Don Kanner [Lane Tech HS,
A Book Review
Don touted the book A History of Mathematical Notations by Florian Cajori [Dover Publication 1994], ISBN 0-486-67766-4. Don cited as an example that Cajori described the origins of the signs + and - to represent addition and subtraction, respectively. They were developed in Germany during the last twenty years of the fifteenth century. The + sign first occurs in print in a book by Johann Widman (1489). [See also Widman's biography: http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Widman.html. It is considered by experts to be a misprint for the symbol vñ, representing vnnd or "und"-- "and" in modern German. The - sign first occurs in print in a book by H Brugsch, and it is given the name minnes. For a biography of Florian Cajori see the website http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Cajori.html.
Monica Seelman [ST James Elementary
Mystery of Straw Worms
Monica began with the following riddle:
Fred Schaal [Lane Tech HS
Fred has been reading the book The Theory of Everything by Stephen Hawking http://www.audiobooksonline.com/shopsite/1590072286.html. Fred indicated that when two black holes collapse together, one would expect the total entropy to be conserved, and that the entropy of a given black hole is proportional to its area. However, this requirement of thermodynamic reversibility does not seem to be true. How come? For more details see these websites on Black Hole Thermodynamics: http://nrumiano.free.fr/Estars/bh_thermo.html and http://www.upscale.utoronto.ca/GeneralInterest/Harrison/BlackHoleThermo/BlackHoleThermo.pdf.
Good question, Fred!
Babatunde Taiwo [Dunbar
Understanding Car Crashes: It's Basic Physics (video)
Babatunde showed a 22 minute video illustrating the concepts of inertia, impulse, momentum and force in car crashes, which was prepared by the Insurance Institute for Highway Safety [call (703) 247-1500 or go to the website http://www.highwaysafety.org/], which may be ordered from Arbor Scientific from the website http://www.arborsci.com/understanding-car-crashes-dvd-s-2. Here is an excerpt from that website:
"What happens to vehicles and their occupants in crashes is determined by science. "You can't argue with the laws of physics," says Griff Jones, award-winning high school physics teacher, who goes behind the scenes at the Institute's Vehicle Research Center to explore the basic science behind car crashes: inertia, crash, forces, momentum, impulse, and a lot more."The following points were made in the film.
Very informative, Babatunde!
Benson Uwumarogie [Dunbar HS,
Special Parts of a Triangle
Benson used patty papers to show us how to construct the altitudes, median lines, angle bisectors, and perpendicular bisectors of a triangle by drawing the triangle on the paper, and then folding the paper appropriately. With these patty papers (presumably named after the paper sheets placed between hamburger patties by butchers), his students constructed these features of triangles for themselves. Unfortunately, the constructions did not show up well on the overhead projector, because the paper was not transparent. By showing his work at various states, Benson illustrated these geometrical concepts. Bill Colson commented that the book Patty Paper Geometry by Michael Serra has been published by Key Curriculum Press. For details see their website http://www.keypress.com, and especially http://www.keypress.com/catalog/products/supplementals/Prod_PattyPpr.html.
A useful approach, Benson!
Bill Colson [Morgan Park HS,
Interdisciplinary Projects with Camera Obscura and Pinhole Camera
Bill also called attention to the article Unified Vision by Urmila Subramanyan, which appeared in the October 2004 issue of Teacher Magazine --- to see the article you must register on the website http://www.educationweek.org/tm/toc/2004/10/01/. The article concerned Ralph Howell, photography teacher at St Mary's Hall school, who first transformed a carnival wagon into a camera obscura [http://www.acmi.net.au/AIC/CAMERA_OBSCURA.html] and subsequently has created a number of interdisciplinary class projects based upon the pinhole camera [ http://www.exploratorium.edu/light_walk/camera_todo.html]. To Ralph Howell, anything's a camera. Just poke a pin through it. Pinhole cameras are anything but routine, according to Howell.
Very interesting, Bill!
We did not have time for the last presentation, Accelerometers by Ann Brandon and Debbie Lojkutz. They will be placed at the top of the schedule for our next meeting, 09 November 2004. See you there!
Notes prepared by Porter Johnson