Coloring Book Math: An Activity


This post is about an activity — so it begins with the ages the activity is intended for.

  1. Ages 3-6: just color the pictures, have fun!
  2. Ages 7-9: color the pictures but also try to answer the first question. A parent or teacher should help, and maybe look at this article on rotational symmetry.
  3. Ages 10-12: color the pictures and use them to answer all the questions if you can. Students may need help from a parent or teacher.
  4. Ages 13+: just color the pictures. Answer the questions if you’re interested.

This week’s Occupy Math is the first post in a new category: materials and activities. In response to a reader comment, Occupy Math is working up math-related activities. This one is a coloring book intended to introduce symmetry. A colored version of one of the images from the book appears above. The first page of the book asks five questions; all the other pages are intended to be colored. This post discusses and answers the five questions for a teacher or parent that might be using the activity.

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Image of the Week #87

This is an evolved generalized Julia set with three parameters.  Occupy Math picked it because it looks really interesting.  if you would like a copy of the scientific paper about evolving this type of fractal, send a request to

Prime Numbers and Teaching Fractions


This week’s post is a follow-up to a post objecting to the way fractions are taught post from a while back. This is also Occupy Math’s third post about prime numbers. It should be much more down to earth than the first and, unlike the second, there are no insects or implications for ecology. This post explains why students who know about prime numbers will find it easier to do arithmetic with fractions. Being able to find the prime factors of numbers gives those numbers character: prime factors are like personality traits. Another way to say it is that numbers with a prime factor in common form a sort of a tribe with common characteristics. Also, there are some games you can play with prime numbers near the end of the post.

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Secrets of the Guild: How Occupy Math found one.

The phrase secrets of the guild was used by Bertie Wooster to describe the reason that his manservant, Jeeves, could not divulge the ingredients of his morning pick-me-up. This post is intended to give pieces that could be used for discovery learning about basket curves, a modified type of petal curve. Occupy Math has looked at petal curves before, to make flowers. This post highlights a “secret” in the form of a not-completely-obvious pattern that permits students to make complex and interesting pictures.

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The Cornucopia of Mathematics

Occupy Math is a working researcher and, at least the way he does research, this means that people come to him with problems. In this week’s post we will talk about the type of problems that come up and what the impact of math on the process of solving problems is. The three examples we will use are the design of a wood burning stove, a 3D ultrasound scanner, and a weird abstract computing problem solved with ideas from a science-fiction novel. In all three examples, the point will be that stirring in math to the process helps. The solution became either much simpler or much more useful because math was present and accounted for.

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Why you don’t write a tax plan in a hurry.

Occupy Math has talked before about complex systems. Few human systems are more complex than the economy of a large country like the United States of America. This post reacts to the recent proposed tax bill in the United States — a very complex collection of modifications to a super-complicated system. Since the US economy is pretty much beyond human comprehension, Occupy Math will start with a much simpler complex system. This relatively simple example builds on an earlier post Evolution Can Do Math That People Can’t. That post was about evolving cellular automata. The way cellular automata work is that we start with a row of zeros, except the middle three numbers in the row are 1,2,1. The numbers can go from 0 to 7. We sum blocks of five adjacent numbers — getting a sum from 0 to 35 — and look up the new numbers using the table of 36 numbers:


So, for example, if the five numbers in a block sum 15, the new value for the number in the center of the block is “3” because the 15th number (starting counting at zero in the list above) is “3”. We apply the rule over and over to generate rows of new numbers — mapping the numbers to colors to draw a picture. The color map is zero;white, one;red; two;green, three;blue, four;yellow, five;violet; six;cyan; and seven;black. The picture for the rule above is:


Here is a simple experiment in complex systems: change one number in the list of numbers that forms the rule for the cellular automata and look at the picture that the new rule draws. There are 36 examples below the fold.

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