Warning: trigonometry can be hazardous to your health
By: Terry Donnelly
Imagine the fun of seeing your high school mathematics teacher turn ashen twice within about two minutes. Most school days don’t include incidents that put teachers and students in life threatening situations or send blood pressures into the stratosphere, but those days do occur and they can be memorable.
Spring of 1964 had sprung in winter-ravaged Kalamazoo, Michigan. The sun was shining and an assortment of 25 high school seniors, primed for spring break, and one tall, math nerd, yet beloved, teacher set out together to conquer the mysteries of sine, cosine and tangent. The ringing of the tardy bell foretold nothing more than a standard trigonometry class as the festivities began.
The teaching/learning cycle began slowly, restless students started being called upon to show skills with a slide rule, and the pace slowly quickened. Posers were posed and a mish-mash of correct, near miss, and far-fetched answers began to shower the front of the room and be recorded in a cloud of dust on the chalkboard for later scrutiny.
The board was nearly filled with an impressive array of chalk lines and arrows leading from one section of writing to another section of numerals all orbiting a neatly constructed, centrally located right triangle when Mr. Rothmann, in his best academic tenor, spoke these now infamous words, “Len, give us a step by step process for finding the dividend for 3,663 divided by the square root of 91 using a slide rule.”
Len was Len Farley, the student everyone universally wanted to be called on in class. His turn in the barrel nearly always sent the class into an uproar and the instructor into a cold sweat. Every time the feckless instructor called on Len to respond he ended up scratching his head and wondering where he had gone wrong in his teaching. This effect was often accompanied by our leader fading into a trance, dreaming about retirement, and writing a great American novel in the serenity of his own den with his basset hound, Pythagoras, peacefully sleeping at his feet. His thoughts also likely turned to wine as well, but that cannot be confirmed.
Beyond a good laugh, the other benefit of having Len asked to stand and deliver was that it always took up a substantial chunk of time that often saved others in the class from being targeted for a response. Everyone loves the class clown. We never could figure out why Mr. Rothmann called on Len as often as he did. Maybe he was so dedicated that he was determined to crack that nut, or it could be he just wanted a few moments of comic relief himself.
True to form, Len stood with his slide rule in hand. He slowly moved the slide bar to and fro remaining mute. He moved the clear plastic cursor to the far end and again focused on the slide bar. This time the slide came completely out of the device and clattered to the floor. Len picked it up, replaced it, and returned to his calculations. Next he began turning the tool upside down and back upright again in front of his eyes, cocking his head as he turned the device, and reading numerals aloud in a way that suggested the oration was more panic than answer. He had put the slide bar in upside down and was trying to come up with something–anything to say.
What came out was this: “Step one, check to be sure the slide rule is properly assembled.”
“Sit down Farley. Sit down.”
The class had just started to quiet their laughter when we all heard the electric simulation of the ringing of a bell transmitted over the intercom system indicating it was time for lunch. That sound initiated a Pavlov reaction that sent us into escape mode. Our schedule called for a split class around our lunch period–thirty minutes of class, thirty minutes for lunch, and thirty minutes more of class to kick off the afternoon.
Lunch always went quickly and soon we found ourselves sated from pizza slices, mac and cheese bought in the cafeteria, or the peanut butter and grape jelly sandwiches on rye brought from home. We all began to herd ourselves back to class and mingled in small cliques around the classroom door. No one dared go into the dark, empty room without Mr. Rothmann giving the okay.
Len was blue all during lunch. He felt like he let Mr. Rothmann down and wanted to get back into his good graces. The problem was that his chance for brilliance had been blown and the opportunities for redemption this day were slim, slimmer, and slimmest.
“How can I get myself out of this? What will make Mr. Rothmann happy again?”
“Send him some flowers and say your sorry,” was the only half doable suggestion uttered from the group.
Len lit up like an octogenarian’s birthday cake. “Hey! That’s a great idea. I saw some flowers growing out in the field. They’re right outside the classroom window. They’ll be perfect!”
I had my lunchroom half-pint milk carton with me, polishing off the last bit of sweet liquid saved specifically for the trip from the cafeteria to the classroom. Len grabbed the now empty container out of my hand, tore loose the staples obliterating the spout, and opened the top wide. He then did the unthinkable. He tiptoed into the classroom but immediately reemerged with a metal compass for drawing circles and a ruler. Len then sprinted out the back door and into the open field that lay behind the school.
Ours was a new school two years before and the building was a beautiful creative design. It had three pods of classrooms plus a gymnasium and an Olympic sized swimming pool attached with corridors to a central office area. The pods made the school seem small and cozy rather than big and frightening. It was fresh and modern causing the cross-town rivals attending the old, downtown school from which most of our school population was gleaned to dub it “the country club.” The building work was all done but landscaping had been neglected. Around the school remained piles of construction materials that needed removal and heaps of dirt that needed grading. The area outside our classroom window looked into a wooded area that was scenic as all get out, but the debris between the window and the woods was unsightly as could be.
Mr. Rothmann, being one who enjoyed natural beauty, had gotten fed up with waiting for the construction team to put the finishing touches on his view. So, he planted a small patch of crocus bulbs so that on spring days he could glimpse a wee bit of beauty and a splash of color as a break from sitting at his desk correcting math papers. He loved his crocus bed and admired it every day the flowers were in bloom.
Len returned with the milk carton filled with dirt and sporting half-dozen or so colorful plants. He had improvised using the tools of math, the compass and the ruler, to dislodge the crocuses from their home and repot them into the wax covered paper carton. He beamed from ear to ear. He was so proud of himself for finding this perfect peace offering that he was bursting his buttons and couldn’t wait for class to resume. All of his former sadness and gloom was instantly replaced with elation and the anticipation of a whole new dawn of mathematic successes.
To put the finishing touches on the surprise, Len crept back into the dark, forbidden room to place the gift on Mr. Rothmann’s desk, planning to announce his genius at finding the perfect addition to the teacher’s desk when Mr. Rothmann spied the treasure and queried, ”Where in the world did these beautiful flowers come from? What student could be so thoughtful and mature to think of his dear teacher and offer such a lovely addition to our class?”
Len’s scheme for entrance back into good graces was all in place. Mr. Rothmann would be returning from lunch at any minute and all would be right with the world once again.
The entirety of the class was in the hall and a couple of us stood with our backs to the door so Len couldn’t get out of the room, rejoin the group, and let his plan evolve. He pushed against the door. It wouldn’t budge. He pushed harder and all he got was a little bump open and then a snap back shut. He began pushing and kicking at the door like the caged animal he had become. Five or six of us were leaning against the door and resisted all Len’s efforts to get out. He began spewing a torrent of random words designed all at once to threaten, cajole, and plead with us to let him out. He got a running start and slammed into the door. No movement. Panic set in. Len had to get out. What could he do other than try again?
He couldn’t crawl out a window–they were too small. He thought about hiding in the teacher’s coat closet and trying to sneak out and slide into his seat undetected after everyone was back in and mulling around before class started again. That seemed like a long shot, so he went back to brute force as his only mode of escape.
About this time we saw Mr. Rothmann coming down the hall rested after lunch and ready to, once again, dig into advanced trigonometry. We could see him from quite a long distance through the glass corridor walls that made for brightly lit halls. He was ready. We all dutifully lined up awaiting his signal to enter the room. He turned the corner. We waited. He approached the room. We waited. He stood about four feet from the now unpopulated entrance ready to step in and reach for the handle to open the door when with what seemed like an explosion and rush of air that could only be explained as a sonic boom, sent the door wildly swinging on its hinges. The door swung so close to Mr. Rothmann that it may have peeled off a layer or two of skin from his nose.
Len found himself sweating from his ordeal and gasping for breath a mere inch from Mr. Rothmann’s face.
Len had taken one more frantic run at the door, which was now unbarred, and blasted through, unimpeded, from darkness into the brightness of the hall.
Len was stunned and blinking eye-to-eye with Mr. Rothmann who was frozen in place and was, unknowingly for only the first time that day, completely without facial color–ashen.
“I’m sorry Mr. Rothmann. I had to go in to…to…I had to go in to…”
Mr. Rothmann silently tottered around Len and into the room. We all followed. It took every ounce of strength the 24 of us could muster not to burst into uncontrolled laughter. It took every ounce of Len’s strength not to wet his pants. He did console himself with the fact that the piece offering still lay, undetected, on the teacher’s desk. It would now have to serve a double duty–first for messing up the slide rule demonstration and secondly for nearly flattening our teacher into a manhole cover sized mass.
Someone turned on the classroom lights and we all scurried to our desks desperately averting our collective eyes, holding our collective breath, and biting our collective tongues trying to control our laughter.
Mr. Rothmann, still wobbly, shuffled over to his desk and placed a hand on top to support some of the weight his legs were refusing to hold up. He mopped his brow with the handkerchief in his free hand. As the florescent lights flickered and began to illuminate the room he saw the crocus bouquet on his desk. As understanding began to seep into his consciousness, he went ashen for the second time in as many minutes. He plucked the milk carton from the desk and, without sound, stumbled to the window. Resting his forehead on the glass and peering out into the field he confirmed his worst nightmare–the crocuses were indeed from his own beloved garden–his once pristine respite from clutter and ugliness. His small retreat into serenity and beauty had been snatched from their arena in nature and were now wilting inside a chocolate milk carton in his very hands and before his very eyes.
Mr. Rothmann, still the color of last year’s Yule log ashes and with a deeply creased brow, slowly turned to face the class. Hoisting the carton of blooms high above his head looking every bit like the Statue of Liberty holding her torch in both stature and hue, he tried to speak. From deep in his chest arose a nearly inhuman sound. The words were those of human speech, but the roar was loud, filled with vitriol, laced with saliva, and inspired by our evolutionary link to the feral animals of the world.
Mr. Rothmann sounded as if he were trying out for the part of Thor in the school play as he thundered, “Who did this?”
