Archive for November 2010
I got Kinect. It’s a lot of fun, although the accuracy of tracking could be better, and the lag is sometimes annoying (I only have the Kinect Adventures game).
I took a few pictures of the infrared pattern projected by the 3D sensor with my Sony F717 camera in the “night shot” mode.
Part of my room illuminated by Kinect. You can see the shape of the “game zone”.
Let P(n) be the number of ways to represent n as the sum of 2 squares. We count ordered pairs of squares of positive and negative integers, e.g. P(2) = 4 : (-1)^2+(-1)^2 = (-1)^2+(1)^2 = (1)^2+(-1)^2 = (1)^2+(1)^2.
What is the average value of P(n), i.e. lim ( P(1)+…+P(k) )/k ?
The answer is Pi.
The proof is very simple and doesn’t involve any number theory.