Tag: Math

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

Students & Educators
Lucy Kosturko 0
Elementary Spotlight: Math

Early math skills—such as number sense, number relations, pattern identification, estimation, and measurement—are the foundation for future math achievement. By mastering these basic concepts, young students can engage in more complex cognitive processing and develop higher-level math skills. Also, early math achievement has been linked to an increased likelihood to take

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

Students & Educators
Staci Lyon 0
Back to School: Math

Kicking off the new school year, you may be looking for ways to ease your students back into math. Here are a few ways that SAS can help. And remember, all of these resources, including apps, are free! CodeSnaps Have some fun coding a Sphero robot using CodeSnaps! With the

Students & Educators
Lucy Kosturko 0
Medal with these Engaging Sports-themed Lessons

Tap into student interest in athletic competitions with these sports themed lessons. Creating and Annotating Maps Our Interactive Atlas (also available in Spanish) is a great tool for project-based learning. Using our map and annotation tools, students demonstrate mastery of content while engaging their research and writing skills. Consider the following sports related activities:

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