
Tweeting with Markov Chains
I'm not sure why I find this so surprising, but it's a somewhat trivial task to write a program that can spew out somewhat coherent sentences, as long as you have a large corpus to work off. Markov Chains Markov Chains are essentially state machines with probabilities assigned to each…

1 + 2 + 3 + ...
Here's something mindblowing: If you take the sum of the first couple of natural numbers you get the triangle numbers: $$T_{1} = 1$$ $$T_{2} = 1 + 2$$ $$T_{3} = 1 + 2 + 3$$ $$T_{n} = (n)(n1)/2$$ So essentially the series 1 + 2 + 3 + 4 + ... is the area of an…

大和
What better place to get sushi in Tokyo, than by going to an actual fish market? By the time we arrived at Tsukiji Fish Market (around 6:00AM in the morning), the lines were already pretty long. Daiwa Sushi (大和) had a significantly shorter wait. We probably only waited for…

Towers of Hanoi
An ageold puzzle that's challenged kids and pancake chefs for ages: The goal of the puzzle is to move an entire stack of disks from one rod/plate to another with the following restrictions: Only one disk can be moved at a time. Each move consists of taking the upper…

Dragon Curve
The dragon curve or Heighway Dragon is a beautiful selfsimilar fractal first investigated by NASA physicists John Heighway, Bruce Banks, and William Harter. Jack [Heighway] came into my office (actually cubicle) and said that if you folded a one dollar bill repeatedly he thought it would make a random walk…