Noisemakers

These lovable critters emerge from the ground in 13- or 17-year cycles, capitalizing on the power of prime numbers to keep away from predators with periodic population cycles and other cicada broods.  Here’s a cool interactive cicada map you can play with. 

Cicadas remind me of the white noise machine I used to have on my bedside table – and not because they sound alike.  As I would fall asleep, I would inevitably begin focusing on the repetition in the “babbling brook” sound pattern - the machine just played back a loop about 30 seconds in duration.

I always thought it would be a better use of the machine’s memory to store two shorter loops and play them together.  For example, a 13-second and a 17-second loop would get you 221 seconds (13x17) of noise before repeating.  

Ask your students: If you’re limited to 30 seconds of memory, are 17 and 13 the best choices for noise loop lengths?  See who comes up with the idea of non-integer loops… 

Dimensions

At this time of year I like to show some of the Dimensions series. Beautifully designed and distributed under a Creative Commons License, the series is free to download and show in class, and gives an excellent overview of projective geometry in two, three, and four dimensions! Incidentally, the animations were created using POV-Ray, a free ray-tracing program that generates photo-realistic images using precise mathematical modeling.

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? 

Fibonacci date!

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

Calendar

April is a good month.  We have the birthdays of Euler, Da Vinci, Gödel, 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.

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.

Your Life in Pi

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):