Pieces of Pi

Pi as a Fraction

22/7 ? Isn’t 24/7 the ratio that we’re used to seeing around, expressing complete availability? 22/7 is a round, too, though its function is more the description of a round…. a round circle. If you’re at all up on your numbers, you’ll recognize that the fraction 22/7 is a good approximation for the ratio between a circle’s circumference and diameter, in other words, pi.  If you are already quickly losing interest and are ready to stop reading  you’re probably one of the multitudes who have suffered while studying the relationships of quantities (math). Now, why am I talking about pi? I don’t think I’m alone in being a bookbinder who has a comfortable connection with numbers: so much of what I do is about measurements, ratios and counting.

PI

I am taking some time this year to take care of health, family, and explore some ideas that have been nipping at my heels for a very long time, which includes playing around with numbers and concepts. About Pi,  I’m more interested in its usefulness, rather than its awesomeness.  Even though I’m totally on-board with appreciating how cool it is that pi is irrational and that it has a long and colorful history, it, generally, also seems to me that when students are first introduced to pi, I think, in about 5th or 6th grade? what is really an easily understandable idea gets lost in translation. Consider this:

Too much Pi can give you a tummy ache

The illustration above refers to 11 different ways to express Pi. Egads.

(addendum: on Jan 22, 2018 Joshua Bowman‏ @Thalesdisciple 23  directed me to another page showing versions of pi: http://thalescircles.tumblr.com/post/79583630809/curiosamathematica-pi-in-its-full-glory)

      I’m planning to do a few posts about Pi, not because I am trying to lose followers, but because I want to try out using paper and pictures to do some playful explorations. Starting off with Coloring Book-style pages sets a tone for me, reminding me that a familiarity with the forms and shapes of math is a comfortable place to be.

Pi

I’m also a big advocate of thinking of pi simply as 3.14 because any real world application that an elementary student is going to do will be accurate enough using 3.14

The most accurate fraction representing pi with a denominator less than 30,000

–which is not say that knowing that 355/113, which is the most accurate representation of pi  with a denominator less than 30,000, should be ignored. After all, even if you leave it out of the equation of learning math, it is certainly a pretty number worth coloring in.

Coloring Book Pages of Pi