The xkcd comic often makes me think and laugh. The comic features physics, math, and statistics among its topics. Many years ago, the comic showed a "binary heart": a grid of binary (0/1) numbers with the certain numbers colored red so that they formed a heart. Some years later, I
O Christmas tree, O Christmas tree, One year a fractal made thee! O Christmas tree, O Christmas tree, A heat map can display thee! From Pascal's matrix we define! Reflect across, divide by nine. O Christmas tree, O Christmas tree, Self-similar and so divine! Eventually I will run out of
Pascal's triangle is the name given to the triangular array of binomial coefficients. The nth row is the set of coefficients in the expansion of the binomial expression (1 + x)n. Complicated stuff, right? Well, yes and no. Pascal's triangle is known to many school children who have never heard of polynomials
When I studied high school geometry, I noticed that many homework problems involved right triangles whose side lengths were integers. The canonical example is the 3-4-5 right triangle, which has legs of length 3 and 4 and a hypotenuse of length 5. The triple (3, 4, 5) is called a
Many people enjoy solving word games such as the daily Cryptoquote puzzle, which uses a simple substitution cipher to disguise a witty or wise quote by a famous person. A common way to attack the puzzle is frequency analysis. In frequency analysis you identify letters and pairs of letters (bigrams)
My previous blog post describes how to implement Conway's Game of Life by using the dynamically linked graphics in SAS/IML Studio. But the Game of Life is not the only kind of cellular automata. This article describes a system of cellular automata that is known as Wolfram's Rule 30. In
A colleague jokingly teases me whenever I write a blog that demonstrates how to write fun and exciting programs by using SAS software. "Why do you get to have all the fun?" he mock-chides. Today I'm ready to face his ribbing, because this article is about Conway's Game of Life
Last week Chris Hemedinger posted an article about spam that is sent to SAS blogs and discussed how anti-spam software helps to block spam. No algorithm can be 100% accurate at distinguishing spam from valid comments because of the inherent trade-off between specificity and sensitivity in any statistical test. Therefore,
Yesterday I blogged about the Hilbert matrix. The (i,j)th element of the Hilbert matrix has the value 1 / (i+j-1), which is the reciprocal of an integer. However, the printed Hilbert matrix did not look exactly like the formula because the elements print as finite-precision decimals. For example, the last
Many geeky mathematical people celebrate "pi day" on March 14, because the date is written 3/14 in the US, which is evocative of the decimal representation of π = 3.14.... Most people are familiar with the decimal representation of π. The media occasionally reports on a new computational tour-de-force that
