The Physical Relationship of Pi to the Area of a Circle

Today is Pi Day. I know I've posted this before, but as a former Navigator and Full Charge Estimator of Earthworks and Utilities, I am proud of this piece of work. I did this many years ago and framed it. I simply wanted to understand why Pi is Pi. And no one could tell me. So, I drew it out to understand it.

I also wanted an easier way to compute the area of circles. To this day I simply use the factor of .785 to arrive at the total area of any circle. I divided the area into 100 squares and counted the squares inside of the circle, using a 6" round piece of pipe for an example. Then I counted the squares outside of the circle.

I then used .5 ft. X .5 ft. (to represent the 6" pipe) X .785 (the total of squares inside the circle). Not a great discovery, but it satisfied my curiosity and sped up my calculations. Having failed Math all through High School, I have always been amazed at having taught myself Trigonometry and Advanced Algebra. At sea,  using a Sextant, I needed those skills. The same applied to Surveying and Estimating.

But nothing has ever given me the satisfaction of this piece of paper, which is framed and hangs on my wall, next to my Third Mates License and the Engineering Certifications in two different states, with no college degree. You see, it wasn't that I couldn't learn math. It was that the people attempting to teach me simply didn't know how to reach me. And that, as Paul Harvey used to say, is the Rest of the Story.....

Happy Pi Day to all. 🙂

P.S. Last night I made a startling discovery. My diagram, hand drawn just as it appears here, is on a web site showing the various "official" visual explanations of Pi. All advanced and carefully laid out. 

The difference between mine and the others is astonishing. While all the others require some advanced knowledge of mathematics, mine is the only one which can be understood by a 6th grader. 

That it is included with the others, is like an honor for me. That is exactly what I was trying to create. You can view the whole layout, with all the other diagrams, by using the following link. Just look for the yellow handrawn one. 

https://www.google.com/search?sca_esv=483c85010fc377d1&sxsrf=ACQVn08yn_NpVuWevqVdtLXi6CuBIwJ4Lw:1710468678145&q=images+of+the+physical+relationship+of+pi+to+the+area+of+a+circle&tbm=isch&source=lnms&prmd=ihvsnbmtz&sa=X&ved=2ahUKEwi49davmPWEAxWxKFkFHSTbDMQQ0pQJegQICxAB&biw=1600&bih=699&dpr=1.2

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.

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!