Mathematics-Physics SMILE High School Meeting
11 April 2000
Notes Prepared by Earl Zwicker

OUR NEXT MEETING... ...will be May 2, 2000 <----NOTE!! 4:15 p.m. 111 LS AT OUR LAST MEETING (Apr 11)...

Porter Johnson (IIT Physics)
placed on the board and announced a Public Lecture, and invited us. The Heald Award Recipient will be Leon Lederman. Leon will talk on the future of education in mathematics and science. This will occur on Monday, May 22,with a buffet supper at 6:00 pm and lecture at 7:00 pm, Wishnick Auditorium. See the website for details --- something we all should find interesting!

Ann Brandon (Joliet West HS)
needs some volunteers for Physics Days at Great America, May 9 and 10, Tuesday & Wednesday. Volunteers are needed to man the four stations for analysis of ride data recorded by students using their Vernier & Texas Instruments Logger Pro equipment & vests. The job involves checking out and in the equipment to teachers whose students will use it, then return it for others to use. Please contact Ann at the email address

Bill Colson (Morgan Park HS)
passed around a Chicago Tribune newspaper clipping on the subject of baseball and bearing a photo and interview of Porter Johnson, our local baseball guru. Porter has a bat over his shoulder, and looks like a real "slugger!" And then Bill passed out a handout titled "All About Mike." Mike (circa 1945) was a chicken with its head cut off that didn't seem to miss his head, and behaved pretty much like any other chicken, except feeding and watering was done with an eyedropper. He lived 18 months in good health, going from 2.5 lb to about 8 lb! See the website for details. Interesting biology here, about how this was possible?

Next, Bill called our attention to two math books: Tour of the Calculus by David Berlinski [Vantage Books/Random House, ISBN 0-679-42645-0, Feb 1997] and a more recent book by the same author: Advent of the Algorithm. He passed them around and noted that they were written for the intelligent layperson. They elicit the same sort of insight and enjoyment as achieved more frequently these days in science by other successful authors. Thanks, Bill!

Bill Blunk (Joliet Central HS)
had his miniature videocamera connected to the big TV in front of us, and he placed a black cube-shaped device (about 2 cm on a side) mounted on a flat metal plate (about 6 cm x 15 cm) on the table. Then he told us about a kindred cross country skier, Bert Kleerum [Eagle River Nordic Skis] and their interest in measuring accelerations encountered in skiing. This has never been done before. They are trying to find a way to do this, and the black cube is an accelerometer used to measure and control airbag deployment. Obtainable through David Vernier [a premier supplier of sensors and electronic displayers and recorders for physics teachers - see any physics teacher on this, or else check the website, and capable of +/- 5g, a very useful range. Bill showed us his Palm Pilot, a pocket size device with a graphic display and capable of recording much data. He focussed his videocamera on its display, so we could see it quite clearly on the large TV. Another device, which plugs into the Palm Pilot, is made by Imagiworks, and Bill plugged the black cube accelerometer into it in turn.

Earl Zwicker gave Bill a hand by moving the accelerometer in various ways: circle, back-and-forth linearly, up-and-down linearly, accelerate and stop linearly - in opposite directions. Each of these motions resulted in a graphical display which we easily saw on the large TV, as Bill held the videocamera focussed on the Palm Pilot. (Which of the motions looked like a sine wave?) It is more compact than TI-CBL, with greater memory. And the Palm Pilot easily dumps its data into a PC to be analyzed by EXCEL. Now - the skier would carry the Palm Pilot in his jacket, connected to the accelerometer mounted on a ski, to record the physics of the ski's motion.

But - Bill still needs to find a way to record position as the skier moves along. This might be done with a permanent magnet under the snow, with a pick-up coil on a ski. The motion of the coil-on-the-ski through the field of the magnet would result in an electromagnetic induced pulse or "blip" to be recorded by the Palm Pilot on top of the acceleration data. Bill had a strip of refrigerator magnet material which could be placed under the snow, but a pick-up coil of about 200 turns of no. 26 wire did not produce a sufficiently strong signal. What to do? Any ideas? Could the difficulty be caused by an impedance mis-match between pick-up coil and the Imagiworks gadget? Let Bill know if you have an idea that might work. Terrific, Bill! Keep us informed!

Post-hypnotic thought/suggestion by PJ: What about just hooking up a GPS device to the calculator, and have it record the position? You can set it for "relative" position, relative to the starting point, and it is pretty accurate on that basis. But, is it accurate enough??

Bill Shanks (Joliet Junior College, Music)
showed us how to generate Pythagorean numbers. He defined these as integers a,b,c that satisfy the relation

a2 + b2 = c2.
An example most of us know is 3,4,5. These are very useful, especially to physics teachers making up exam problems involving vectors where you want the answers to work out as integers. Bill asked us to give him a 2 digit odd number, so one of us named "17." Bill wrote it on the board, and then he wrote
172 + 1442 = 1452.
How did he do that in his head?!! He did it again with 14 (left as an exercise to the reader!), but then he explained. For the sides of a right triangle write: side a, side b, and hypotenuse c = b+2. Then
a2 + b2 = (b+2)2.
A little algebra results in b = (a/2)22 - 1. Let a = 2x, and let x be any integer you like, say 4. Then, a = 8, b = 15, and c = b + 2 = 17. So
82 + 152 = 172!
It really works! Now make a table with x taking on various integer values, 3,4,5,6,... and you thus generate a whole series of Pythagorean numbers! Wow! Thanks, Bill!

Earl Zwicker (IIT Physics, ret)
showed us a chunk of # 3 coaxial power cable from ComEd. It was installed about 3 - 4 ft underground without need to dig a trench, a few hundred feet at a time. How is this done? Relatively recent technology. Photos at a future meeting.

Fred Schaal (Lane Tech HS)
asked us a few riddles:

Fred wondered whether any of us had solved the problem of how to maximize the volume of a truncated cone by cutting the appropriate angular segment from a plane circle. ie. What should be the angle of the segment to do this? (See notes from March 28, 2000.) No one volunteered an answer, so -- maybe next meeting?! (Can't anyone do this?!)

Arlyn Van Ek (Iliana Christian HS)
somewhat randomly handed out Genetrons to us. (See the Arbor Scientific Catalog, or the website

Cranking Up: physics lab

Each Genetron is a fist-sized, roughly ellipically-shaped plastic generator/motor with a crank sticking out of one end and a pair of wires from the other end. Arlyn had the wires connected to a small light bulb mounted in a socket. When he turned the crank, the bulb lit up. When he opened the connection to the bulb and cranked again, he said it felt different, and invited those of us with Genetrons to check this out. Sure enough! We could see the our friends break into smiles! Then others tried it. It was much harder (took more work) to crank with the bulb in the circuit and lighting up, than out of the circuit and remaining dark. A beautiful way to show students just how much (electrochemical) work a battery is doing when it is lighting a bulb!

Next, Arlyn connected three bulbs in series with each other and an ammeter, then turned the crank hard and fast as he could to light the bulbs. We read 0.3 amperes. He repeated this with the same three bulbs in parallel, and we read 0.9 amperes. More current! (Think about it!)

Finally, he connected his Genetron to a small capacitor and cranked, charging the capacitor. He noted that as the capacitor became charged, it took less effort to turn the crank. When he released the crank, somewhat to our amazement, the crank continued to turn by itself! -- and even more interesting -- in the same direction as Arlyn had been cranking it! "How come??" Arlyn wanted to know. How do we explain this? John Bozovsky and Camille Gales connected their two Genetrons together, and when John cranked his, the handle on Camille's rotated! Ahah! The Genetron being cranked by John was converting mechanical energy to electrical. The electrical energy was fed to Camille's Genetron which acted as a motor so that its handle then turned. Neat! When John reversed the direction of his cranking, the motion of the handle on Camille's Genetron reversed itself. When we thought about it, we saw this should be an expected symmetry in behavior between the two Genetrons, and it was pleasing to see. Wonderful physics, Arlyn! Thanks!

Carl Martikean (Wallace HS, Gary, IN)
placed a capped jar with a greenish liquid in it on the table, then wrote on the board: Pediculus humanus capitus. "Does anyone know that this is?" he asked, referring to the writing. One person raised her hand. "What's the answer?" asked Carl. To which she replied, "Head lice!" And Carl said, "Right! Head lice!" Carl said that the liquid in the jar was sewer water, and twisted off the cap. Then he opened a plastic bag that he said contained new insects that live in sewers, and dumped some into the jar of sewer water. "Just look!" Carl said, pointing to the jar. "They come to life almost immediately!" -- as the particles moved up and down in the jar. "Would anybody like to drink some of this?" asked Carl. With no volunteers, Carl said,"OK - I'll drink some myself!" - and much to our disgust and astonishment - he did! "More?" asked Carl. And then he drank down half the jar. Of course, by now most of us guessed it was a fake. Carl explained that the "sewer water" was really a mix of ginger ale (for carbonation) and Frosh (a soft drink for green color). The "insects" from the plastic bag were really dried currants. "Kids will believe almost anything you tell them," Carl said. He explained that he wants his students to question him (and what they see on TV and elsewhere) about everything, and this is one way he tries to make skeptics of them.