High School Mathematics Physics SMILE Meeting
24 September 2002
Notes Prepared by Porter Johnson

Bill Colson (Morgan Park HS Mathematics) When Written Instructions Are Not Enough
challenged us by handing out copies of the following:

The Balloon Story
If the balloon popped, the sound wouldn't be able to carry since everything would be too far away from the correct floor.  A closed window would also prevent the sound from carrying, since most buildings tend to be well insulated.  Because the whole operation depends upon a steady flow of electricity, a break in the middle of the wire would also cause problems.  Of course, the fellow could shout, but the human voice is not loud enough to carry that far.  An additional problem is that a string could break on the instrument.  Then there could be no accompaniment to the message.  It is clear that the best situation would involve less distance.  Then there would be fewer potential problems.  With face-to-face contact, the least number of things could go wrong.
Your mission, if you should decide to accept it, is to draw a picture to describe what MIGHT BE under discussion.  Here is one possibility, which Bill had drawn:
. . . CAN YOU DO BETTER?? . . .

read a dispatch from the October 2002 issue of Teacher Magazine [http://www.teachermagazine.org/] describing legislation under consideration in France, under which students who insult their teacher might be sent to prison for up to six months and/or pay heavy fines, in order to re-establish respect for authority figures. Supporters, including President Jacques Chirac, claim that punishing young people for such petty offenses as incivility with deter them from committing more serious crimes. How do you say spare the rod and spoil the child in French?  Very interesting, Bill!  Porter Johnson remarked that there are some significant differences in the rights guaranteed to citizens by the US Constitution, and Code Napoleon [http://www.pbs.org/empires/napoleon/n_clas/lawsliveon.html], the French / Continental European counterpart.  For a discussion of the impact of French Law in the US, see Louisiana and the Code Napoleon, http://www.la-legal.com/history_louisiana_law.htm.

Roy Coleman (Morgan Park HS, Physics) 1000 Thinks / Fermi Problems
asked us the following question: 

Q:  A gambler found dead at the race track had a $2 ticket that paid $20 in his pocket.  When/how did he die?  A:  Ten-to-one; a long shot!
Roy then showed us the following book
Title: 1000 PLAYTHINKS  Games of Science, Art, & Mathematics by Ivan Moscovich; Workman Publishing [http://www.amazon.com/Big-Book-Brain-Games-Mathematics/dp/0761134662] 2002;  ISBN: 0-7611-1826-8 
Description: Games can help you change the way your students think. They can make your students more inventive, more creative, and can inspire them to tackle the unknowable - all in the name of fun. And fun (slyly mixed with educational challenges) abounds in the 1,000 full-color puzzles found in 1000 Play Thinks. Obsessive and head-scratching, this is a must-have collection of mental games, riddles, visual challenges, and puzzles, ranked in difficulty from 1 to 10. Complete with answer key. Grade Level: 3-12+ Information source: Zephyr Press [ through Amazon.com]. A list of errata for that manuscript is maintained by Nick Baxter on the website 1000 Playthinks Errata [ http://www.baxterweb.com/puzzles/playthinks.htm].

Roy next brought up Fermi Questions.  For example, how might we obtain estimates for the following questions to within a factor of 10:

  1. Q:  How many blades of grass are there in the city of Chicago?
  2. Q.  How many times does a tire rotate in going from Chicago to Miami?
  3. Q:  How many marbles does it take to fill a bathtub?  [Be sure to plug the drain hole first!]
  4. Q:  What is the mass of the most popular car in the US, in grams?  A:  10 grams --- Matchbox cars
For a more complete compilation of such questions, see his SMILE lesson, 10HUH? at website ph8804.html.

Fred Farnell (Lane Tech, Physics) More Instructions

What Are These Instructions For?
After you figure out what the instructions below are for, rewrite the instructions using language that would be appropriate for the task described.  Any errors in the text below are intentional. The rewrite should contain 0.000 errors.
The Description of the Task
Take 4 pieces of French bread sliced to 0.200 m.  Coat each piece of bread with about 1.0 g of O LEE O.  Place too toe may toes with a d of 0.0400 m on top of each piece of bread.  Sprinkle about 0.25 g of garlic powder on the bread.  Place the bread in a pan.  Allow a 12 A heating device to reach 477 K.  Place the bread inside the heating device so that is is 0.1500 m from the heating element.  Place some thick materials with a low thermal conductivity on your hands.  Remove the bread from the heating device after 180 s.  Allow heat to flow away from the bread before serving.
Fred suggested this might be a recipe for making Bruschetta.  Here is a somewhat more practical Bruschetta recipe. 
4 slices of nice bread, 1 red onion, 2 cloves of garlic, Olive oil, 1/2 teaspoon balsamic vinegar, 5 vine tomatoes, 2 or more tablespoons of vegan pesto, Salt & Black Pepper, Fresh Basil or Coriander - chopped
  1. Put the bread in the oven for about 5 minutes (180ºC/375ºF-ish)
  2. Slice the onion and one clove of garlic, and fry in olive oil until slightly browned. (Or you could roast them in the oven).
  3.  Peel the tomatoes (with a potato peeler or put them in a jug of boiling water for a minute until you can peel the skins off easily), discard the seeds and chop finely. Put the chopped tomato in a bowl, and season with salt and pepper, balsamic vinegar and a drizzle of olive oil (optional)
  4. Cut the other clove of garlic in half, and rub the cut sides onto all the slices of crispy bread. Spread each piece of bread with vegan pesto, then spoon the onion on top, and top with the chopped tomato. Garnish with chopped herbs.
This recipe was obtained from Cherry's Vegan Recipes on the Parsley Soup website:  http://www.parsleysoup.co.uk/MainPages/soups.htm; note that a "vegan" refers to "vegetarian without eggs or dairy products".  Unfortunately, the rumor that it is what people eat a on planet orbiting the star Vega is unfounded.  Fred, you made us hungry!

Fred also described his visit to the IMAX Theater at Navy Pier [http://www.imax.com/theatres/t/navy-pier-imax/].  The layout is different from that at the more familiar OMNIMAX theaters.  In IMAX Theaters, you wear a headset connected to 3-d glasses, and get a three dimensional coordinated visual and sonic image with reduced probability of getting headaches, as with the old stereoptic systems. And, just what is stereoptic vision?

stereoptic vision The perception of depth and three dimensions accompanying binocular vision resulting from differences in parallax producing different images on the retina of each eye. [see: http://www.vision3d.com/stereo.html]
We see what you mean, Fred!

Betty Roombos passed around her Viewmaster [http://www.houseof3d.com/pete/applets/wireframe/stereo/viewmaster.html] loaded with 3-d photographs she had taken at a site of geothermal activity in Yellowstone National Park.  She said that such stereographic slides are easy to make; you just take a slide while leaning to the right, and then take one leaning to the left!  Many stereoptic cards and stereographic images are well over a century old!. Interesting, Betty --- and be careful when leaning over those geothermal ponds.

Larry Alofs (Kenwood Academy, Physics) Catsup / Ketchup Saver
recently acquired a Ketchup Saver at K-Mart, at a cost of around $2 The device was a cap, which contained three different sets of threads on either side, so that a nearly empty bottle could be held in place above a nearly full bottle, enabling the contents of the top bottle to flow into the bottom one without wasting very much valuable Ketchup.  The Ketchup Saver [Zebra code number 32368- 06036] is distributed by Johari/US Inc, 1205 Venture Court, Carrollton TX 25006.  He found that the device could be used to attached two two liter plastic pop bottles together, for making a Vortex Tornado Tube.  The device is similar to one  distributed by Edmund Scientific [Mailing addressScientifics; 60 Pearce Avenue; Tonawanda NY 14150-6711, Tel: 1 - 800 - 728-6711; website: http://www.scientificsonline.com].
Larry filled the bottom bottle with water, tightened the  cap onto the bottom bottle and the inverted  top bottle, and turned everything upside down. The water dribbled slowly from the top bottle into the bottom bottle. He repeated the process, moving the inverted system in a horizontal circle a few times, to produce slight a slight rotation of the water in the top bottle.  This time, the water flowed more rapidly to the bottom bottle, producing a whirlpool or vortex down the column of water along the vertical central axis of the system.  Larry then asked why the water went around more rapidly as the second bottle becomes empty.  The answer is "Conservation of angular Momentum", which he wrote in this form:

L =m v R = m V r.
That is, the velocity becomes larger as the orbit radius increases. Larry remarked that a formula such as L = I w should not be used, since the fluid is not a rigid body.

Larry illustrated angular momentum conservation by attaching a light object [mass about 20 grams] to one end of a string of length about 1 meter, and inserting the other end of the string through a hollow tube of about diameter 1 cm and length about 20 cm.  He held the tube vertically just above his head with one hand, and held onto the string with the other.  Then he swung the mass around [slingshot style] in a horizontal plane above his head, while holding onto the string.  The mass moved in a circle with moderate speed.  When he pulled the string down through the tube with his other hand, decreasing the radius of the circle-of-rotation, the mass obviously speeded up.  Larry mentioned a demo done by Earl Zwicker several years ago, in which he sloshed sand around in a funnel while it was draining into a container below.  As the sand emptied from the funnel, it began to slosh around more violently.  Larry commented that this demonstration has practically nothing to do with the Coriolis Force, and neither does the "draining bathtub", which is essentially similar to these.  Very clever and thoughtful, Larry!

Ann Brandon (Joliet West HS, Physics) Walking the Dog, continued; Graphs and More Graphs
brought in a different Walking the Dog Physics Toy, which she obtained last spring for all-important St Patrick's Day festivities.  She obtained the [green] toy from Oriental Trading Center; [Address: PO Box 2308; Omaha NE 68103-2308; Tel: 1 - 800 - 228-2269; website: http://www.orientaltrading.com].  When just the right amount of weight was attached to the dog [see the minutes of the last SMILE meeting], the Ersatz Animal walked slowly to the edge of the table and then stopped, although it was rumored that the back legs had been dragging.  Very good, Ann, is there an obedience school for plastic dogs?

Next Ann showed a graph based upon one of the favorite stories of her childhood, Ben and Me: Astonishing Life of Benjamin Franklin As written by His Good Mouse Amos by Robert Lawson [Little, Brown & Company; 1988; ISBN: 0-3165-1730-5] recommended for ages 8 to 12.  Publisher's description:  "The true story of Ben Franklin, as told by his closest friend and advisor, Amos the mouse. According to Amos, it was really he who was  responsible for Ben Franklin's inventions and discoveries." Others seem to like this book; for example, see Ben and Us: Sparking the Standards: http://teachersnetwork.org/impactII/profiles00_01/block.htm. and Ben and Me: http://www.amazon.com/Ben-Me-Astonishing-Benjamin-Franklin/dp/0316517305Ann related this to graphing by showing a rather unusual-looking distance versus time graph, and explaining that it described Amos's first departure from his home, in which, over a 20 second period, he went from just in front of his mouse-hole toward the middle of the room, then came some closer to home,  saw the cat, rushed back into the hole, and peeked out to see if the cat was still there.  The graph represents  a visual summary of these events, and serves to re-enforce the connection between the graph and Amos's travels. 

Ann then showed a set of 4 graphs of d versus t , along with 4 graphs of velocity versus time, as well as 4 graphs of acceleration versus time, as in the SMILE meeting of 25 September 2001:  mp092501.htm. We then began to try to match the graphs with one another.  She made the following chart to formalize the matching process:

Quantity to Determine
d - t Read Graph Slope:
D d / D t
"smile": a > 0
"frown": a < 0  
"line": a = 0
v - t Area Read Graph   Slope:
D v / D t
a - t (calculus--ugh)   Area Read Graph
The entry in the upper right corner means that, if the d-t curve is a "smile" [convex upward] the acceleration is positive; when it is a "frown" [concave downward] the acceleration is negative, and when the d-t graph is a straight line [up, down, or sideways] the acceleration is zero.  A wealth of good  ideas, Ann, and keep smiling!

Bill Blunk (Joliet Central HS, Physics) Slow Motion Climbatron
showed us a genuinely new Physics Toy, which he acquired during  his most recent annual pilgrimage to the Amazing Toys establishment in Great Falls MT. [ http://www.amazingtoys.net/ for information on the establishment and discussion of one of his previous visits see the SMILE write-up mp091101.htm]. This robotic toy, equipped with four suction-cup feet and driven by two AAA batteries, could climb windows, blackboards, and walls.  It even "walked" on a flat table held upside down.  A primitive internal cam converted driven longitudinal oscillation into transverse oscillations.  Thus,  the suction feet moved transversely, with those on the right side in opposite phase to those on the left side, one small step at a time. This toy is distributed by Action Products International, Inc; Orlando FL, and listed as Item # 56214 on the package.
Bill remarked that physics teachers should seek, find and play with new toys in order to maintain their enthusiasm for teaching, as well as to keep up with the technology, etc.  After all, education is a journey of discovery, and we cannot transmit enthusiasm for discovery to our students, unless and until we genuinely feel and display such enthusiasm ourselves.  Good point, Bill, and thanks!

Hoi Hyunh ( HS, Physics) Math Notation and Visual Geometry
began by suggesting the mnemonic that D is really a D, which stands for Difference.  [Do you remember "trouble that begins with T, which rhymes with P, and stands for Pool".] Hoi then showed us an ordinary-looking, box-like configuration that she had constructed as follows:

Amazingly enough, the device was quite flexible, and it could be twisted around to make a wide variety of shapes and figures. Very nice work, Hoi!

Don Kanner (Lane Tech HS, Physics) Grading On the Curve
showed various "grading curves" [or, better yet, grading algorithms], which were presented as graphs of Grade  [A, B, C, D, E. on vertical axis] versus Percentage of Correctness [i.e., 0, 20, 40, 60, 80, 100 on horizontal axis]. He asked us to make a verbal description of the meaning of graphs such as  "vertical line at 50" and "horizontal line at C", etc.  We enjoyed your lesson, Don, but just what grading curve should we use for grading your lesson?

Notes taken by Porter Johnson