Quick! Which fraction is bigger, 40/83 or 27/56? It's not always easy to mentally compare two fractions to determine which is larger. For this example, you can easily see that both fractions are a little less than 1/2, but to compare the numbers you need to compare the products 40*56

## Tag: **Math**

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

Do you know that you can create a vector that has a specific correlation with another vector? That is, given a vector, x, and a correlation coefficient, ρ, you can find a vector, y, such that corr(x, y) = ρ. The vectors x and y can have an arbitrary number

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

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

I recently showed how to use linear interpolation in SAS. Linear interpolation is a common way to interpolate between a set of planar points, but the interpolating function (the interpolant) is not smooth. If you want a smoother interpolant, you can use cubic spline interpolation. This article describes how to

I've previously written about how to generate points that are uniformly distributed in the unit disk. A seemingly unrelated topic is the distribution of eigenvalues (in the complex plane) of various kinds of random matrices. However, I recently learned that these topics are somewhat related! A mathematical result called the

Recently, I saw a graphic on Twitter by @neilrkaye that showed the rapid convergence of a regular polygon to a circle as you increase the number of sides for the polygon. The author remarked that polygons that have 40 or more sides "all look like circles to me." That is,

This article discusses how to restrict a multivariate function to a linear subspace. This is a useful technique in many situations, including visualizing an objective function that is constrained by linear equalities. For example, the graph to the right is from a previous article about how to evaluate quadratic polynomials.

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