A Cute Angle
As printed in Proteus, the Journal of the Delaware Valley Mensa  (Jan 2012)
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         One impressive aspect of the martial arts is the age range of its participants, running from just-started-walking through, well, as high as human ages go. As such, through karate, I am connected with adults who have trained for longer than I have been alive, as well as with kids who have just started high school. The latter end of that spectrum exposes me to questions I might not otherwise see at this stage of my life, such as, “Can anyone help me with this math problem?”

         That recent question was accompanied by the following image. If you are anything like me and have a strange urge to work out the problem, FYI, the answer is at the end of this column. The top and bottom lines are parallel, and your goal is to solve for y.

         I was killing time at the airport when I saw this image, which reminded me that I quite enjoyed geometry way, way back when I took the class. My teacher’s name was Ray Vehar. This is notable because, when he was teaching us how to represent rays (with a right-facing arrow above two letters), he smiled and told us of a clever student who realized that our teacher could write his name like this:

         I’m pretty sure that all of us wished we’d have thought of it ourselves. Remembering that story doesn’t surprise me. What did surprise me was remembering that, when two parallel lines are cut by a transversal, alternate interior angles are equal.

         Whoa, what? Where did that come from?

         You know how when you recite the pledge of allegiance, you don’t have to put forth any effort once you get started? The words just flow, always in order, always with the same intonation, always with the pauses in their designated places. “I pledge allegiance (pause) to the flag (pause) of the United States of America. And to the republic (pause) for which it stands (pause)....”

         You know what, while we’re on this, why are those pauses there? They’re mid-sentence. They’re totally unnecessary. And what’s with the sing-songy voice we all use? The rhythm and melody are so consistent, it could probably be written in musical notation. If you’re ever called upon to recite it again in a group, I dare you to say it like this instead, like you’re doing a spoken word piece at Open Mic Night. Or like you’re Captain Kirk.

         I! Pledge! ALLEGIANCEtotheflaaaaaagOF (pause) the UNITED (pause) States of America ANNND (pause) totherepublicforWHICH (pause) IT (pause) STAAAAAAAAAANDS...”

         Irony of ironies. The national pledge would feel foreign to you. But let it run the way it wants to, and the words are one long, unbroken line that you might just remember for as long as you live. Kind of like the Alternate Interior Angles song, which I didn’t realize I knew until that flashback in the airport.

         There I was in geometry class again, Ray VR at the chalkboard wearing what a friend and I referred to as his raspberry sherbet slacks (he was known for his daring collection of pants), saying, “When two parallel lines are cut by a transversal, alternate interior angles are equal.” To keep it lively, he would sometimes make a chopping gesture with his hand on the word “cut,” but otherwise he always said it the same way, in an unbroken line. OK, a line segment. The point is that this class was more than 20 years ago. If I remembered this much, could I answer the question? One way to find out. I pulled out a notebook and a pen, jotted down the problem, and got started.

         It might not be accurate to say that killing time at an airport rendered information on alternate interior angles “useful” in my life. Nothing urgent was at stake in my attempt to solve for y, other than my interest in whether I “still got it.” But I have made use of at least some of the info I gleaned in the days when I put brown paper covers on my school books. And decorated them. With my twelve color pen.

         English - I do a yearly haiku challenge, for goodness’ sake. 

         Science – the one tidbit that stands out right now is from a particularly disturbing episode of Mr. Wizard’s World. Evidently, Little Miss Muffet added lemon juice to a bowl of milk, and voilà. Curds and whey. My stomach is still turning decades later. Thanks, Mr. Wizard. On the plus, at least I’ve never made that mistake with my tea. So yeah, thanks again, I guess.

         Spanish/French - I’ve used each with tourists here in the US, and as a tourist elsewhere. It’s pretty amazing to see cracks form in a language barrier. And it all started in 7th grade with, “Levantense. Sientense.” Thanks, Mr. Kneblewics.

         History - My love of early ‘80s Saturday morning television prepared me for the moment when jazz musician Bob Dorough, co-creator of my beloved Schoolhouse Rock, performed in Philadelphia. One of his backup singers gestured for people singing along in the audience to join them during “The Preamble.” I handed my camera to my friend – “take pictures,” I said – and skipped to the front of the room to join the other hardy soul who had stepped up to the plate. Err, microphone. The bass player was amazed that we really knew the words.

         Math - If a sweater needs to measure 40 inches around and calls for knitting 6 stitches per inch, but I knit more tightly at 7 stitches per inch, I can either change the way I knit (not happening), or change the pattern. Algebra to the rescue! Ms. Alperin would be proud. By the way, the karate kid confirmed that yes, y=60. Still got it, Ray VR! Booyow!

         Schoolhouse Rock fans will recognize “booyow” as an interjection.

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