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) .

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.


Yet another sketch...

This time from my sophmore biology lab book. This is a sketch of a bullfrog hand from when we were doing dissections. I've got quite a few sketches from my lab book, so I'll post them periodically.


Math Puzzler #2

Take a power of two. Rearrange the digits. Can you ever have a second power of two? For simple problem, neglect leading zeros. For a harder one (which I haven't yet solved), don't.

Solutions after the jump.


Another sketch...

Normally, I can't draw anything. I really can't. No perspective, and my scaling is horrible. Once in a while though, something just comes out. This picture came out yesterday. It's not great, but hey, it's better than most of my scribbles! I was thinking about fruit flies and dinosaurs, and I drew this in the midst of my randomness. So here it is. Enjoy!


Math Puzzler #1

I'm going to post math problems, both those I write, and those I find interesting. So for the first math problem!
Two quadratics both pass through opposite corners of a rectangle whose sides are parallel to the xy-Cartesian axes. One quadratic has it's vertex on the lower left corner, but also passes through the upper right corner, and the second has it's vertex on the upper right, but also passes through the lower left. These two quadratics form a region within the rectangle. What fraction of the area of the rectangle is the area of this region?


On grades

This week has not been my best. The long and short of it is that my academics is in, if not dire, at least mediocre straits, and I have no one to blame but myself, as usual. The damage I've done is not horrible, and with hard work over the next few weeks, I can mostly erase it, but it falls inconveniently across a progress report, so I will likely catch some flack from my parents. More than that though, I've realized that I've been, up to now, motivated out of fear of my parents.
My academic goals are not really my own, and that needs to change. It isn't the first time I've realized this, but nevertheless, I truly want to change this. A first step, I figure, is putting my thoughts into words on a page, so I can comeback and revisit my conviction when I feel unmotivated in the future.