Pi Day

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's 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. I was, like my mother; and remember, it was my mother who said it; used to tell me, “You take after me and I could never understand math. But you can read well, and your brother can’t.” What a stupid statement to make to any child, even your own! Water under the bridge. Having navigated around the world, by sextant, in the days before Nav Sats etc., I can truly say that I am perfectly capable of working out any mathematical problem thrown my way. The failure was in the teaching method.

Had they wanted to really engage my passion all they would have had to do was make the problems relevant to real life. Like, you are on a ship and headed in this direction for 8 days at so many mils per hour. How far have you gone? That would have got me interested. And by high school, rather than the mundane tasks of geometry and trigonometry, nautical astronomy would have proven more effective at teaching not only both of those subjects, but given the student a true perspective of just where we were on the terrestrial plane, and also how insignificant we actually are; individually, or collectively, in the grand scheme of things.

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 40 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.

But I kept running into Pi while figuring it out, and then rechecking my figures. So, I did what Captain Ellison used to tell us at the Baltimore School of Navigation; “Draw it out!” And, I did. And while putting some of my papers in order a few years ago; I actually did 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.

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.

The Niagara Suspension Bridge Shell

I found this interesting shell about 25 years ago in Burtonsville, Md. while working as an assistant to a surveyor. I would compute the formulas in the field in order to get a quick “traverse” of the properties we surveyed. This was before the computer stuff took over. I was good at it due to my experience as a Quartermaster in the Navy and later as a Navigators Assistant while serving as Third Mate in the Merchant Marine.

Anyway, there was an old mobile home on one property and I went in to look around; maybe see what treasures might have been left behind; expecting nothing. I found this in the kitchen area and it evoked in me the scene from “Grapes of Wrath” where Jane Darwell is going through her old memory chest and finds the pin from the St. Louis Exposition of 1903. It must have meant a great deal to someone a long time ago.

At the time internet was still in its infancy and I couldn't find out too much about this bridge, which of course was long gone. While reading a book today I came across an item mentioning that James Roebling had built a suspension bridge over the Niagara in 1855. I Googled it and came up with a wonderful Wikipedia article on it. I wondered where the shell was and happily found it in our china closet, way in the rear where it could not be seen.

 

The bridge was taken down in 1897 which finally gives me an age for the shell. It is from the 1890’s or older. And the illustration is so much like the one etched in the shell that I wanted to share it. For more on this brige and it’s remarkable history hit the link;

http://en.wikipedia.org/wiki/Niagara_Falls_Suspension_Bridge

Meantime the shell is now out of the closet so to speak, and occupies a prominent place on the piano.

Understanding Pi

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. I was, like my mother; and remember, it was my mother who said it; used to tell me, “You take after me and I could never understand math. But you can read well, and your brother can’t.” What a stupid statement to make to any child, even your own! Water under the bridge. Having navigated around the world, by sextant, in the days before Nav Sats etc., I can truly say that I am perfectly capable of working out any mathematical problem thrown my way. The failure was in the teaching method.

Had they wanted to really engage my passion all they would have had to do was make the problems relevant to real life. Like, you are on a ship and headed in this direction for 8 days at so many mils per hour. How far have you gone? That would have got me interested. And by high school, rather than the mundane tasks of geometry and trigonometry, nautical astronomy would have proven more effective at teaching not only both of those subjects, but given the student a true perspective of just where we were on the terrestrial plane, and also how insignificant we actually are; individually, or collectively, in the grand scheme of things.

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.

But I kept running into Pi while figuring it out, and then rechecking my figures. So, I did what Captain Ellison used to tell us at the Baltimore School of Navigation; “Draw it out!” So, 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. Forgive the non-pun. Hope someone finds this useful and lets me know! Pi for now!