O Christmas tree, O Christmas tree, How lovely are your branches! SAS programmers have a long history of creating yuletide-themed graphics. Christmas trees are a popular image because of their simplicity. I admit that I have indulged more than once in this holiday tradition: An old-school ASCII art image A
I recently wrote about the Number-Word Game, which is an iterative algorithm that generates a sequence of natural numbers by using the lengths of the words for the numbers. In English, the words are "one", "two", "three", and so on. You can play the Number-Word Game in any alphabetic language
Have you heard about the Number-Word Game? This is a simple game that has the following rules: Start with any positive integer. Write down the English word for the integer. Count the number of letters in the word. This gives a new positive integer. Go to (2). Repeat until a
Some hearts are famous. For example, there is the "Heart of Gold" (Neil Young), the "Heart of Glass" (Blondie), and the Heart of Darkness (Joseph Conrad). But have you heard of the "Heart of Ellipses"? No? Well, in 2023, Ted Conway published an amusingly titled article, "Total Ellipse of the
SAS programmers love to make special graphs for Valentine's Day. In fact, there is a long history of heart-shaped graphs and love-inspired programs written in SAS! Last year, I added to the collection by showing how a ball bounces on a heart-shaped billiards table. This year, I create a similar
For Christmas 2021, I wrote an article about palettes of Christmas colors, chiefly shades of red, green, silver, and gold. One of my readers joked that she would like to use my custom palette to design her own Christmas wrapping paper! I remembered her jest when I saw some artwork
One of the benefits of social media is the opportunity to learn new things. Recently, I saw a post on Twitter that intrigued me. The tweet said that the expected volume of a random tetrahedron in the unit cube (in 3-D) is E[Volume] = 0.0138427757.... This number seems surprisingly small!
I recently showed how to represent positive integers in any base and gave examples of base 2 (binary), base 8 (octal), and base 16 (hexadecimal). One fun application is that you can use base 26 to associate a positive integer to every string of English characters. This article shows how
On this Pi Day, let's explore the "πth roots of unity." (Pi Day is celebrated in the US on 3/14 to celebrate π ≈ 3.14159....) It's okay if you've never heard of the πth roots of unity. This article starts by reviewing the better-known nth roots of unity. It then
Did you know that you can use π to partition the positive integers into two disjoint groups? It's not hard. One group is generated by the integer portions of multiples of π. The FLOOR function gives the integer portion of a positive number, so you can write integer that are
