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