## Tag: Math

Programming Tips
0
The continued fraction representation of a rational number

Continued fractions show up in surprising places. They are used in the numerical approximations of certain functions, including the evaluation of the normal cumulative distribution function (normal CDF) for large values of x (El-bolkiny, 1995, p. 75-77) and in approximating the Lambert W function, which has applications in the modeling

3
The intersection of two line segments

Back in high school, you probably learned to find the intersection of two lines in the plane. The intersection requires solving a system of two linear equations. There are three cases: (1) the lines intersect in a unique point, (2) the lines are parallel and do not intersect, or (3)

1
Visualize a torus in SAS

This article uses graphical techniques to visualize one of my favorite geometric objects: the surface of a three-dimensional torus. Along the way, this article demonstrates techniques that are useful for visualizing more mundane 3-D point clouds that arise in statistical data analysis. Define points on a torus A torus is

0
Cantor sets, the devil's staircase, and probability

Last week I blogged about how to draw the Cantor function in SAS. The Cantor function is used in mathematics as a pathological example of a function that is constant almost everywhere yet somehow manages to "climb upwards," thus earning the nickname "the devil's staircase." The Cantor function has three

Learn SAS
5
What is a moving average?

A moving average (also called a rolling average) is a statistical technique that is used to smooth a time series. Moving averages are used in finance, economics, and quality control. You can overlay a moving average curve on a time series to visualize how each value compares to a rolling

7
Compute the centroid of a polygon in SAS

Recently I blogged about how to compute a weighted mean and showed that you can use a weighted mean to compute the center of mass for a system of N point masses in the plane. That led me to think about a related problem: computing the center of mass (called

14
Lo, how a polar rose e'er blooming

Lo how a rose e'er blooming From tender stem hath sprung As I write this blog post, a radio station is playing Chrismas music. One of my favorite Christmas songs is the old German hymn that many of us know as "Lo, How a Rose E're Blooming." I was humming

2
The sensitivity of Newton's method to an initial guess

In my article about finding an initial guess for root-finding algorithms, I stated that Newton's root-finding method "might not converge or might converge to a root that is far away from the root that you wanted to find." A reader wanted more information about that statement. I have previously shown

20
The spiral of splatter

"Daddy, help! Help me! Come quick!" I heard my daughter's screams from the upstairs bathroom and bounded up the stairs two at a time. Was she hurt? Bleeding? Was the toilet overflowing? When I arrived in the doorway, she pointed at the wall and at the floor. The wall was