10 October 2000

Notes prepared by Earl Zwicker

**Don Kanner (Lane Tech HS)**
showed us a "Test Tube Black Box."
He held up a cardboard tube about ** 45 cm** long and ** 7 cm **in diameter.
About ** 2 cm** from the left end, a string passed through the tube
through a pair of diametrically opposed holes. (On each end of the
string were small metal rings to prevent the string from coming
free of the tube.) Another string passed through the tube at its
right end, in an identical manner, except it was longer. Looking at
us with a grin, ** Don** pulled down on the left string, and the string
on the right end shortened. When he pulled down on the right end
string, the left end string shortened. But then he pulled ** UP** on the
right end string - and it moved straight up until it was stopped by
its bottom ring. And the left end string did not become shorter or
move at all! How was this possible!? After showing us again with
some variations, **Don** challenged us to come up with an explanation
or make our own version. He explained that a chemistry colleague at
**Lane Tech ** uses this to catch the attention of his
students and to make them put their minds to work. **So ...** how about
us!? Any ideas? Maybe **Don** will show us more next time.

**
Ed Robinson (De LaCruz School)**

gave each of us a sheet of blank
paper, then challenged us to find a pattern in playing a game that
he called "Nim Mod." The first step was to sketch a rectangle and
divide it into 4 boxes; ** (N = 4)**. The game is played similarly to **
tic-tac-toe**, with one player making Xs and the other making Os. The
loser of the game is always the player who is forced to fill in the
last empty box, because none other is left. But each player, on his
turn, may fill in ** 1, 2, or 3 ** boxes with his ** X (or O**). With ** N =
4**,
it is clear that the ** Starter player (S) ** can fill in three boxes, leaving
only one box empty, and forcing the second player to fill in the
last box to become the loser of that particular game:

N = 7, S wins

...

N= 9, S ??

**
Marilynn Stone (Lane Tech HS)**

gave each of us a resealable
sandwich bag containing these items:

She then challenged us to assemble the pieces together to form a rectangle. (2 green rectangles

3 blue squares

4 red triangles.

Good reinforcement.

**
Fred Schaal (Lane Tech HS)**

showed us "T**he Occurrence of Concurrence**". He explained that if 3
straight lines in a plane intersect in a single, common point, it is called "**concurrence.**"
With the aid of a meter stick, he constructed a large, nice looking
triangle on the white board. With a large compass having a marker
pen attached at its "chalk" end, ** Fred** used the compass to construct
the line which **bisected** one of the angles of the triangle. He did
this in a contrasting color. Then he constructed the **bisectors** of
the other two angles the triangle. If the board had not been so
slippery and the compass marker had made legible marks, the
**bisectors** of the three angles would have intersected at a single
point within the triangle: **concurrence**! Unfortunately, the
construction was not precise, and it didn't work out. But you made
your mark, **Fred**! Thanks for an interesting lesson.

**Roy Coleman (Morgan Park HS)
**asked if anyone could tell him how
their school deals with the scheduling of exams if every class is
to be a 2 hour class. No explanations were forthcoming.

**Betty Roombos (Lane Tech HS)**

explained how she shows her
students to do vector problems. We are given two displacement vectors:

5 km at 20

**Fred Farnell (Lane Tech HS)**

explained why the fit of a straight line equation to experimental
constant velocity points (and its subsequent ** v vs t** graph) at the
last meeting was so poor.
It turned out that the constant (non zero) velocity occurred over an **
8 second** period, but the data taking ran for **15 seconds**, and the velocity
was zero for the last ** 7 seconds**! When ** Fred ** ran new data and ** kept only the
portion for non-zero velocity**, the fit turned out great! He did
this "live". Same story for motion of constant acceleration. Thanks for
restoring our faith, **Fred**!

SEE YOU THERE!!