High School Mathematics-Physics SMILE Meeting
11 September 2001
Notes Prepared by Porter Johnson

Don Kanner (Lane Tech HS) Summer Vacation in New Brunswick, Nova Scotia, and Prince Edward Island
He showed a video that he made on the North Cape of Prince Edward Island.  First he showed a Windmill Farm, and then we saw the wave interference pattern set up [in late June] by waves coming in from the Atlantic Ocean that interfered with waves from the Gulf of St Lawrence.  Don is working on an edited version of his tapes, which will be useful in the classroom.  If anybody can make multiple copies, Don will share this.

Don described his theory of wave formation by wind blowing toward the shore, and raised the question of why don't you see big waves going out from the shore into the sea?  He also described seeing a Bore Tide at the Bay of Fundy, between Nova Scotia and New Brunswick, home of the world's largest tides.  It was pointed out that the second largest tides occur near Anchorage Alaska.  Also, see the website http://www.iit.edu/~johnsonp/smart00/lesson4.htm.

Bill Colson (Morgan Park HS, Mathematics)
passed out copies of a page from Popular Science Flash Forward Summer 2001, entitled Famous Last Words.  It contained such entries as the following:

He also passed around a copy of the book Flatterland:  Like Flatland, only More So by Ian Stewart [Perseus Publishing 2001 ISBN 0 - 7382 - 04420].  This book stands as a sequel to the classic book Flatland by Edwin Abbott [Dover 1982 ISBN: 048627263X ].  Like its predecessor, it delves into travel from one dimension to another, including the "fractal forest", or the "Mandel Blot".  Porter Johnson pointed out that theories involving gravity in ten dimensional spacetime are currently under serious investigation.

Monica Seelman (Williams and St James Schools)
Discussed an example of a Venn Diagram.  In Particular, she considered the following sets:

She pointed out that all two-digit numbers in set C are also in set B, but that the three-digit numbers in C are not in B, because they are not divisible by 11.  But the four digit numbers with identical digits are divisible by 11 [5555 = 101 ´ 55]. As an extension, all numbers with an even number of identical digits are divisible by 11, whereas those with an odd number of digits are not.  Interesting  results in "eleven-ology"!

Ann Brandon (Joliet West HS, Physics)
took a transparent plastic tennis ball tube, and attached washers from its inside bottom end with rubber bands.  The rubber bands were then stretched so that the washers lay outside the open top end.  She stood on the lab table and dropped the system. Surprise!  As it fell, we saw that the stretched rubber bands pulled the washers back inside and went limp.  She dropped it several times, so that we could be certain of what we were seeing.

Bill Blunk (Joliet Central HS, Physics)
made another pilgrimage this past summer to his favorite*** toy store, namely

Amazing Toys
319 Central Ave
Great Falls MT 59401
[406] 727-5557 [Bob Pechlin]

There he discovered a new plaything, called a Sonic Lightning Ball, which he showed to us.  When you drop the plastic ball [with electronic components clearly visible inside], it makes different sounds and colorful light flashes when it bounces up from the floor.  The sounds and lights change with the orientation of the ball, as well as the drop height. Thus, the magnitude and direction of the impact force are relevant for the effects that follow the rebound.  The device was passed around the room, and some of us got sounds by squeezing on the ball.
***In the interest of full disclosure, Bill indicated that he had no commercial interest in the store.

Roy Coleman (Morgan Park HS, Physics)
indicated that  an up-to-date SMILE CD ROM is available from him for $10, plus any shipping costs.  You may send him an email at coleman@iit.edu.

Earnest Garrison (Robeson HS, Physics)
handed out a write-up of a Paper Clip Lab, in which fatigue and fracture of solids was studied using paper clips.  The idea is to determine the distribution in the number of times one must bend a paper clip back and forth in a controlled fashion to get it to break at the "little loop", the "big loop", and on the "straight section".  

Earnest also showed us an exercise in estimating the area of an irregularly shaped lake on a map, by overlaying a square lattice of dimension 1 cm.  The idea is to estimate the area as follows:

The area of the lake is estimated to be J + K + L/2.  This estimate is fairly accurate, in practice! And, students ware surprised at how closely their results agree with one another.

Fred Schaal (Lane Tech HS, Mathematics)
suggested that "conditional logic" should be considered as an alternative to "deductive logic", and "inductive logic".  In conditional logic we have the statements A ® B and B ® C, from which we conclude that A ® C. As an example, he considered the syllogism

All animals named Flicka are horses.
All horses have four legs:
\ All animals named Flicka have four legs.

Note that A ® B and C ® B does not permit the conclusion A ® C, so that the following syllogism is incorrect.

All horses have four legs.
All animals named Flicka have four legs:
\ All horses are named Flicka.

See you Tuesday, 25 September!

Notes taken by Porter Johnson