Fred Schaal [Lane Tech HS Math]
He investigated determinants and the magic squares. Using the TI graphing calculator's internal ability to solve determinants he put in a 5x5 array and showed some to the abilities of the TI graphing calculator. Fred tried the numbers forming a "golden square" as well as a Fibonacci sequence, and in neither case did the determinant vanish.
Porter commented that the result was not what Fred expected because the elements did not have the proper relationship where an element or the ray wasn't a factor of the other numbers. Determinants can be thought of in geometric terms, where the points can be identified as vectors, and the vectors are added. there can be a solution when they reside in the same plane. You can write two equations in two unknowns in the form
A1 · X = b1
A2 · X = b2
The object is to determine the two dimensional vector X when its scalar products with the vectors A1 and A2 are given. There is no solution when A1 and A2 are parallel to one another, or when the determinant of coefficients vanishes. So it goes...
Walter O McDonald [CPS Substitute]
He brought in an manipulative he purchased at Robot World in the Wisconsin Dells.
It was a little difficult to see why the figure was called "Moons of
Jupiter" because it was a pendulum driven by a battery mechanism. In
base there is a driver coil activated by a transistor keyed by another
sensing coil. When a magnet passes the pickup coil, thus triggering a
power pulse (in the coil this causes a magnetic pulse) pushing away the
magnet in the pendulum.
The main pendulum is on the stand and there are attached to the pendulum two other sets of balls that rotate on their own pivot pulse. As the pendulum swings the smaller set of balls on each side of the pendulum would spin in a chaotic-appearing form.
Discussions of rotational and frequency formulas were noted. The period seemed to be about 1.4 seconds and trial of stopping the secondary ball seemed to indicate the additional movement caused the main pendulum to have less amplitude as the secondary balls were active.
Porter commented that Chaos can occur only when there are at least three degrees of freedom. For our case, we have the motion of the main pendulum, the oscillation of the weights on the right side, and the motion of the other set on the left side. The balls on the left were affected by a magnet reacting with the set on the right.
We did not see why it was sold with the Jupiter name, but Jupiter is often used by NASA as a way of "sling-shoting" satellites on into outer space.
Carol Zimmerman [Lane Tech HS Physics]
She brought in 2 newspaper articles.
Porter Johnson commented about Whistlers that appeared on the radio frequencies, and these were alleged to come from static discharges [lightning] occurring in the southern hemisphere and heard in the northern as a change is frequency due the distortions. Being helical polarization each polarization travels differently, thus the whistler-change in time causing change in frequency.
Ann Brandon [Joliet West HS Physics]
Reading Analog meters.
She started with going 55 in Canada, where the speed limit is in Kph and we think of Mph --more than numbers . She had two set-ups one for a voltage and the other using ammeters. Having both digital and analog meters making measurements.