Category Archives: modeling

Modeling Hexnut Mass

Let me encourage you to go to your hardware store and get some hexnuts. You won’t regret it. Now let’s see if I can write a post about it in under, like, four hours. (Also, get a micrometer on eBay … Continue reading

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Model Shop! One volume done!

Hooray, I have finally finished what used to be called EGADs and is now the first volume of The Model Shop. Calling it the first volume is, of course, a treacherous decision. So. This is a book of 42 activities … Continue reading

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The Index of Clumpiness, Part Three: One Dimension

In the last two posts, we talked about clumpiness in two-dimensional “star fields.” In the first, we discussed the problem in general and used a measure of clumpiness created by taking the mean of the distances from the stars to … Continue reading

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The Index of Clumpiness, Part Two

Last time, we discussed random and not-so-random star fields, and saw how we could use the mean of the minimum distances between stars as a measure of clumpiness. The smaller the mean minimum distance, the more clumpy. What other measures … Continue reading

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The Index of Clumpiness, Part One

There really is such a thing. Some background: The illustration shows a random collection of 1000 dots. Each coordinate (x and y) is a (pseudo-)random number in the range [0, 1) — multiplied by 300 to get a reasonable number … Continue reading

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Bayes is Baaack

Actually teaching every day again has seriously cut into my already-sporadic posting. So let me be brief, and hope I can get back soon with the many insights that are rattling around and beg to be written down so I … Continue reading

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Hanging Slinky Analysis 2: The Pre-Tension Wrinkle

Last time, we saw how the length of a hanging slinky is quadratic in the the number of links, namely, , where M is the mass of the hanging part of the slinky, g is the acceleration of gravity, and is the … Continue reading

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Hanging Slinky Analysis 1: Sums to Integrals

Last time, we (re-)introduced the Hanging Slinky problem, designed a few years back as a physics lab but suitable for a math class, say Algebra II or beyond. We looked at the length of the hanging slinky as a function … Continue reading

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The Hanging Slinky

Slinkies are great. You can demonstrate waves. You can make them go down stairs. They are super-dynamic physics toys. They make a great sound. But they are also pretty great when static. Consider, for example, a hanging slinky. How far down … Continue reading

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Does Modeling Mean Using Harder Functions?

Here’s something I’m puzzled about in trying to push this picture of math education, the one where we collect data and try to model it with functions: when I come up with ideas for suitable activities, they often require “harder” … Continue reading

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