The Beauty of the Triangle

Right triangleMajor confession: Back in grade school, I was on the Math Team. And our mentor was an amazing lady who taught us both a love of all things mathematics and the reason behind why arithmetic works. She coached us not to look at math as concrete numbers, but as fluid measurements that have a beauty of their own, provided you followed a very stable set of rules. Once you had an absolute grasp on the algebraic and geometric principles, anything was fair game.

I learned the ability to work with small numbers and large numbers. She had us memorize squares and cubes. That two-squared is four. But what is 19-squared? (I forgot, but get out your calculator if you really want to know the answer.)

She opened up math in a special way to me. I did not truly appreciate it at the time, but I do now. I reaped her (and my) hard work for years to come. Our team even took fifth in a Southern Californian math contest. Although I was not the top guy in our club (that would be the kid who is a current chess Grandmaster), I worked to pull my weight.

On the math SAT, I ended up only missing 2 or 3 questions, mostly because all the math on that test involved the basic principles she had drilled into us. I almost felt like I was cheating. For years, I hummed through tests because I had a strong grasp of the basics.

Once I know someone is taking math now, I volunteer to help them. And I’ve lost count of the navy folks I’ve tutored. Truly it may be twenty or more. One mother at work invited me home for a meal and a tutoring session for her daughter. Who was floundering in college calc. My mantra: this never changes. Once you learn something math-wise, it will always be that way again.

So come yesterday, I had a meeting with several Phds and smart civilian folks on a program I am part of. We were discussing a geometric issue that involved several important factors: radio wave propagation, weather, nautical miles, etc. I did not think much of it, but I asked the guy at the computer to type arctan such-and-such into google. And we got the answer we needed.

One of the guys looked at me squinty-eyed and said: what did you do there again?

And I talked him through the five or so steps I used to solve the problem. The big trick was to divide the triangle in half, to get two right triangles. These 90 degree triangles have some very definite rules about them. In my head, I have several of them memorized. (The most common being the 3, 4, 5.)

Right triangleIt was a good way to earn a little respect for the uniform, that I am not a knuckle-dragging Sailor. Who thinks in abstract as well as naval terms. (Some civvies can be quite dismissive of us until you have proven yourself.)

One last point, I never was quite a nerd. It may have been a relief to be accepted by the nerdier folks, but somehow I never was. Now who complains about that? That the nerds won’t embrace him?

And let me end with this thought: that anything I achieved I owe to a great teacher. . .

6 thoughts on “The Beauty of the Triangle”

  1. I had a similar experience. We were hanging out at lunch and the science room windows were open and a couple of upper-classwomen were hanging out in there (a privilege/teachers pets). I was chatting them up and asked what that giant ruler was hanging on the wall. She then taught me some basics about the slide rule. I went home and told my dad. He then produced several and a nerd was born. (I was probably a nerd before that, a band nerd.)
    Imagine the surprise of the high school when I announced I was joining the knuckle dragging Marine Corps. Yeah…people are surprised still today to learn I am a Marine.
    So with that, I’m a nerd and I embrace your genius.

    1. Neat, I’ve never learned the slide rule. I puzzled at one once when I was kid, but I was born just after they were replaced by calculators. And I salute your nerdship, but I’m no genius. Just a guy who got a great teacher at the right time. I have math “common-sense” if that makes any sense.

  2. I’ve encountered a teacher or two who instructed me in the area of math…and to be honest I never thought I had a true appreciation of that particular mindset…but these teachers took an interest in me and taught me the basics of all mathematics and the general rules that build upon each other to get all the answers…I loved the way they think and how they arrived at their conclusions. I had an Algebra teacher in high school that taught the basic principles continuously until even I grasped it and decided for myself it was fun….and then I took a remedial math class in college because I needed two math classes to complete that requirement and it had been so long since I’d had that instruction, it seemed a wise idea. When I was done, that same college professor who provided her insights to the class, asked if I would tutor those who had difficulty….even though it was basic algebra, I was proud for once in my life for this accomplishment despite the fact I declined. I don’t know why but I suddenly realized my fear of math for most of my life had been completely groundless…I still had difficulty with those two college courses afterwards but I did finish them and got Bs for my efforts…and I learned one other thing: it’s better to confront what you fear head to solve the real problems you encounter in life….you never solve anything by avoidance and procrastination……k

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