High School Mathematics-Physics SMILE Meeting
1997-2006 Academic Years

26 October 1999: Roy Coleman (Morgan Park HS)
showed us his GPS Locator ($199) by Garmin: http://www.garmin.com/. On its screen it has a resolution of 0.1 mile, it computes magnitude and direction of the speed of the vehicle in which it is mounted, and has a resolution of 5 ft. It gave us our location as 40o 50.317m latitude, and 87o 37.858m longitude. Works outside only, and shows the path home. Remarkable!

12 September 2000 Porter Johnson (IIT)
told us about a vacation trip which took him through Pestigo, WI. At the same time as the Great Chicago Fire of 1871 [http://en.wikipedia.org/wiki/Great_Chicago_Fire], there was an even greater fire around Pestigo [http://www.peshtigofire.info/], which was a much greater disaster than the Chicago fire in terms of lives lost and destruction of property and farm animals. There was a sign in Pestigo which marked a feature in common with Traverse City, MI and Egg Harbor, WI. What is it? The 45th parallel! The sign said that the person reading it was half-way to the North Pole from the equator. But - according to a second sign a little North of Pestigo - if one accounts for the fact that the earth is not a perfect sphere, but has the shape of an oblate spheroid (flat at the poles and bulging at the equator), then one must travel a little farther North of the 45th parallel to really be half-way to the North Pole in terms of travel on earth's surface. Porter proved that this was wrong (and showed us at the board that the halfway point is South of the 45th parallel!), but was too polite to let them know they are in error. Fascinating!

07 November 2000 Bill Colson (Morgan Park HS)
passed out several small world globes (about 1.3 in diameter) and then placed an inflatable globe about 16 inches in diameter on the table. It was transparent, but showed the various countries and the lines of longitude and latitude as well. He explained that when he introduces the topic of spherical geometry to his students, he likes to let them convince themselves that plane geometry is not always sufficient to deal with the problems one may face in real life.

Sailors, ships, planes which follow the curved surface of earth will have trouble if they assume they are traveling on a flat plane instead of a spherical earth. Euclid set forth postulates for the flat plane, which must differ from those for the geometry of a spherical surface. A point is the same in either geometry. But what about a straight line? What does that mean on the surface of a sphere? And what about parallel lines never meeting in a plane? Is there such a thing as parallel lines on a spherical surface? What are great circles? Bill wrapped a string around the globe to show a great circle. We saw that the equator is a great circle, but the smaller circles marking a constant latitude are not. He held up a map of the world which was a Mercator projection, showing earth on a flat surface. [See the website http://mathworld.wolfram.com/MercatorProjection.html.]  The longitude and latitude lines look parallel on a that flat map, but not on the globe. The distortion in size of various continents could be seen when comparing with how they appeared on the globe.

07 November 2000 Porter Johnson stretched a string on the Mercator map to show the distance between Frankfort, Germany and Fairbanks, Alaska. And then between Frankfort and Chicago - which appeared to be a much shorter distance. But when the same comparison with the string was done on the global map, the distances were very nearly the same!

Bill passed out a copy of an article by Cecil Adams in the Chicago Reader about the QIBLA, which is the Arabic name given to the direction toward Great Mosque in Mecca.  Muslims should pray while facing in that direction, the QIBLA, and it is often marked by an arrow in locations for prayers.  This need to determine the "prayer direction" catalyzed interest in astronomy, navigation, and geography, and put the Muslim world far ahead of western societies in these areas.  Most Muslim authorities agree that the QIBLA should lie along the "great circle" geodesic from one's location to Mecca.  In North America that direction is generally North of due East.  For more information see the websites http://en.wikipedia.org/wiki/Qibla, http://moonsighting.com/qibla.html and http://www.brasscompass.com/qiblacompass.htm.

28 January 2003 Porter Johnson (IIT physics) GPS Measurements
pointed out that you can measure elevation, as well as latitude, longitude, and velocity, with even a simple Global Positioning Sensor [GPS], with surprising accuracy. [± 6 meters absolute, according to specifications by a manufacturer, Garmin International Inchttp://www.garmin.com/]. Remarkably enough, there are elevation changes even in the Chicago region.  Most of the city of Chicago lies at about 185 meters above sea level, but on the Northwest Tollway from Schaumburg to Hoffman Estates the elevation rises to around 260 meters, and drops at the Fox River to 230 meters. [You can  usually maintain contact of the device with the synchronous satellites through your car window, although not through the walls or windows of a building.]  Roy Coleman pointed out that this highest point in Cook County is the library in [of all places] Chicago HeightsWho would have thunk it?

22 April 2003: Porter Johnson [IIT Physics]      GPS Data
These readings were taken at Back Entrance (near State Street), Life Sciences Building 
Elevation: + 218 meters above sea level
Latitude:     41 degrees 50 minutes 14.3 seconds
Longitude:  87 degrees 50 minutes 33.7 seconds

09 March 2004: Brenda Daniels [Collins HS]         How Big is the Continent of Africa?
had made a trip to Kinko's® to make a Big! map of Africa from a smaller one. She taped the big map to the board, and each of us was given a smaller map of Africa.  We cut out maps of the USA, China, Western Europe, India, Argentina, and New Zealand -- all drawn to the same scale. We found that the combined area of these countries was about the same as the area of Africa --- about 30 million square kilometers. We could fit all these images on top of the image of the African continent, with very little sticking over its edges. Africa is BIG!

This puts the world in its proper proportion.  Very nice, Brenda!

24 April 2004: Marva Anyanwu [Green Elementary School]         Apple Model of the Earth
started by asking why we thought an apple might be a good model of the earth.  Our answers included the facts that it has a core, it has a skin (crust), it contains layers, and it contains a visible axis.  Also, an apple -- like the earth itself -- will get rotten if it is not given proper care.  We then followed these procedures:

Food for thought and graphic excellence! Thanks, Marva!

12 April 2005: Ed Scanlon [Morgan Park HS]                         Scrapbook
Ed asked for our help with this project, which is for his students in Earth Science. Ed provided students with an outline of each of three chapters. Ed wanted the students to write a paragraph summarizing the main focus of the chapter. In addition, Ed asked the students to find an article (in the newspaper, within the last year) appropriate to each chapter, and write a five paragraph essay about the article. Then Ed asked each student to design and describe an experiment to test some topic in each chapter. Finally, Ed asked them to write a summary of their work. All their work would be handed in as a "scrapbook." Three of Ed's classes did an awful job with this assignment. So Ed is looking for our counsel on how he might alter the assignment to increase the compliance rate without watering down the assignment. Here is what we came up with:

Thanks, Ed.

26 October 2004: Ed Scanlon  [Morgan Park HS, Biology]                 Impact Craters (handout)

Some useful information for this experiment is the masses of these three "projectiles":

Ping pong ball: 0.3 g
Marble: 5.3 g
Golf ball: 45.2 g
In the laboratory, the students could determine the masses themselves using a balance.

A big enough object traveling fast enough could potentially make a huge crater on impact with the earth, and eject a huge amount of dust/debris into the atmosphere. One widely held view (for which there is considerable evidence) is that such an impact created so much dust in the atmosphere that a huge global cooling occurred, leading to the extinction of the dinosaurs and other species. For details see the Smithsonian National Museum of Natural History website:  http://www.nmnh.si.edu/paleo/blast/k_t_boundary.htm.

10 May 2005: Ed Scanlon [Morgan Park HS, biology]                     Predicting the weather
shared the following lesson with us. He had drawn three consecutive daily weather maps of the USA, copied from those appearing in newspapers. Ed then had his students determine the pattern (ie, direction) of movement of the high and low pressure centers, the warm and cold fronts, and the temperatures over the three-day period, and then predict on a blank map representing the fourth day, where the highs and lows, and warm and cold fronts would appear. He also had the students predict the temperatures in various parts of the country on day four, extrapolating from the first three days.  He did the same for precipitation, and whether the precipitation would be rain or snow. Ed then asked the students to explain how they had reached their conclusions.
This exercise is very simple, but quite interesting and profound! Thanks, Ed.

20 May 2005: Terri Donatello [ST Edwards School]                                  More on map reading
showed how contour maps can be used to work on math and graphing skills, using the elevation numbers on the contours to plot a graph of elevation versus linear distance to get another view of what terrain with elevation changes looks like. Terri also brought some stereo contour maps that could be seen in three dimensions using a stereo viewer.

13 December 2005: Earl Zwicker [IIT]             What is Zulu time?
called attention to a recent answer to the question "What is ZULU time?" by meteorologist Tom Skilling.  It appeared in the Chicago Tribune on Monday, 12 December 2005 on the weather page under the heading Ask Tom Why. The earth's surface is divided into 24 time zones, each representing a longitudinal width of 15 degrees.  Each time zone is represented by a letter  For the time zone of the Prime Meridian the corresponding letter is Z, which is identified with the word Zulu in the phonetic alphabet .... Able, Baker, Charlie, .... ZuluTres Simple! For additional details see http://en.wikipedia.org/wiki/List_of_military_time_zone  
Thanks, Earl!

18 April 2006: Ed Scanlon (Morgan Park HS)               Predicting the Weather
described a unit that he does in his Earth Science classes, as described in a handout. His students must bring in weather maps (from the newspaper, internet, ...) for five consecutive days.  Then, by looking at the maps, they are to decide whether they can trace the changes in fronts, low and high pressure areas, precipitation, etc. The students then get a blank map from Ed, on which they are asked to predict the weather pattern for the 6th day. To show us how this might work, Ed supplied us with 4 maps from consecutive days as well as a blank map, so that we could try it.   A real hands-on approach, Ed! Thanks.

02 May 2006: Marva Anyanwu (Wendell Green Elementary School)                     Earthquakes, and Other Things
Marva asked how many earthquakes occur in a day worldwide? It turns out that one occurs every 10 seconds (about 3 million per year that register significantly on the Richter Scale; see http://neic.usgs.gov/neis/eqlists/eqstats.html). Marva also brought in an article about the proposed 10th planet [http://www.gps.caltech.edu/~mbrown/planetlila/]. She discussed whether Pluto should be considered as a planet, and whether the number of planets should be 8, 9, or 10. Marva also passed out a table listing the densities of planets in the solar system:  http://www.enchantedlearning.com/subjects/astronomy/planets/
Fascinating, Marva!  Thanks.