Reading a Book and Doing the Math

I don’t post regular reviews anymore; I’m taking the time to really enjoy what I’m reading. But that takes a little extra time for me. For instance, I am reading a book which says that 600 acres are equal to One square mile. I am always curious as to the veracity of any numbers thrown at me, and almost always check them out- longhand.

In spite of failing mathematics throughout my school years I have spent my entire life working at jobs which all dealt with numbers. From navigating a ship by star to estimating earthwork (try it sometime by emptying a pot of dirt and then seeing if you can get it all back in; or digging a hole and then throwing the dirt back in without having some left over) I have in love with the little digits and their perfection. They simply do not lie. Statistics do; but not mathematics. So, you see I just had to check the figure out and determine for myself how many acres are in a square mile.

To begin with I know that a mile is 5,280 LF long so you multiply that by itself and come to the sum of 27,878,400 square feet to a square mile.

   

Now we need to take the acreage. There are 43,560 sq ft in an acre. The assertion is that there are 600 of these acres in a square mile. So you multiply the 600 acres by the 43,560 square feet per acre and come to 26,136,000 square feet in 600 acres. We have a problem. The acrerage stated in the book is short.

Taking 43, 560 square feet and multiplying it by x for the unknown acreage and making it equal to the square footage we know to be a square mile (27,878,400 square feet) you get 43,560x = 27,878,400, as in square feet. Then you isolate the x.

The equation looks like this; (cross multiplication)

43,560X = 27,878,400 sq ft  = 640

43,560         43,560

And the proof is self-evident. You simply multiply 640 acres by 43,560 square feet to each one and come up with the same number of square feet then divide that back by 43,560 square feet for a total of 640 acres; 40 acres more than stated in the book. It's no big deal; just something I do. 

As usual with any post dealing with mathematics I dedicate this to my father, William Llewellyn Williams, who was so good at numbers that he couldn’t teach me to count;, believing that his failure was my shortcoming. 

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!

Ones

Today is 1-11-11. Thanks to Suzy at http://mendogardens.blogspot.com/ for the reminder! We won't have another Day of the One's until November 11th. Enjoy it while you can!

"Proofiness" by Charles Seife

This is an unusual little book about numbers and the way they are used to manipulate us in our everyday lives. From the collapse of Enron to the folly of the color coded Terrorist Alert Levels, Mr. Seife does a wonderful job at showing us just how clever the powers that be are when it comes to deceiving us about almost anything you can imagine.

From Political Pollsters to Erectile Dysfunction, the author pokes holes in all of the major concepts which we embrace on the basis of numerical proof, which is often proof of nothing at all. From "pattern matching" to crowd estimates, all is often "smoke and mirrors" when numbers are used as "proof."

A very light and easily read book about a seemingly complex subject. That is, if you believe the polls.