Plots of the Exponential Function over the Complex Plane

I was inspired by this tumblr post, and this wikimedia page to make some pretty pictures of the exponential function over the complex plane. Go there to read in more detail how the images were created, including how the colors were created. Code is found here. Hi definition images are found here. Update: Here’s what […]

Tracking Venus and Earth over 8 years

I came about this tweet: If you track the relative positions of Earth and Venus over an 8 year period, this is the resulting pattern. pic.twitter.com/lOoeUtAXH2 — SciencePorn (@SciencePorn) May 16, 2015 It reminded me strongly of the waning moon and linear mod art projects that I’ve been playing with. For instance, here’s a screenshot […]

The Mandelbrot Set Viewed through Precalculus

I’ve given this presentation in November 2014 at AMTNYS in Syracuse, and in April 2015 at NCTM in Boston. I’ll be giving the presentation in May 2015 at the NY Master Teacher Conference, and in July 2015 at Twitter Math Camp in Claremont CA.  Drive Why use the Mandelbrot fractal to get the students to […]

Using the arctan Power Series to Calculate Pi

(Note: this post is an extension on the calculating pi with python post from a couple of years back. Also here’s another way to inefficiently calculate pi with Buffon’s Needles.) We’re currently working with Power series and Taylor series in Calculus. One particularity pretty derivation is going from the series for to the series for […]

How do I start Programming?

These excerpts are from a response to a reader on the wonderful tumblr by Jerome Herr, Experiments In Processing. Learning to code is like learning a natural language: it’s quite hard and slow at first but if you hold on just a little then suddenly you start seeing all the beauty of it and you’re […]

Kaprekar’s constant

A student talked about Kaprekar’s constant (6174) during their my favorite presentation. Really cool. Steps (from wikipedia): Take any four-digit number, using at least two different digits. (Leading zeros are allowed.) Arrange the digits in descending and then in ascending order to get two four-digit numbers, adding leading zeros if necessary. Subtract the smaller number […]

Mandelbrot Fractal v2

I had so much fun with the original Mandelbrot program that I decided to see if I could improve it. I was amazed by how easily I was able to generate a fractal picture that looked exactly like other pictures online. I didn’t look at anyone else’s code, just went down the path and the amazing […]