## Tuesday, May 14, 2013

### Right triangle days

On Mothers Day I wrote out the date and noticed 5/12/13 could be the sides of a right triangle.  That made it doubly special – but is it really that special? How many dates have that property?  Which years have the most?  Would they be evenly distributed throughout the century?

## Wednesday, May 8, 2013

### Fibonacci date!

Well I should have seen that coming – but we’ll be prepared next time, right?  When’s the next Fibonacci date again?

## Tuesday, April 9, 2013

### Calendar

April is a good month.  We have the birthdays of Euler, Da Vinci, GĂ¶del, and Gauss to celebrate, (not to mention my wife and son’s)!  Plus, the American Mathematical Society honored me with the inclusion of one of my fractal pancakes in their 2013 Calendar of Mathematical Imagery.

Admittedly, mine is the weakest of the lot, but it was nice to be included.

## Monday, March 25, 2013

### Automata on the beach

I found this shell on the beach in Saipan last year.

Its pattern reminded me of the some of the cellular automata I had seen in Wolfram’s A New Kind of Science (chapter 3) – it turns out that this is no coincidence.  The process by which some species of mollusks color their shells can be modeled by cellular automata: as the shell grows, the coloring of each row is affected by the coloring of the previous row through a small set of rules.

Dr. Coombes of the University of Nottingham gives a brief overview of some of the mathematics behind the structure and pigmentation of seashells here.

## Wednesday, March 6, 2013

Here’s a fun idea to talk about with your students this Pi Day:

What else can you do on Pi Day? As always, www.piday.org has some good ideas for you.  I like to have students do Bouffon’s needle experiment with toothpicks and compile the results with multiple classes.

Discuss why an accurate value might be necessary, and some historical approximations:
•3.16045 (=16²/9²) Egypt, 2000 BC
•3.1418 (average of 3+1/7 and 3+10/71) Archimedes, 250 BC
•3.125 (=25/8) Vitruvius, 20 BC
•3.1622 (=√10) Chang Hong, 130 BC
•3.14166 Ptolemy, 150
•3.14159 Liu Hui, 263
•3.141592920 (=355/113) Zu Chongzhi, 480
•3.1416 (=62832/2000) Aryabhata, 499
•3.1622 (=√10) Brahmagupta, 640
•3.1416 Al-Khwarizmi, 800
•3.141818 Fibonacci, 1220
•3.14159265358979 Al-Kashi, 1430

A digit contest at the end of the day is always fun too.  Here’s the hand-out I give to kids a few days in advance if they want to try memorizing for fun (it has a spacer every 50 digits):

## Wednesday, February 27, 2013

### Bring coding to your students

I’ve griped before about the lack of computer programming opportunities that our students have today.  Here’s a free and painless way for kids to get started – something you could devote one period to (to hook the intrinsically motivated), or build an entire curriculum around:

www.code.org

## Wednesday, February 13, 2013

### Visualizing music

After besting me at snowflake making recently, Vi Hart came out with one her best video ideas to date, in my opinion.

Playing with the symmetries in music in a visual way, she reminded me of the visualization I made for Bach’s “Crab Canon,” which sounds the same forward as backward and “looks” like this:

I’ve always been a fan of music visualization videos because they allow you to appreciate some of the patterns, structures, and relationships (what we might call “math”) that you may otherwise miss.