# Squiggles, Spheres, and Taxes

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!

### 13 Responses »

• Awesome, Max! Let us know how it turns out!
Justin

1. Spherikal is amazing!! Working with 3D for a year and a half really pays off. It’s pretty cool how you can do so much with just a sphere. I like the beginning how every time the sphere would rotate round would bea different spiral and how it would twist in the middle of the whole sphere. When the multiple lines were made and it would come out as a sphere and then there was so many lines it was completely black was pretty impressive. Overall I enjoyed watching the video and how fascinating it was that so many things could be created to become a sphere.

2. Hi justin

• Hi Bob!

3. I really love the Spherikal video!! The 3D animation is incredible and fascinating! I really love the part in the video where it looks like white string is moving to form the sphere, I just wish it would have completed the process instead of it being swallowed by the white. Its really interesting to see the different animations that can be created into a sphere. I loved how the sphere rotated so you can see all around it. The video is amazing and I can watch it all day!

• Hi Arianna!
I’m glad you enjoyed the Spherikal video so much! I think it’s fascinating how many different takes on a sphere Ion came up with. Mathematical objects–even very simple ones–contain a lot of potential within them. Can you think of a shape that you’d like to explore?
Given that you liked this video so much, you might also enjoy the Cut ‘n Slide applet and video at the end of this post:
http://mathmunch.org/2013/06/09/the-numbers-project-math-and-epidemics-and-cut-n-slide/
Bon appetit!
Justin

4. I really like 3D art. This video is amazing since it is a spherikal video. I like how the sphere rotates because you can see al around it.

5. I really like this spherikal video. I liked how the sphere rotated in different directions, I liked how it did that. This is one of my favorites so far.

6. I really like this spherikal video. I like how the sphere rotated in different directions, I thought it was cool how it did that. This is one of my favorite videos so far.

7. I like this spherikal video. Its really cool that the sphere goes all around. This video is really cool , and I can probably watch it every day.