Last week I compared the overhand shuffle to the riffle shuffle. I used random operations to simulate both kinds of shuffles and then compared how well they mix cards. The article caused one my colleague and fellow blogger, Rob Pratt, to ask if I was familiar with a bit of
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My colleague Robert Allison recently blogged about using the diameter of Texas as a unit of measurement. The largest distance across Texas is about 801 miles, so Robert wanted to find the set of all points such that the distance from the point to Texas is less than or equal
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Out of the bosom of the Air, Out of the cloud-folds of her garments shaken, Over the woodlands brown and bare, Over the harvest-fields forsaken, Silent, and soft, and slow Descends the snow. "Snow-flakes" by Henry Wadsworth Longfellow Happy holidays to all my readers! In my last post I showed
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I have a fondness for fractals. In previous articles, I've used SAS to create some of my favorite fractals, including a fractal Christmas tree and the "devil's staircase" (Cantor ) function. Because winter is almost here, I think it is time to construct the Koch snowflake fractal in SAS. A
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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
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I was a freshman in college the first time I saw the Cantor middle-thirds set and the related Cantor "Devil's staircase" function. (Shown at left.) These constructions expanded my mind and led me to study fractals, real analysis, topology, and other mathematical areas. The Cantor function and the Cantor middle-thirds
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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
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In my previous blog post, I showed how you can use SAS to program a "weaving" algorithm that takes an image, cuts it into strips, and weaves the strips together to create mathematical art. I used matrices and heat maps for the computations and visualization. At the end of the
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