In this post we look at the problem of finding a sum of consecutive numbers that has a specified value. This is one of Occupy Math’s new activity posts. Let’s look at an example. “Find a sum of consecutive whole numbers that add to 100” could be solved by 18+19+20+21+22=100. This sort of problem is good for practicing arithmetic while also building the logic muscles. Best of all, if you are a parent or teacher, this post will show you how to find exactly which of these problems have answers, which don’t, and for the ones that do have answers, what all the possible answers are.
This is a leaf convergence zoom into the Mandelbrot set. Its a deep zoom near a minibrot which creates very complex texture.
In this post we are going to look at a trick for figuring out what a whole type of fractals look like, before doing all the calculations needed to generate them. Occupy Math has posted on fractals before. The clue we will use to search for beautiful fractals is, itself, a very special fractal called the Mandelbrot set. Here is the core fact for today’s post. The Mandelbrot set lives in the complex numbers, which form a plane. Given that, the way the Mandelbrot set looks near a particular place (or number) in the plane of complex numbers is the way the Julia set based on that number looks all over. Another way to say this is that the Mandelbrot set indexes Julia sets.
This week Occupy Math presents another 32nd order Julia set. Cool, no?
Occupy Math’s editor tells him that activity posts must say what age they are for. Because this is a nifty activity that uses graph theory, it has a broad age range. A sharp kid who can count can always do this activity, but the official age range is 7th-12th grade.
Occupy Math has posted about graph theory before. The post “Cookies or calculus?” makes a case that graph theory would be better than calculus as a first math class in university. The post Map Coloring and Conflict Resolution shows an interesting application of coloring graphs. The post on an unsolved mystery used graph theory as well. In this post we look at another property of graphs — diagrammed as maps — that is a good activity for building math skills. It’s also a magic trick that can intrigue students.
The current Image of the Week is a thirty-second power Julia set — Occupy Math is experimenting with the round boundaries you get from this sort of high power.
This post is on a really easy method to solve some hard problems, including locating a pretty fractal. It is called the bisection method, but you may know it as a high-low game. One person thinks of a number and the other guesses. The person who knows the number replies “high” or “low”. A good strategy is for the guesser to move half way between their most recent high and low guesses. Bisection is fancy math talk for “move half way”. The thing is that this method can solve hard problems and do COOL things. Read on to find out.
This week, Occupy Math’s Image of the week is a three parameter Julia set located with a high-low game. This is a zoom into its center.
This post is about an activity that helps students practice recognizing which numbers are factors of others. It is intended for grade five and above. The activity has several different forms and we will comment on which are harder as each variant is described. In order to run this activity, the parent or teacher will play the part of the Sphinx. If you have an Egyptian head dress or other prop, that helps set the mood.
This is a Julia set with two complex parameters. Occuy math set on of them to 0.01i and then chose the other using iterated bisection driven by the appearance of the fractal. It came out pretty well. One of the future Thursday blogs will be about iterated bisection.