Holophonic Sound (Head Design)

After some Searching in the SketchUp Warehouse, I found this model of a shaved head. It's exactly what I was looking for: accurate, but very low poly and not overdone. I decided to take a lateral slice every inch, and disaster struck.

The slicer plugin I use has some problems, especially when it's working with complex or imported models (I think this was originally put together in Collada), it tends to "miss" slices. It's free, and it usually works like a charm, so I can't really complain, but it still hung me up for a while.

Holophonic Sound (Overview)

Given that I'm about done with my 3D scanner (I promise I'll put an overview up soon), I've been looking around for a new project. I recently happened across this mp3 (Headphones are needed for the full effect)

It's not the first time I've heard it, but it's still impressive. On a whim, I decided I'd try my hand at my own holophonic recording setup (might make long distance Skype calls more pleasant if the audio is good enough), and I started to do some research. Cetera doesn't seem to have commercialized their technique, and I couldn't find much in the way of software to simulate the effect, so it comes down to the physical setup (which also doesn't seem to be commercialized), and homebrew code tinkering.

Equations Work!

With some help from this post, my blog now supports awesome looking equations (no more blurry bitmaps!). As such, I no longer hesitate to note that E=m c^2 , e^{\pi i}+1=0, and of course that \frac{d}{dx}\int_C^x f(t) dt = f(x) .
Cheers!
Ninjinuity

Note: Equations seem to look best in Firefox. They don't work at all in IE (no surprises there), and they don't quite work in Chrome. I'll keep looking into this. The script also seems to be picking up weird elements of the page and replacing them. I need to stop that.

Edit: The old equations code was inconsistent and had a habit of changing stuff not inside it's tags. With this new back end, they should work everywhere.

Math Puzzler #3

There are six Dudeney numbers, positive integers whose decimal digit sum cubed is equal to the original number. they are
amath 1=1^3=(1)^3 endmath,
amath 512=8^3=(5+1+2)^3 endmath,
amath 4913=17^3=(4+9+1+3)^3 endmath,
amath 5832=18^3=(5+8+3+2)^3 endmath,
amath 17576=26^3=(1+7+5+7+6)^3 endmath,
and amath 19683=27^3=(1+9+6+8+3)^3 amath.

1. Prove there are no larger Dudeney numbers.
2. Find all numbers where the fourth power of the digit sum is equal to the number itself.

Hint: A computer may be useful to check cases, but it is possible to do this problem by hand, albeit with a bit of paper.
Solution 1 after the jump, Solution 2 next week.

Still pinching myself.

I waited for a day to make this post, to make sure there was no mistake.

I got in to MIT. I suppose its hard to communicate how excited I am about this. It's been a major goal since middle school, but always kind of the ideal that I shot for, never expecting to really make it. Now I'm in. Surreal feeling, let me tell you.