I was recently talking to an undergraduate student who mentioned his numerical analysis course at the University of Colorado. It’s odd that even after six years of doing almost nothing with my thesis work, how eager I am to jump in and think about it again. More than once over the last few months, I’ve had this urge to nestle in with my thesis and relax… Continue reading Numerical Analysis
Category Archives: Pseudorandom
KOPRI’s Antarctic Station
The National Snow and Ice Data Center (NSIDC) was recently visited by the Korean Polar Research Institute (KOPRI), and after their visit, they left us with a few 3D models of one of their Antarctic research stations. I was lucky enough to get one, and I recently spent some time putting it together.
Pictures after the jump. Continue reading KOPRI’s Antarctic Station
The Scanning and Location Problem
A couple weeks ago, I posted a math problem that I was playing around with. This problem was born of our some ideas for my new role-playing game, as well as the basic scanning mechanism of EVE Online.
In EVE Online, if you are trying to scan down an object in space, you launch some probes and they report back the distance from the probe to the anomaly, with some amount of error, up to some maximum range. Your ship’s computer then aggregates that information and renders it as an overlay on the scanning screen. If two of your probes received responses, you would get a circle where the two spheres intersect, with three you would get two points, and with four you would get a single point (with some degree of error). You then decrease the range of the probes (increasing their signal strength) to narrow in on your target – a pretty simple and fun min-game which tickles my imagination and makes me think I know something about how science fiction scanning might occur. Continue reading The Scanning and Location Problem
A Solution for the Mathematically Inclined
The answer to my post last week is yes. Here’s the quick (intuitive) proof:
First, note that 
and 
is the surface of two spheres in three dimensions, and their intersection is either a circle or a point (we know they are not the same sphere since a and b are distinct and that they must intersect because we know p exists). If it is a point, then p is that point (and since we have not used gamma we have proved the hypothesis).
If the intersection is a circle, it intersects the plane containing a, b, and c at two points, but only one is inside the triangular prism, and that must be the point p. We know it cannot be a point not on the plane, since if it was, two points would satisfy 
, and not satisfy the uniqueness condition.
I personally prefer algebraic proofs though, so let’s crank some algebra! Continue reading A Solution for the Mathematically Inclined
Just a Quick Pick-Me-Up
There’s nothing quite like watching Nathan Barnatt dance when you’re having a rough day.
For the Mathematically Inclined
I’ve been thinking about the following math problem lately (I occasionally get distracted by such things):
Suppose you have four points in 3D space, a, b, c, and p, where a, b, and c are distinct and non-colinear and their positions are known, and p is the unique point defined by the following:
- p lies in the interior of the triangular prism defined by a, b, and c that is perpendicular to the plane containing a, b, and c.
As an image:
If there is only one point satisfying the above criteria, can it be found without knowing γ? I plan on posting my proof next week Thursday, 2016-02-25.
Michael Jackson – Smooth Criminal
I unabashedly love this video. Some may find it overly cheesy, but I find the choreography simply stunning, and the whole scene tells so many stories…
Blogs with Text
As I’ve been writing the last few months, I’ve noticed a very particular pattern about my posts: most of them are entirely text. It took me a bit to notice this, and, in fact, my Gamerstable blog was the wake-up call. That entry made it live without a single hyperlink. I noticed it later when I reread that entry and said to myself, “I just spent a whole blog entry talking about my favorite podcast, and I never once linked to it… …That is a problem.”
This, I think, is the result of two factors of my writing. First, as I’ve mentioned before, I write on my bus ride to work where I do not have internet access. Second, my personal style is to say things with words rather than other expressive elements. Continue reading Blogs with Text
J. R. R. Tolkien on War
The Germans have just as much right to declare the Poles and Jews exterminable vermin, subhuman, as we have to select the Germans: in other words, no right, whatever they have done.
–J. R. R. Tolkien (in a letter to his son Christopher, 1944)
The Most Interesting Operator
I don’t always deploy code…
…But when I do, I deploy it to production