Tag: Math

Learn SAS
Rick Wicklin 0
The elliptical heart

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

Analytics
Rick Wicklin 0
The Farey sequence

Here is an interesting math question: How many reduced fractions in the interval (0, 1) have a denominator less than 100? The question is difficult is because of the word "reduced." If we only care about the total number of fractions in (0,1) whose denominator is less than 100, we

Analytics
Rick Wicklin 0
Intransitive dice

Most games of skill are transitive. If Player A wins against Player B and Player B wins against Player C, then you expect Player A to win against Player C, should they play. Because of this, you can rank the players: A > B > C Interestingly, not all games

Advanced Analytics | Machine Learning
Rick Wicklin 0
The Kullback–Leibler divergence between discrete probability distributions

If you have been learning about machine learning or mathematical statistics, you might have heard about the Kullback–Leibler divergence. The Kullback–Leibler divergence is a measure of dissimilarity between two probability distributions. It measures how much one distribution differs from a reference distribution. This article explains the Kullback–Leibler divergence and shows

Programming Tips
Rick Wicklin 0
What is a geometric mean?

There are several different kinds of means. They all try to find an average value from among a set of numbers. Although the most popular mean is the arithmetic mean, the geometric mean can be useful for problems in statistics, finance, and biology. A common application of the geometric mean

Programming Tips
Rick Wicklin 0
Distances on rectangular grids

Given a rectangular grid with unit spacing, what is the expected distance between two random vertices, where distance is measured in the L1 metric? (Here "random" means "uniformly at random.") I recently needed this answer for some small grids, such as the one to the right, which is a 7 x 6

1 2