Approximating Pi

I think it’s irrational that Pi Day turned out to be on a Saturday this year.  Next week is Spring Break so students won’t really get to enjoy the day.

As I sit here reading and just loving the Pi stories, I’m flipping them away into a new Pi Flipboard.  (Here, if you care.)

It was actually pretty depressing reading some of the words used in the stories.  Things like “dork”  or “geek” reflect the attitude towards mathematics from certain sectors.  It’s politically correct to make fun on those whose passion is mathematics and even more politically correct to praise those who do amazing things in the Arts.  At the same time, I’m watching the Formula 1 qualifying from Melbourne and I couldn’t help but notice the beautiful blend of mathematics, engineering, and the arts that make for such a spectacle.

Is it because mathematics is so precise that people get this mindset?

I thought back to the couple of times that I taught mathematics…I was told that you could tell what elementary school the students came from based upon their understanding of mathematics.  It actually was kind of true.  I remember asking the class what Pi was.  The answers were all over the map, although all correct at some level.  “It’s an irrational number”, “It’s a math concept”, “3.14”, “22/7”, “It has something to do with circles” …  The students who gave the first couple of numbers were really able to elaborate on the concept.  The others just knew that 22/7 or 3.14 were numbers that were inserted into problems.  It was a good example of understanding versus rote memorization for me.

I was thinking about this and was reflecting upon my initial discovery of Pi.  I still remember Pi written in paper going around the classroom written on paper over the top of the chalkboards — 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647

(I did have to look it up.  My memory only goes to 3.1415926535.)

But, I do remember my introduction to 22/7.  It was a classroom activity that had us engaged in groups.  We’d done the investigations with measurements to come to determine just what 3.141 might mean.  I still remember our teacher’s instructions.  “What would you think if I told you that you can approximate Pi with a fraction composed of numbers for the numerator and denominator somewhere between 1 and 30?”  When you place it into an equation to solve, often you can divide the denominator into the equation and easily solve things.

Our groups were given chart paper and we were asked to create a table with the headings “Numerator”, “Denominator”, and “Result”.  Our results were calculated by simplifying the fraction and our goal was to find the answer that best approximated Pi.  I’m sure the process kept us busy for quite a while!  But, we persevered.

It was a nice memory as I was dog walking this morning and I sat down and wrote a program in Python when we got home since my memory had actually generated the algorithm.  The logic went something like this:

set pi to 3.14

for numerator = 1 to 30

   for denominator = 1 to 30

      result := numerator / denominator

      if result is closer to pi

         set best_approx to result

         set best_numerator to numerator

         set best_ denominator to denominator

      end if

   end for

end for

print best_numerator, best_denominator, best_approx

There are lots of ways to learn about Pi and explore its significance.  Hopefully, simply memorizing one number or one fraction isn’t one of them.  There’s passion to be expressed in the learning of mathematics.  Witness how worked up the world gets over one number.  Wouldn’t it be nice if all mathematics was approached this way?

In the meantime, enjoy this video….

OTR Links 03/15/2015

Posted from Diigo. The rest of my favorite links are here.