Tuesday, May 03, 2011

Mathematical Wrinkle

Now that exams are over (see picture at bottom of post), I get to switch gears and am looking forward to a change of pace. I love teaching, but it doesn't leave much time for anything else, and I am so looking forward to reading and writing - doing my own study for a while instead of guiding others in theirs!

While moving into my new mode today I grabbed a book off my shelf that I had forgotten I had. It was first published in 1912, and I see by the markings inside that I purchased it at the local used bookstore, Yesterday's Books. It's called Mathematical Wrinkles and is by S. I. Jones "Formerly Professor of Mathematics, David Lipscomb College, and Assistant Secretary and Treasurer of Life and Casualty Insurance Company, Nashville Tennessee" (as it says behind his name on the title page) - a serious-sounding gentleman.

I paged through it and realize I must have picked it up for its collection of contest-type problems. I often write tests for math competitions, so I'm always looking for new or old or different ideas. I find I can use some of the ideas, but many problems are clearly from a more agricultural time in our nation and/or use archaic language:

"A square field contains 10 acres. What will it cost to fence it at $1.25 per rod?"

"A banker discounts a note at 9% per annum, thereby getting 10% per annum interest. How long does the note run?"

The author seemed to have two intents in publishing, one was to provide recreational problems for math clubs (which is why I picked it up) and another was to provide supplemental problems for classroom teachers. He puts it as follows:

"About the time the First Edition appeared, the first Mathematics Clubs in Secondary Schools in this country were being organized. Since that time greater interest has been aroused in the study of the by-paths of Mathematics and new emphasis has been placed on recreational values. The mind has always found pleasure in puzzles, tricks and curiosities of all kinds. This is true of both young and old, of every land, age, and clime."


"This book is intended to be helpful to be a helpful companion to teachers, and to impart to students a knowledge of the applications of mathematical principles, which cannot be obtained from text-books. The present-day teacher has little time for selection of suitable problems of supplementary work. This book is designed to meet the requirements of teachers who feel such extra assignments essential to thorough work."

It is a quaint and lovely little volume, and (with appropriate changes) I have used some of the problems to inform my contest writing, but what really caught my attention in terms of change in our society is that in this serious little volume by this august-sounding author, written for public school teachers and math clubs in secondary schools, is a section on the fourth dimension which quotes a variety of Bible verses in a manner that clearly assumes everyone is familiar with them and speaks unabashedly of the spiritual implications of higher dimensional geometry. Here is a sample:

"The question now arises: Why may there not be a space of four dimensions and thus a geometry of four dimensions in which the exact position of a point may be determined by measuring in four perpendicular directions? This question is one we cannot escape. Paul may have had the fourth dimension in mind, when, speaking of spiritual life, he said, `That Christ may dwell in your hearts by faith, that ye being rooted and grounded in love, may be able to comprehend with all saints what is the breadth, and length, and depth, and height' (Eph. 3:17, 18); or when he wrote, `I knew a man whether in the body, or out of the body, I cannot tell, how that he was caught up into paradise and heard unspeakable words' (2 Cor. 12:2, 3). What did John mean when he `was in the spirit viewing the Heavenly Jerusalem' and said, `The city lieth foursquare' (Rev. 21:16)? Was Christ's transfigured body which appeared in the midst of a closed room a four-dimensional body? Was the ascension like a disappearance? Although these questions cannot be answered by man, we are certain that the term fourth-dimensional came to us from a firm believer in spiritual life."

"Now, if there be a four-dimensional world, our three-dimensional space must lie in its midst. All people would then be three-dimensional shadows of four-dimensional beings. We could only become endowed with four-dimensional knowledge or become four-dimensional beings by supernatural means. We could move in a four-dimensional being, and not understand how such a thing is possible. If there be such a thing as a four-dimensional being, it would perhaps assist us in understanding the following scripture, `That they should seek the Lord, if haply they might feel after him, and find him, though he be not far from every one of us: for in him we live, and move, and have our being' (Acts 17:27, 28)"

Speaking of the fourth dimension, paging through this book has made me feel like I've traveled in time and had a glimpse of a very different era! I'm eager to read further! I'm also just eager to continue to peruse my book shelves, to discover and learn, to read and to write. Ahhhh...summer... :-)

As promised, here is a photo of what my very recent past contained. I think I will develop a new term for measure, and that term is "a tome of grading!" These are the final exams I graded this weekend juxtaposed with the longest novel I possess! The exams comprised somewhat more than a tome of grading!

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