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