Tag Archives: math

Michael Albert's Pi collage

Happy Pi Day (3.14, March 14)

We’ve been celebrating Pi (π) Day for half a decade or so now, but some of you may be new to the idea.  At the very least, it is an excuse to eat pie, and on the other end of the spectrum it is  a great day to celebrate math and the beauty of nature in numbers.

For those looking to eat pie, why not try to bake your own?  It could be sweet or savory.  Wikipedia has a list of pies to get you started, and AllRecipes has a lot of recipes on making pies available.  Perhaps you want to aim for a Steak & Kidney pie and combine two pseudo-holidays into one?

If you’re musical, there are many pi songs and raps out there you can try to learn.  My favourite is Dr. Arthur Benjamin‘s version of “American Pi”, captured here during a presentation he did at The Archimedeans (Cambridge University Mathematical Society).  We were lucky enough to participate in Dr. Benjamin’s show last year (thanks Ontario Science Centre) and the kids still sing his song (and we have a signed copy of his pi to 60 digits that he wrote out).   We will probably also watch at least one of his lectures from his Great Courses where he focuses on pi too.

There are many crafts and activities to do for those with kids.  Drawing and cutting out and measure circles with paper and string is all it takes to get started.   Don’t be shy about working in some physical activity too — maybe do a 3.14km hike?

A new discovery for me this year is the Pi Search Page which instantaneously finds a series of digits in the first 200 million digits of pi.  My 8 digit birthday occurs three times in those first 200 digits, while my wife’s only occurs once.  Try it out with any other ‘special’ numbers to you and see what you find.  Irrational.

In your pi studies, don’t forget what many mathies consider the epitome of numbers, Euler's Identity (e^π*i = -1) aka Euler’s Identity.

Numberphile has a great playlist for all their pi related videos (1h25m worth of content).  Last year the kids enjoyed watching Calculating Pi with Real Pies.  And let’s not forget ViHart’s pi playlist either.

And for the whimsical here is FlippyCat’s contribution to pi day in dominoes.

Please share how you ended up celebrating this special day, and get ready for next year when in 2015 3/14/15 will be the Longest Pi Day of our lives when it goes to 10 digits at 9:26:53am/pm.

Here are a few additional links to drive your research and insatiable curiosity.

table power of 10

Scale of the Universe and Powers of 10 resources

The concept of the scale of the universe has come up multiple times with my kids, and our friends, so I thought I’d put together a few links and resources we’ve used.

There is the ‘classic’ video (film-strip style) from the Eames Office, Powers of Ten and now with its accompanying website.

There is the superb flash animation: Scale of the Universe 2 by Cary Huang and Michael Huang (the (at the time) 14-year-old htwins).  [Hmmm… embedding it doesn’t work, sorry]

There is The Known Universe by American Museum of Natural History, which you can interact with via their Digital Universe 3D Atlas software (powered by Partiview) and presented by one of the makers at TED (Carter Emmart).

If you want to just think about really big numbers too, check out Numberphile‘s video of Googols and Googolplexs.


Koch Snowflakes

Came across Sal‘s discussion of the Koch Snowflake (on wikipedia) yesterday.

Got a little obsessed and wanted to draw it programmatic like I did 20+ years ago when I first saw the Sierpinski Gasket on a NOVA tv show (which I re-did using Khan’s software a few months ago).  After a few failed attempts (and a failing to recognizing my usage of sine and cosine), today I went and looked for someone else’s code just to get me through it (oh the aging brain!) and found N-Wing’s code over at everything2.

Here it is: Koch Snowflake Fractal (Doh, WordPress isn’t allowing me to embed the program right here in the blog).

Vi Hart shows them in her Triangle Party Doodling too if you like her style (who doesn’t?).

Howto Try Trihexaflexagon

We finally managed to get a hexaflexagon working!  Check out the video of my son demonstrating.

If you’re having trouble getting started too, here’s a recap of our journey.

We were introduced to them a few weeks ago thanks to vihart‘s great video (via my friend Kate), but stumbled around at first trying to figure them out.   We watched Danny Halvern’s Hexahexaflexagon movie and had some success putting them together with a compass and ruler but it was very time-consuming and we didn’t get many iterations before giving up.  We read over the hexaflexagon construction instructions but were still overwhelmed.  We found a page that talked about the different ways to flex it, but it was still too much to get us off the ground.  I went back to basics and read Martin Gardner‘s original Scientific American Book of Puzzles and Games which probably would have worked if I had taken the time doing it myself, but couldn’t work trying to get the kids to do them as well.  I found a template (and was confused by the having both sides on one side) but, didn’t have a colour printer available so was stumped again.  How were we ever going to get folding?!

And along came the Celebration of Mind Gathering for Gardner.  Their party organizer’s kit finally collected together a simple set of Trihexaflexagon templates in the same spot that we could work with.  We printed out numerous of their blank templates (note to self: modify this to include the numbers for the absolute newbs) and after a few attempts at numbering and colouring it for the kids we got one put together.  Woot!  My son has already modify it to include putting the pattern in the middle and watching it go to the outside and he wanted to do two more before bed, but there is plenty of time for it now.  Are hexahexaflexagon’s next?

Update: Day Two.  We’ve made a few more videos as we worked through our folds and more.  First up is me walking you through the tri and the hexa hexaflexagons.