Dave Peterson

(Doctor Peterson) A former software engineer with degrees in math, I found my experience as a Math Doctor starting in 1998 so stimulating that in 2004 I took a new job teaching math at a community college in order to help the same sorts of people face to face. I have three adult children, and live near Rochester, N.Y. I am the author and instigator of anything on the site that is not attributed to someone else.

More Handshake Problems

Last week we looked at problems about counting diagonals in a polygon, and the very similar problem of counting handshakes when everyone in a group shakes with everyone else. In the course of searching for those problems, I also found some very different problems that are also about handshakes. We’ll look at those here, just …

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Overlapping Square Tiles

(A new question of the week) An interesting geometry question came to us in July, about the area of overlap between two squares. The discussion was not long, but leads to some interesting ideas. Here is the initial question, from Vignesh: This is the problem I need help with: Two square tiles of area 9 …

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Polygons and Handshakes

We’ll spend the next couple weeks looking at various counting problems. This topic, called combinatorics, is often studied along with probability, but many of the topics we’ll see here feel more like geometry problems! Here, we’ll be counting the diagonals of a polygon, and handshakes between people at a party. Counting diagonals We’ll start with …

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The Symmetric Derivative

To close out this series on the definition of the derivative, I want to look at a few questions about alternative versions of the definition, primarily the “symmetric difference quotient”. We’ll see that this leads to a slightly different result, not always equivalent to the original, and we’ll observe some associated ways that calculators can …

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What Do dx and dy Mean?

We’ve looked at the meaning of the derivative, and of its various notations, including dy/dx. This leads to the next question: What does dx or dy mean on its own? This was touched on last time, but there’s a lot more to say that I couldn’t fit there. We’ll look at more advanced approaches to …

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