Pi Day. Understanding Pi. (.785)

At 9:26:53 AM/PM today the numbers will stack up to a representation of the factor Pi. While it is generally used to compute the areas of circles or the volumes of pipe, it has many other uses in space exploration, etc. This is partly a re-post from a few years ago; with some portions rewritten.

We all take Pi for granted. It’s loaded into our computers and calculators for us, and we use it in equations all the time without ever thinking of it beyond it formulaic utility. Some years ago, while working as an estimator of utilities, I found it necessary; or maybe desirable; to understand the exact meaning of Pi and how it worked in relation to the circle.

Having failed at the subject all through high school, and even before that, I had this “fear” of math brought on by my parent’s assertions that I was not able to understand the subject, coupled with a school system which was geared to teaching to the test, rather than teaching an understanding the subject at hand.Had they wanted to really engage my passion all they would have had to do was make the problems relevant to real life. 

For example, you are on a ship and headed in any given direction for 8 days at so many miles per hour. How far have you gone? That would have got me interested in math early on. And by high school, rather than teaching geometry and trigonometry to pass a test, using Nautical Astronomy as an example would have proven more effective at teaching not only both of those subjects, but given the student a true perspective of what mathematics is actually used for. Inadvertently, it would also have taught the subject; which was supposed to be the point.

What is Pi? 3.14159 is the most common answer. Then browse Wikipedia for what that means. Ask the “math” student in your family. The answers you get will all be concerned with the number rather than what it really means, or stands for. That was the purpose of charting it, as I did above, almost 30 years ago while estimating the volume of pipe necessary to hold a specific amount of water. I used a 6” pipe for the example, mostly because it was easily equated to decimal form, and I had a boatload of 6” pipe on hand. However, the resultant .785 factor will work with any size of circle for are, or pipe for volume.

I kept running into Pi while figuring things out, and then rechecking my figures. But, like most folks, I never really understood what it represented, apart from an arbitrary factor that worked. And I really wanted to know why it did. So, I did what Captain Ellison used to tell us at the Baltimore School of Navigation; “Draw it out!” Well, I did. And while putting some of my papers in order the other evening; I am actually doing that; I ran across this and decided to post it for posterity.

In short, while Pi represents the factor used to determine the area within a circle, by careful calculation; and drawing the problem out; it becomes apparent that Pi actually represents .785% of the area of any circle. Will this change the world as we know it? I hardly think so. But it is an example of the beauty and perfection of numbers. 

While I have rounded off the number to obtain this new factor, it should not pose any real problems for any calculations confined to construction, travel etc. Would I use it to build a spaceship and plan a trip to Mars? Hardly. But for the average needs of an estimator; or carpenter; this factor works out just fine.

I hope someone finds this useful and lets me know! Pi for now!

Note: Though I was able to find something about the factor .785 referenced on line; and one fellow even describes drawing a square with a circle inside the perimeters; I still find this explanation and diagram easier to follow.

New Math

Not too long ago I was at the checkout in my local supermarket. I used my Debit Card to pay the bill and wanted some “cash back.” The bill was $37.67 and I wanted change to make the total $50 even. I swiped my card and punched in the code and selected “yes” for Cash back. I then quickly entered the $12.33 I wanted back in change.

The astonished cashier, a young woman about 19 years old, looked at me and said “How did you figure that out so quickly?” Without missing a beat I quickly replied, “I am so old that I have memorized all of the possible combinations of numbers.” With a look of complete awe she responded, “Wow, that’s really great!”

So I was not too surprised when I received the following e-mail, one of those forwarded things that I usually find annoying. I cleaned this one up a bit- it was kind of political in nature, although the general message is the same. We have been “dumbed down” as a society. The basic things we took for granted as part of a general education have been supplanted by newer ways of thinking. This reminded me of the “new math” we were taught in elementary school, and which, by the time I was raising my own kids, had been replaced by “newer math.” This is a funny recap of the last 50 years of teaching basic math;

1. Teaching Math In the 1960’s
A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price. What is his profit ?

2. Teaching Math In the 1970’s
A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price, or $80. What is his profit?

3. Teaching Math In the 1980’s
A logger sells a truckload of lumber for $100. His cost of production is $80. Did he make a profit?

4. Teaching Math In the 1990’s
A logger sells a truckload of lumber for $100. His cost of production is $80 and his profit is $20. Your assignment: Underline the number which represents his profit.

5. Teaching Math In the Early 2000's
A logger cuts down a beautiful forest because he is selfish and inconsiderate and cares nothing for the habitat of animals or the preservation of our woodlands. He does this so he can make a profit of $20. What do you think of this way of making a living? Topic for class participation after answering the question: How did the birds and squirrels feel as the logger cut down their homes? (There are no wrong answers, and if you feel like crying, it's ok.)

6. Teaching Math In 2010
Who cares, just steal the lumber from your neighbor's property. It's OK anyway because it’s a redistribution of wealth.