh performance, go see it even if you have to pay extra. It’s both a cultural, as well as a mathematical art that is to be enjoyed. If it so happens that the Noh is playing a story you don’t know, don’t worry. Some things just transcend the language barrier. Math and art are one of those things. As such, Noh is too.

Oohayo! (That’s good morning in Japanese.) Firstly, I must say I’m sorry for the horrible lack of updates. I was busy for a period of time, followed by another period of time in Japan. Then when I tried to update, I found out I couldn’t upload pictures (turns out,the pictures I had been trying to upload were too big) - that’s resolved now

I noticed something when I was in Japan. Fractals are a big thing. Of course, there is Hokusai, which I once featured here in Math-Art, but Japanese people seem to love fractals and the concept of self-similarity a lot. Of course, one of the few things you’ll realize in Japan is that everything is so orderly and perfect - there is almost a mathematical precision about the way they do things, from the way they individually wrap fruits (yeah, you buy individually wrapped oranges and apples). I think self-similarity ties in to their culture a lot - on how the self affects the society as a whole - I’ll talk about that a bit later.

But back to the self-similarity bit. Self-similarity and Japanese culture seem to go hand in hand. Today’s math-art has been featured before - it’s Hokusai’s Great Wave off Kanagawa. But where else do you see a huge reproduction of the painting for only 1890 yen? That’s AUD19.00. I saw this in art shop in a market in Kyoto, but too bad I didn’t have the time to go in.

In my next article, I’ll explore an ancient Japanese cultural practice that strongly exhibits the concept of self-similarity - the Noh performance.