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.

Sight Reduction Tables - Not So Obselete

Someday my children; or perhaps grandchildren; will come across these volumes of carefully arranged numbers and wonder just what in the hell they are; and what they were used for. That will explain this post.

I used these books while in the Navy; and later as a Merchant Mariner; to find where we were while at sea. They were commonly called “lattice tables” if my memory holds correct. When shooting the sun or stars for a position these books were invaluable since they saved you hours of the computations necessary to obtain the information already contained in the book.

The book itself   is the finished product of about 3,000 years of observations and calculations made by mariners who were sometimes representative of nations who were at war with one another. But still the knowledge was shared. That’s how important these books were. Now, of course, everything is on computer and smartphones, navigation satellites, etc. but at one time you had to actually know what the numbers represented. And how to use them.

Basically the numbers are published in six volumes, with each spanning a 15 degree segment of latitude. The one at top would be used in latitudes from Northern Brazil to the lower southern United States.; or any other location in the world within those boundaries. They are used for navigating by sextant while crossing the ocean and out of sight of land.

Their use is outlined in the beginning pages so that anyone can open the book up and teach themselves. That’s what I did. You take your longitude in relation the Aries; this is called your Local Hour Angle. That, along with your assumed latitude and sextant reading will yield you the precise mathematical location of the star, or planet, which you have “shot” with your sextant. Converted, this will give you a line of position. Ideally, you do this for several stars.

These lines of position will then be used to lay lines on the chart to the points where the stars would be if they were at sea level. Just like a lighthouse, or bouy. The point where all of your lines cross represents the position you are at on the terrestrial plane.The satisfaction of making these computations is enormous, as they give you a sense of just how small you, and your ship, are in comparison to the larger picture. Nowadays there is a place to go online and the computer will make these calculations for you.

You may have seen these for sale on e-bay. They run anywhere from $9 to $20. I suppose many of the people snatching them up are survivalists, waiting for the end times when all the technology will come crashing down and  knowledge will be magic. More power to them. I’m holding onto mine because when I hold it in my hands I am 26 years old again, “punching pubs” at dawn; or dusk; beneath a red light to preserve my night vision. The ship is rolling and the air smells like diesel; or maybe that was me. 

The Power of Doubles

Stop me if you've heard this one before.

A man; or woman; comes up to you and asks if you would be interested in working for 30 days at 1 cent for the first day, with the daily rate to double for the 30 days. There is only one catch; at the end of the month long assignment you can no longer work again; anywhere, at anything.

Do you take the job? Hopefully your answer is yes; because the last 3 days alone with net you a whopping $11 million or so. Do the math, it’s kind of fun and it gives you a whole new perspective on numbers.

Related to this would be artists royalties on records; either as performers or writers; the pennies they receive each time their records are played amount to millions over the period of just 1 year alone. And those pennies; unlike the 30 day $11 million dollar deal above; go on forever.

The same process applies to pandemics. The first person gives it to another person who gives it to 2 more who pass it on to 4 more, etc., etc. The Spanish Flu Pandemic of 1919 is a great case in point. The same is also true of the AIDS epidemic in the 1980’s.

Numbers have always fascinated me; even when I was failing math in grammar school. I knew that there was a magic there which I couldn’t decipher yet. Later; when I learned to navigate by the stars; I found the numbers to be every bit as fascinating as I knew they would be. And still are.

If you want to see the math  behind this 30 day plan, visit the following site. Great minds think alike, and as I was looking around on the net to see if anyone had posted on this before, I came up with the following site. Totally different articles about the same thing. That's what I love about the internet. Perspectives.

http://www.1500days.com/the-magical-doubling-penny/ 

"The Book of the Seven Seas" by Peter Freuchen

Not since the publication of the "American Practical Navigator" in 1802, by Nathaniel Bowditch, has there been a book written about the sea that is so all encompasing, as is the case in this 1958 publication by Peter Freuchen. That's him on the cover, looking exactly as one would expect from his writing.

This is a work of non-fiction which explores the beginnings of earth, and the "Big Bang" theory, as a way of explaining how the ocean basins were physically formed when the sun cast off a ball of flaming gases, which became the earth. The basins were formed by the violence attendant in the cooling process of the molten sphere that would become our home. During this process, a chunk of the sphere broke off, becoming our "moon." This moon would come to control our tides. The pits, valleys and craters left on the earth by this process were then filled by an enormous rain, one which lasted for about 40 centuries and produced 300,000,000 cubic miles of rain.

This book is organized into 11 parts, among them The Shape of the Sea, Life in the Sea, Great Voyages, Treasures of the Seven Seas, Law and the Seven Seas, and even a section on Strange Tales from the Seven Seas. In short, this book has something of interest for anyone who has an interest in the oceans, and the legends and history that go with them.

This book is also a political and military history. It follows the Voyages of Discovery and delves into the settlements of the "new worlds" beyond the horizons of Europe. Along with the tales of pirates and ghost ships, this book packs in quite a bit of science and information about how the oceans current's are formed, as well as the effects of the weather upon the motion of the oceans.

This is an example of one of those rare books that can be found "in the stacks" at the Mooresville Public Library. My usual modus upon entering the library, after greeting the librarians, is to head towards the shelf of newly released books. This is my effort to maintain "relevancy." If there is nothing there to catch my eye, I wander into "the stacks", that great expanse of books from decades gone by. My tastes run, for the most part, between the 600's and the high 900's in the old Dewey Decimal System.

That's the joy of the library, you go in with a vague notion of what you might want, and leave with some things you never even thought of. This is a large and scientific book written by a man who spent 6 decades at sea. So, I will have to visit it more than once. The good thing is that I will know exactly where to find it when I need it again. On the shelf at my Piblic Library. Think about that as you watch the politicians turn off the lights in libraries all across America, even while awarding themselves bonuses, and planning new projects that we just can't afford right now.

And then, think of Peter Freuchen and the knowledge contained in this book. Locked away in an underfunded library it would be of no value to anyone, and much of what it is written, on all topics, will become forgotten footnotes to history.