Evolving π


This morning on This Week in Ontario Edublogs, we featured a blog post from Tina Bergman about self-regulation and mathematics. You can read the post here:

https://medium.com/@tinabergman_52322/the-truths-about-self-regulation-maths-84d627c6a398

I’m a sucker for mathematics posts; I love the subject and have experienced the highs and lows of studying the subject.

When I think back to mathematics teachers that I had, I think I was lucky; I don’t remember any of my teachers strugging with the topics at grade level. Except in Grade 8, every home room teacher taught their own mathematics. In Grade 8, the principal taught us. I’m sure that there was a reason why and knowing what I know today, I’d probably ask. Like all the teachers, I really do have fond memories of mathematics with him.

As I look at people analysing mathematics in schools these day, I think I was rather fortunate with the luck of the draw of the teachers I had. You’d think the subject would be cut and dried since there’s typically one right answer to a question (and a lot of wrong ones).

There’s one thing that has changed over the years and students could be understood for wondering ….

It’s the value of π.

We started by accepting that π was 22/7.

Then, we learned that wasn’t good enough and π became 3.14. That was especially important because it explains why March 14 is πday.

Then, that wasn’t good enough either and π became 3.1415926 (typed from memory) It was there that I learned that 22/7 wasn’t even close. It’s actually 3.1428571. A teacher somewhere told us that that was a big enough error to miss the moon if landing was dependent on your calculations.

Then, we learned that we didn’t always have to have an exact number and the answer of 3π + 4 was OK.

Then, along came calculators and even the cheapest ones came with a π key that you could tap when appropriate.

Somewhere along the line, we learned the beauty of mathematics and discussed the joy and uniqueness of π being a constant and yet was irrational. I’m sure that by that point in time, we knew that the number was anything but rational.

Then, in computing, we learned about extended precision which allowed us to use more than 8 digits with a decimal place to calculate things requiring π.

The internet and powerful computers let people do things like calculate the first million digits of π.

(this is a small part of the number – click through for the complete million)

Then, this week comes this bit of information about π.

One million digits is not enough – we now have calculated π to 62.8 trillion digits. (We as in the collective we of humanity)

Any predictions about what’s next?

In a subject area where we’ve come to expect right and wrong answers, this one little character continues to push the envelope.

OTR Links 08/19/2021


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