Fall 2004 SMILE Schedule 

14 September  First class / registration 
28 September  Second class / late registration 
12 October  Third class 
26 October  Hallowe'en week 
09 November  A week after national elections 
23 November  Thanksgiving week 
07 December  and ... just 1 week later ... 
14 December  Last class 
"Over half of the lessons have strong visual, auditory or tactile components, which also makes them meaningful to handicapped students. Furthermore, the content of most of the lessons is readily adaptable to students at various levels, including students with special educational needs."Many thanks to Roy Coleman for help in preparing this revised document!
"Biologist Martin Wikelski is helping to settle a longstanding debate over how migratory birds manage to navigate for thousands of miles in darkness and bad weather.Who would have guessed it?
With two colleagues in Illinois and Germany, Wikelski has found that birds rely on a builtin magnetic compass, which they recalibrate each evening based on the direction of the setting sun. The scientists published their findings in the April 16 issue of Science.
The research, which involved attaching radio transmitters to birds and following them by truck for hundreds of miles across the American Midwest, is the first extensive study of bird navigation in the wild. The results appear to resolve conflicts between earlier laboratorybased studies, which had identified several possible navigational mechanisms, but produced no consensus. Previous theories suggested that birds use some combination of magnetism, stars, landmarks, smells and other mechanisms as navigational aides."
Benson Uwumarogie [Dunbar,
Mathematics]
Algeblocks
Benson showed us how he uses the ETA/Cuisenaire Algeblocks system
[http://www.etacuisenaire.com/algeblocks/algeblocks.jsp]
and associated workmats [http://www.etacuisenaire.com/algeblocks/workmats.jsp]
to illustrate the concepts and manipulations of abstract algebra by
placing colorcoded plastic, blocks on panels: Basic Mat,
Quadratic Mat,
Sentences Mat, and a transparent Factor Track.
Connections with
algebra and geometry are more evident with this system. For
example, one
may use the blocks representing x, y, and xy
to build the geometric figure of area given by algebraic equation
(x+y)^{2}.
Benson has found this system to work quite well in his
classes.
Thanks for the info and ideas, Benson!
Karlene Joseph [Lane Tech HS,
Physics]
Birthday
Candles and Spectroscopes
Karlene recently purchased from her local drugstore a set of Color
Flame Birthday Candles
[http://jdjiaxuan.en.alibaba.com/product/50003665/50029791/Color_Flame_Birthday_Candle/Color_Flame_Birthday__Candle.html]:
5 ´ 50 mm, which produce red,
green, yellow, blue, and purple
flames and last for
about 8 minutes. Karlene passed out a supply of
CENCO
Quantitative Analysis Spectroscopes  CP3010500,
available from SargentWelch
at https://sargentwelch.com/store/catalog/product.jsp?catalog_number=WLS180996.
She lit the red candle, and we each looked at the spectral lines
obtained for
it, which included reddish hues, as well as other colors. After a few
minutes,
she lit the green candle, let us look at it for a few minutes  and
then the
yellow  and then the blue  and then the purple candle. It
was
fascinating to see the light from each candle, decomposed into its
component
wavelengths, and to associate them with different chemical elements.
Even though it wasn't our birthday, we saw the light! Thanks for sharing this with us, Karlene!
Fred Schaal [Lane Tech HS,
Mathematics]
Fraction Action
Fred reminded us of a universal feature of programming
algorithms on
digital computers, in that they perform arithmetic exactly with
integers,
whereas with real numbers the calculations may be inexact because of
roundoff
error. Consequently, arithmetic with fractions can be done
exactly 
provided the numbers that arise are not too large. On his trusty
TI81 programmable calculator,
Fred went into fraction
mode, and was able to verify the relation:
Richard Goberville [Joliet Central HS,
physics]
Lightning Reaction
Richard recently purchased the Lightning Reaction toy
[See
this image].
Here is a description taken from The Stupid Store page:
"Here's how Lightning Reaction works  Anywhere from two to four people can play at once. You remove a handle from the base and get ready. When you press the button in the center, a red light pulses and suspenseful music plays. As soon as the red light turns green, you press the red trigger button as quickly as possible. If you're the slowest player, you will get rewarded with a painful electric shock. If you were faster than your opponents, you can simply laugh as the loser screams in pain.It was certainly a memorable experience when Bill Shanks, Don Kanner and others tested the operation of this fine device, which contains three AA batteries, and presumably a stepup transformer as well! Richard also showed us some cartoons with sciencebased components. Thanks, Richard!
Leticia Rodriguez [Peck Elementary School] and Bud Schultz
[Aurora West
HS,
physics]
Copernic
Agent
Leticia and Bud touted the use of the Copernic Agent
Basic
search engine: http://www.copernic.com/en/products/agent/basic.html.
This software package, which requires only 8 kB of memory, can
be
downloaded for free. Its features include automatically
combining the
results from many search engines, producing a lists of results for each
search,
providing more convenient followup searches within these lists.
They
tried, without success, to show us a video, The Lightning Story.
For a similar exhibition, see the National Geographic page Lightning:
The Shocking Story: http://environment.nationalgeographic.com/environment/naturaldisasters/lightningprofile.html.
Check out this new freeware! Thanks for telling us about it,
Leticia and
Bud!
Don Kanner [Lane Tech HS,
physics]
Funnel Multiplication
Don recently learned of a novel method of multiplication, which he
illustrated with an example such as 4567 ´
9876
= 45103692. He wrote the numbers directly below one
another, and
performed the following manipulations:
numbers arranged in 4  5  6  7We could write out the multinomial product of decimal numbers a b c d ´ e f g h in the following form:
four columns of two ´ 9  8  7  6
=
product of numbers in same column 3 64 04 24 2
sum of diag products; adjacent cols: 7 78 38 5
sum of diag products; next col pairs 8 38 6
sum of diag products; 1st and last cols: 8 7
(now, add everything up) 
(et, voilá!) 4 51 03 69 2
For discussion of an ancient description of this algorithm for multiplication, see the Iowa State University Department of Mathematics webpage Math Night Module: Multiple Methods of Multiplication [ http://www.math.iastate.edu/mathnight/activities/modules/multiply/aboutmod.shtml] from which the following has been excerpted:
"The history of mathematics in India is ancient. The Hindu Vedic tradition is an oral tradition of knowledge passed down in short verses, dating to before the invention of paper. The Vedas encompass a broad spectrum of knowledge, including the sutras (verses) pertaining to mathematics. In the early 20th century Swami Shri Bharati Krishna Tirthaji Maharaja claimed to have rediscovered a collection of 16 ancient mathematical sutras from the Vedas and published it in a book called Vedic Mathematics. Historians do not agree on whether or not these were truly part of the Vedic tradition. If these sutras date back to the Vedic era they were certainly part of an oral rather than a written tradition. However, they are a novel and useful approach to computation: they are flexible in application and easy to remember. They can often be applied in algebraic contexts as well as in simple arithmetic. 'Vertically and Crosswise' [sic: URDHVATIRYAGBHYAM] bridges the gap between arithmetic and algebra: the algorithm is very similar to the standard algorithm used in the US and also is similar to the "FOIL" (first, outer, inner, last) rule used for multiplying binomials in algebra."For additional discussion of this and other ancient multiplication methods see also http://www.math.iastate.edu/mathnight/activities/modules/multiply/ and http://www.pballew.net/old_mult.htm.
Thanks, Don!
Walter McDonald
[CPS Substitute: Radiology Technician at Veterans
Administration]
Is a 2nd Earth out there?
Walter passed around a recent article by Pamela Simpson (AP)
that
recently appeared in the Chicago Sun Times, which involved the
discovery
of a solar system on star HU 70642, a star similar to our sun,
which lies
about 94 light years from earth, and around which a planet lies in an
orbit
similar in shape and distance to the planet Jupiter in our own solar
system. The article appears on the Red Nova News website
at
http://www.redorbit.com/news/scifigaming/11557/is_a_2nd_earth_out_there__jupiterlike_planet_found/index.html.
See also the article Celestial Soulmate? Jupiterlike Plane Found in
System
Similar to Ours by Tariq Malik:
http://www.space.com/scienceastronomy/jupiterlike_planet_030703.html.
According to Alan Penny of Rutherford Appleton Laboratory
"This is the first one that is really like our own solar system of the 110 that we've found. We think it's a substantial step on the way to finding another earth.
Comment by PJ: Planets in nearby stars, while quite undetectable through direct observation, can be identified through detection of timedependent Doppler shift of light coming from that star. For the case in which there is only one major planet, the star and major planet rotate about their center of mass, with a period determined through Newtonian gravitation in terms of the distance between the star and the planet. The magnitude of the Doppler shift of light from the star is proportional to the the orbital velocity of the star about that center of mass. In practice, only planets the size of Jupiter or larger can be found, and they must be fairly close to the star, since otherwise the Doppler shift would be too small for detection with current techniques. For HU70642, the planet is twice the mass of Jupiter, and lies at a distance of 3.5 Astronomical Units. The Jupiterlike planet would sweep the solar system of unwanted debris and stabilize the orbits of the inner planets  perhaps one like our own planet Earth.
Very interesting Walter!
Bill Blunk [Joliet Central,
physics]
Series Circuits  or What?
Bill showed us a simplelooking circuit that consisted
of two
identical light bulbs in sockets, hooked together in series
and attached to
wires with a plug on the end. When the circuit was plugged into
the 115
VAC line, both
lights went on with equal intensity, as expected. However, when
Bill
unscrewed one of the bulbs, the other one continued to burn.
How
come? A similar thing happened when he screwed that bulb back
in and
unscrewed the other bulb. Although Bill claimed to be a
magician who would
not reveal his secrets, we suspected that he had slipped diodes under
the
sockets. Are we right, or are we right? Better luck next
time! Thanks
for the show, Bill!
Ann Brandon [Joliet West HS, physics] Sophie Germain; phone cord
Ann passed around the article Sophie Germain: Genius
with a Pseudonym [http://sciencewomen.blogspot.com/2008/11/sophiegermainmathematicalgenius.html],
which appeared in the Program for the Goodman Theater
production of the play Proof by David Auburn [http://math.cofc.edu/kasman/MATHFICT/mfview.php?callnumber=mf139],
which deals with a fragile young woman without formal mathematical
training who makes an important discovery concerning prime
numbers. Sophie Germain (17761831) [http://wwwgroups.dcs.stand.ac.uk/~history/Mathematicians/Germain.html]
alias Monsieur Le Blanc  obtained important results on
Fermat's Last Theorem [http://wwwgroups.dcs.stand.ac.uk/~history/HistTopics/Fermat's_last_theorem.html#40]
for Germain Primes  prime numbers n for which 2n+1 is also a
prime. See also the column This Month in Physics History in
the APS NEWS, 02 May 2004 [http://www.aps.org/apsnews/] Revolutionary
Pursuits: Circa May 1816: Germain Forms Theory of Elastic
Surfaces. Sophia Germain was instrumental in saving
the life of the most famous mathematician in the world, Carl
Frederich Gauss [
http://wwwgroups.dcs.stand.ac.uk/~history/Mathematicians/Gauss.html],
from the invading armies of Napoleon Bonaparte. Gauss
once said that she must have "the noblest courage, quite extraordinary
talents, and superior genius".
Ann also showed us a novel use for an ordinary phone cord, a coiled wire that connects the handset to the main body of the telephone. These cords are available separately at low cost  for example, try the Dollar Store. Simply hold the cord at both ends and stretch it  the cord can be used to display transverse waves much more easily and reliably than with our usual choice, Mr Slinky. Very nice ideas, Ann. Excellent!
Sally Hill [Clemente HS, Dean of
Students]
Optical Illusions
Sally passed around a set of optical illusions which she has
assembled,.
She uses them in her new position to put parents and visitors at
ease. Here is a
partial list of the titles of the various illusions:
Several of these illusions are available on the BAM Magic Club website: http://www.mandrgames.com/illusions.htm.
Thanks for sharing these with us, Sally!
Notes prepared by Porter Johnson