Tuesday, January 29, 2013
Monday, January 21, 2013
You remember Benford’s Law? Wolfram sums it up:
Benford's law states that in listings, tables of statistics, etc., the digit 1 tends to occur with probability ~30%, much greater than the expected 11.1% (i.e., one digit out of 9).
I think Wolfram meant to add that the law applies to the leading digits of the figures you’re using. In any case, the law applies when you have a large sample of “real” data, as opposed to computer-generated random numbers, and so it’s useful to forensic accountants trying to detect fraud (or so I hear).
It may seem counterintuitive (shouldn’t all digits occur with equal probability?) – but the last few minutes (start at 7:53) of this Numberphile video helped me get a grip on what’s going on:
Wednesday, January 9, 2013
I hung a rope between two trees for my kids to play on the other day, and when I looked out the window later I saw a catenary graph.
The catenary is a curve describing the shape of a in idealized hanging chain, and looks a lot like a parabola (enough so to trick Galileo). Its equation was determined independently by three people in response to a contest challenge.
I like to think of it as the sum of two exponential functions:
Here’s y = ex and y = e-x
…and their sum