3D and Math

While watching this video (from here) on how to turn a sphere inside out without cutting it, I thought of taking the game at planarity.net that was mentioned by Mehran Sahami in a CS class and modifying it to make the edges bezier curves.

Curves similar to the ones shown below, in a picture I took at Macy’s of the lasers from what I believe is called an omnidirectional barcode scanner. 
Which looks surprisingly similar to a spirograph (video of one being drawn with an amusement park ride below – it’ll start drawing 10 seconds in to the clip, cool interactive ones online here and here).

Which bears striking resemblance to the spirals in a sunflower.

While I don’t have the toy version of a spirograph, I did order the Ball of Whacks, which I’ve been carrying around with me wherever I go.  Here’s some stuff I made:

I haven’t been able to make anything like this dodecahedron, printed in 3D sugar by Windell Oshakay from Evil Mad Scientist Labs (check out this picture, one of the first prototypes using the printer) and presented to me at a recent meeting of the Open Source Group:

Some other games that are in 3D include 3D versions of chess, go, John Conway’s Game of Life, and Mandelbrot’s 3d fractals.  Then there was the sphere-packing problem (what’s the most spatially-efficient way to stack a pile of oranges?) that, when solved (with the aid of a computer, like the 4-color map theorem), verified the common-sense answer.

Though what really fascinated me was this optical illusion from the excellent Tim Robbins film The Hudsucker Proxy:

which I tried to reproduce in Mathematica with some help (what I have so far is just 2 tilted toruses).  I really want to watch the film adaptation of the book Flatland.

The Boston Museum of Science had a really nice quincunx to demonstrate the normal distribution, as balls fell down and bumped into the pegs (which I couldn’t figure out at first, until I realized the balls were not starting uniformly distributed across the top, but at the middle). Is there a 3d equivalent of Pascal’s triangle?

Manifold Destiny

Great piece in the New Yorker about Grigori Perelman, the Russian mathematician who solved the long-standing Poincare conjecture and refused the Fields medal. The draft of the first part of his proof is here. An excerpt:
“

When a member of a hiring committee at Stanford asked him for a C.V. to include with requests for letters of recommendation, Perelman balked. “If they know my work, they don’t need my C.V.,” he said. “If they need my C.V., they don’t know my work.”

”
and…
“

The acting director of the mathematics institute, attempting to explain the relative contributions of the different mathematicians who had worked on the Poincaré, said, “Hamilton contributed over fifty per cent; the Russian, Perelman, about twenty-five per cent; and the Chinese, Yau, Zhu, and Cao et al., about thirty per cent.” (Evidently, simple addition can sometimes trip up even a mathematician.)

”

Slide Rules Still have their Uses

I was at the North Face store when this caught my eye:

They had no idea what I was talking about when I asked them if they had any spare ones, but were nice enough to give me one off of another jacket… then of course there’s the convenient wind chill chart from the National Weather Service which indicates how long you have until you get frostbite – problem with both being they’re in Fahrenheit. Apparently above 40 MPH winds there’s no further chilling effect.

The Language of College Mathematics

and their true, more mundane meanings:

* Order of Magnitude = so much larger/smaller than you can imagine
* Q.E.D. = I’m done
* Beyond the scope of this text…. = the modern version of Fermat’s “not enough space to write in this margin.”
* non-trivial = the problem is a pain
* well-posed problem = it’s not something I thought of in a dream
* without loss of generality = extrapolating beyond the realms of imagination
* hand-waving = what you do when you try to conceal the fact that you don’t know/can’t remember how to get from one step to another

My Erdos number is currently at infinity…