High School Math-Physics SMILE Meeting
09 September 2003
Notes Prepared by Porter Johnson

Roy Coleman used our new electronic projector and his ancient laptop computer to show us samples of the content of a CD containing all information on the SMILE and SMART websites.  It also contains the following items:

All for just $10! And on a CD nicely packaged in a beautifully labeled jewel case.

Don Kanner [Lane Tech HS, physics]        Hygroscope
showed us the String Thing executive toy manufactured by Can You Imagine http://www.cyi.net/.  The following entry is excerpted from that site:

"The Amazing String Thing creates magical string effect nearly 3 feet in the air! Point it up, down, even sideways and watch as the string playfully dances in mid-air, gently touching the string generates wave patterns and interactive shapes that seem to defy gravity. The String Thing can be used with its own display cradle or you can hold the lightweight unit in your hand! Blacklight Responsive string looks great under any light. Battery Operated."
Don also presented Earl Zwicker with the device, which very nicely displays the "dimple effect" discussed in the Mathematics-Physics SMILE meeting of 05 February 2002. mp020502.html. Very visual, Don!

Don touted the venerable book A History of Physics by Florian Cajori [1899].  The book is readable, and contains a number of interesting quotes, insights, and examples that refer to original sources.  For example, Count Rumford [American Loyalist who died as a Bavarian nobleman] is quoted as saying that he expected to live long enough to see Caloric entombed along with Phlogiston--but he did not live that long.  In addition, he learned about the Hygroscope, a device used by Nicclaes de Cusa [1401-1446] to measure the moisture content of air.  The idea is to balance a scale with rocks on one side, and dry wool on the other side.  As time goes on, the wool will absorb water from the atmosphere, and become heavier than the rocks.  Don used a digital scale with a micro-camera attached to a small television set to show the scale reading.  He began by putting 11.78 grams of dry wool on the scale.  Here is a record of the readings (taken by Porter Johnson) every five minutes

Time Mass
in mass  
Elapsed time  
mass change
4:45   11.78 0.00 0 0.00
4:50 12.11 0.33 5 0.19
4:55 12.24 0.46 10 0.35
5:00 12.34 0.56 15 0.47
5:05 12.41 0.63 20 0.57
5:10 12.46 0.68 25 0.66
5:15 12.51 0.73 30 0.73
5:20 12.57 0.79 35 0.78
5:15 12.60 0.82 40 0.81
5:30 12.63 0.85 45 0.85
5:35 12.66 0.88 50 0.88
5:40 12.68 0.90 55 0.90
5:45 12.70 0.92 60 0.92
5:50 12.72 0.94 65 0.93
5:55 12.73 0.95 70 0.94
6:00 12.74 0.96 75 0.95
6:05 12.75 0.97 80 0.96

The dry wool was prepared by heating ordinary wool in an oven at 95 - 100 °C for 30 minutes, and then enclosing it in a sealed container.  After it is placed on the scale in the open air, the mass of the wool continually increases with time.  That rate of increase decreases with time, and it appears to level off after a little over an hour.

Note by Porter Johnson:  Let us make the simplifying assumption that the increase of mass of  the wool gradually levels off according to the formula

Dm (t) = Dm (¥) [ 1 - e -t / T ]
where T is a characteristic time for the wool to come into equilibrium.  From the facts that Dm = 0.73 g at t = 30 minutes and Dm = 0.92 g at t = 60 minutes, we obtain T = 22.3 minutes and D m (¥) = 0.99 grams. The data calculated using this formula appear in the last column above.  The simple exponential is not an adequate representation of the data, so that the effect cannot be explained by this single absorption time.

Don, you certainly pulled the wool over our eyes! Good work, and keep reading those ancient tomes!

Fred Schaal  [Lane Tech HS, mathematics]        Tank Cars and Mars
noticed while traveling on Amtrak through Kansas last summer that there were pipes connecting a large number of tanker cars together.  Does anybody know what was being transported, and why the tanks were connected? Fred also expressed disappointment at being unable to see the planet Mars during its closest approach to earth in several thousand years.  Has anybody else seen its polar ice capsYou may have left Kansas and gone into the Land of Oz, Fred!  Interesting questions!

John Bozovsky [Chicago Discovery Academy at Bowen HS, physics]        Now You See It; Now You Don't
began by recounting the sad tale of the mathematics teacher who was detained while attempting to board an airplane at Heathrow Airport, London, UK.  He had a graphing calculator, compass, and protractor among his effects. He was suspected of belonging to the Al-gebra group, and was accused of attempting to board a plane with instruments of math instruction. Verrry interesting, John!

John held up a large and colorful poster with a high-quality image of patterns.  By staring at the poster and allowing your eyes to focus at a distant object, most people may be able to see three-dimensional images.  John had many different posters, which he held up for us to see. He offered to sell them to us at $2.00 each.  He had obtained them at a warehouse. Some of us could see dragons and dinosaurs chasing and being chased across the landscape, whereas others were unable to see the three dimensional images.

For more information see the website Seeing Objects among the Dots http://explorepdx.com/visphenom.html. and Stereopsis:  http://home.pacifier.com/~ppenn/page17.html.  We'll think about this one.  Thanks, John!

Larry Alofs [Kenwood Academy, physics]        Crude Explanation of the Effect
explained that stereographic images come from nearby repeated patterns present in ordinary images, that lead us to visualize a three-dimensional super-image. Consider the following image:



| |


| \

(left) (right)
eye eye
You will interpret the objects A and B in perspective, with A closer than B. Thus, three dimensional images appear, when one focuses on both A's, making them appear as a single image further away. Correspondingly, the image of A appears closer to us. For additional information see the Citeseer website http://citeseer.ist.psu.edu/context/660573/0, from which the following has been excerpted:
"...a stereoscope. It might seem that stereopsis necessarily requires two separate pictures, or at least some method of splitting a single picture into two to give each eye a separate view (using, for instance, red green filters, polarized light, or interference, as in holograms) Recently, however, Tyler and Clarke (1990) realized that a pair of random dot stereograms can be combined together, the result being called a single image random dot stereogram (SIRDS) or, more generally, an autostereogram. Essentially, one overlays the two separate random dot patterns carefully placing the dots so that each one serves ....
....out that very convincing images with vivid depth can be constructed in this way, and the advantage of this ingenious approach is that no special viewing equipment is required. It does take a little practice to see depth in the pictures, but the experience is very satisfying when first achieved. Tyler and Clarke (1990) described a simple but asymmetric algorithm, which meant, for example, that some people can only see the intended effect when the picture is held upside down. This paper presents a new, simple, and symmetric algorithm for generating single image stereograms from any solid model. It also avoids ...."

We think we get the picture now!  Thanks, John and Larry!

Bill Colson [Morgan Park HS, mathematics]        Flashy Doo-Dah's
showed us Tetra-tops, a set of flashing and colorful polyhedron tops, with trading cards. Bill bought them at Walgreens for about $5.00.Tetra-tops http://tetratops.com/menu.html are manufactured by Duncan Toys Company https://www.yo-yo.com/, the famous YO-YO manufacturer.  This excerpt is taken from the website above:

"Tops have fascinated humans since they were first discovered. No one knows when or where they were first spun, but they have been found in nearly every culture on Earth. The variety of designs is endless, however there is one remarkable similarity to all of them. Traditional tops all have only ONE axis of spin! Unlike traditional tops, Duncan's new TETRA-TOPS™ all have multiple axes of spin!"
These spinning tops include the five Platonic solids [ http://www.math.utah.edu/~alfeld/math/polyhedra/polyhedra.html], the tetrahedron, cube, octahedron, dodecahedron, and icosahedron.  Nifty, Bill!

Ann Brandon [Joliet West HS, physics]      Space Inversion Mask
Ann obtained a white face mask from Oriental Trading Company: http://www.orientaltrading.com/: [PLASTIC WHITE FULL MASKS, Item Number: IN-25/1185]  We viewed the back (inside) of the mask as it was being illuminated from below by the lamp from an overhead projector.  Curiously enough, it appeared to us that we were seeing the front of the mask.  How come?  Ann explained that we use shadows to establish our orientation of an object, and that we are accustomed to seeing objects as illuminated from above.  In this case, the shadows appear the same as when the front of the mask is illuminated from above.  Thus, we think that we are seeing the front of the mask.  Simple but profound!  Very good, Ann!

Fred Farnell [Lane Tech HS, physics]        Balancing an Egg on End
began by describing this activity as an illustration of the application of the Scientific Method.  He showed a dozen fresh eggs, which he had asked his class to vote on the following hypothesis concerning balancing an egg on end:

Number of Votes
Not possible 45
Only on vernal equinox 34
Only on autumnal equinox  7
Broad end only 35
Pointy end only 1
On either end 10
Only at equator 1
Four eggs were successfully  balanced on their broad ends, by  Marilyn Stone and Betty Roombos [twins!].  Others tried to balance the eggs, without success.  The moral is that it requires patience, steady nerves, and effort to balance an egg. It is also possible to balance an egg on its pointy end. This question is discussed in the book Bad Astronomy: Misconceptions and Misuses Revealed, from Astrology to the moon-landing hoax by Phillip Plait [Wiley 2002, ISBN 0-4714-09766].  Note that some of the choices are not reasonable, such as the fact that balancing can be done on the vernal equinox, but not on the autumnal equinox.  Still, there are many people who believe in such pseudo-scientific folklore.  For details see the Egg Balancing Website: http://www.badastronomy.com/bad/misc/egg_spin.html.

Thanks for sharing this with us, Fred!

Notes taken by Porter Johnson