Archive for the ‘math’ tag
Fun With Numerology: White Elephant Gifting Patterns
Ever notice an interesting number pattern and think, what are the odds of that happening? For example, I kept noticing when the odometer on my car would read a palindrome (e.g. 142241). What are the odds of that happening?
Turns out – about once every thousand miles.
The fact is, though, our brains are wired for pattern recognition. What we don’t realize is that the number of patterns we would recognize are much larger than we are aware of, significantly raising the chances we run into a pattern. This is the foundation of numerology – the study of the significance of patterns. Read the rest of this entry »
Everything Returns to the Central Limit Theorem
Mathematicians are very humble, so you know that when you see the word “Central” in the name of a theorem, it must be pretty important. In fact, the Central Limit theorem is the foundation for all of statistics.
What is the central limit theorem? In a nutshell, “everything eventually is normally distributed”. What does that mean? Well, you’ll just have to read on.
Perlin Noise: Oscar-winning Randomness
Since when does math win Oscars? Back in 1982, Ken Perlin created a random distribution function that efficiently generates life-like textures for computer graphics. Featured in the movie Tron, Perlin won an Academy Award for Technical Achievement for his now ubiquitous formula. In this article, we’ll talk about the most famous math function used in computer graphics today.
Exploring Mandelbrot’s Mathematical Beauty
I was planning on posting this later, but in light of Benoit Mandelbrot’s recent passing, I think I’ll post it today. Back in 2002, I wrote a program to draw fractals from the Mandelbrot set. Immediately, I was fascinated by all the shapes and colors I could generate with a little math and a simple program. Over time, I started gathering more and more pictures. Here’s what I gathered, although I hope to expand and improve on the collection someday.
Counting Without Numbers: Parable of the Trader
"Many" bricks
I once heard this story in my probability and statistics class. The idea is actually closely related to combinatorics. Here’s my version of the story:
Once upon a time, there was a wealthy Wall Street trader who was looking to make a good deal. He found that bricks were selling for a price of $1 per brick. Normally, this trader wouldn’t buy and sell bricks at that price, but then he heard about these farmers from a distant land and came up with a scheme for cheating them out of making a good profit.