Posts Tagged ‘ Just for Fun ’

Cantor sets, the devil’s staircase, and probability

July 5, 2016
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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

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Visualize the Cantor function in SAS

June 29, 2016
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Visualize the Cantor function in SAS

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 polar rose e’er blooming

December 16, 2015
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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

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Mathematical art (part 2): Unweaving matrices

September 4, 2015
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Mathematical art (part 2): Unweaving matrices

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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Mathematical art: Weaving matrices

September 2, 2015
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Mathematical art: Weaving matrices

An artist friend of mine recently created a beautiful abstract image and described the process on her blog. She says that "after painting my initial square, I cut it into strips and split them down the middle, then wove them together.... I had no idea when I started piecing these

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The distribution of Pythagorean triples by angle

April 15, 2015
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The distribution of Pythagorean triples by angle

Last week I was chatting with some mathematicians and I mentioned the blog post that I wrote last year on the distribution of Pythagorean triples. In my previous article, I showed that there is an algorithm that uses matrix multiplication to generate every primitive Pythagorean triple by starting with the

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Analyzing the first 10 million digits of pi: Randomness within structure

March 12, 2015
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Analyzing the first 10 million digits of pi: Randomness within structure

Saturday, March 14, 2015, is Pi Day, and this year is a super-special Pi Day! This is your once-in-a-lifetime chance to celebrate the first 10 digits of pi (π) by doing something special on 3/14/15 at 9:26:53. Apologies to my European friends, but Pi Day requires that you represent dates

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Fundamental theorems of mathematics and statistics

February 12, 2014
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Although I currently work as a statistician, my original training was in mathematics. In many mathematical fields there is a result that is so profound that it earns the name "The Fundamental Theorem of ." A fundamental theorem is a deep (often surprising) result that connects two or more
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