Robert (gurdonark) wrote,
Robert
gurdonark

Geometry



Yesterday afternoon I pitched in for an hour of helping one of the neighbors, a high school student, with a geometry assignment. I had not looked at a geometry textbook for years. The assignment involved using graph paper to solve multi-variable computations. As I solve multi-variable computations with a bit of hunt-and-peck, some simple algebra, and a lot of trial-and-error, I was not, at first, any great help on the problems.

Fortunately, we had at our command Chapter 9 of that resource known as the Cliff's Notes to Mathematics. This Chapter, entitled something useful like "graphing", illustrated for me how people use graph paper to pictorially represent an elaborate program of hunt-and-peck, some simple algebra, and a lot of trial-and-error, featuring tables of values and a display of ascending and cascading numerals.

Soon I was able to grasp the lessons which this particular assignment was out to teach, including that if one solves an equation with the variables x and y, and supplies the assumption x = 0, then one acquires something called a "y intercept", which is the point at which an imaginary line crosses an imaginary y line on an imaginary diagram, rendered in ink. I also learned that the word "slope", which I associate with ski trips I've never taken and with certain foreheads and one parson in Victorian fiction, actually is a word that, as in a video game, means something surprisingly complex for something sonically so easy. It turned out to mean, roughly, that:

a. solve an equation with x and y in it, using different assumptions for x, and calculating for y;
b. subtract the two y answers from each other, and then subtract the two x answers from each other
c. divide the y difference by the x difference, for almost no apparent reason
d. call that quotient the "slope".

Slope, it turns out, lets you figure out how many up the line goes for each across, which no doubt benefits atomic scientists, interior designers and crossword puzzle aficionados. Once one understands this, of course, the assignment to solve for it proves to be child's play.

Yet the sky had not finished opening to show its sunlight. The book then turned us to a fascinating fact, which ran:

y = mx + b

where m is the slope and b is the y-intercept,

which all begins to sound a lot like jargon, to me, but actually is useful information.
With this equation, one can become a 9th grade math teacher, and write entire textbooks of plotting m,y, x, a, b, slope, y intercept, and escape. So the horrid cycle perpetuates itself.
I enjoyed renewing my knowledge of geometry.

By the way, I use algebra and accounting (a course I did not take) very often in my practice, which, I suppose, shows that not everyone can accurately say "I'll never use this again". Geometry is actually pretty cool, because, unlike the novels available in airports and the Fox News Service, it actually makes sense and is useful.

In my family, in my childhood, one's genius was measured by how good one was at math. I took three calculus courses, but literally passed the third one by the barest margin. My brother got a degree in mathematics.

I am grateful, though, that the limitations I have encountered in my chosen pursuits are matters of aptitude and lack of assiduous pursuit, rather than physical or material limitations. I can imagine how hard it would be if it were otherwise.

It still puzzles me why we did not get better-written versions of the Cliff Notes instead of textbooks.

Parenthetically, I like the George Burns tag about how it's a shame how all the people who could really run this country are too busy cutting hair and driving taxicabs.
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