Welcome to this week’s Math Munch!

Check out this cool doodle animation from the blog of Matt Henderson. Matt studied math at Cambridge as an undergrad and now does research on speech and language technology. His idea for a doodle was to start with an equilateral triangle and then encircle it with squiggles until it eventually turned into a square.

Matt Henderson

Matt’s triangle-to-square squiggle

Matt has all kinds of beautiful and intricate mathematical images on his blog, many of them animated using computer code. He made a similar squiggle-doodle that evolves a straight line into a profile of his face; an animation of rolling a ball on a merry-go-round; a million dot generator; and many more!

Along the same “lines” as Matt’s squiggle, Ted Theodosopoulos wrote an article in Peer Points reviewing a research paper by Stanford mathematician Ravi Vakil. The title of Ravi’s paper is “The Mathematics of Doodling.”

Ravi’s doodle

Next up, check out this cool visualization of a sphere.

The title of the video is Spherikal and was created by Ion Lucin, a graphic artist in Spain.

Something neat comes out about Ion’s attitude toward learning and sharing in a comment he makes:

“Thanks for appreciating my work. I was thinking the same, not to reveal my secrets, but then, i to learned from the videos and tutorials of others, i have been working with 3D for a year and a half, and all i know about it i learned it by myself, by seeing tutorials, im from fine arts. In a way a feel i must share , like other did and helped me”

What a great attitude!

Another spherical idea comes from a post on one of my favorite websites: MathOverflow, a question-and-answer site for research-level mathematicians…and anyone else! The question I have in mind was posted by Joe O’Rourke, a mathematician at Smith College and one of my favorite posters on MathOverflow. It’s about a certain kind of random walk on a sphere. Check it out!

For this step distance, it looks like a random walk will fill up the whole sphere. What about other step distances?

Again, such a cool picture is created by translating a mathematical scenario into some computer code!

Since this week is when federal income taxes are due, I’ll leave you with a few links about taxes and the federal budget. First, here’s the IRS’s website for kids. (Yes, for real.)

Next, this infographic lets you examine how President Obama’s 2011 budget proposal divvied up funds to all of the different departments and projects of the federal government. Can you find NASA’s budget?

On a more personal scale, this applet called “Where did my tax dollars go?” does just that—when you give it a yearly personal income, it will calculate how much of it will go toward different ends.

Finally, this applet lets you tinker with the existing tax brackets and see the effect on total revenue generated for the federal government. Can you find a flat tax rate that would keep total tax revenue the same?

Whew! That was a lot; I hope you didn’t find it too taxing. Bon appetit!