High School Mathematics Physics SMILE Meeting
23 September 2003
Notes Prepared by Porter Johnson

Research or Rsceearch?

The paomnnehil pweor of the hmuan mnid.
Aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht the frist and lsat ltteer be at the rghit pclae.
The rset can be a total mses and you can sitll raed  it wouthit porbelm.
Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe. Amzanig huh?
--- [
Courtesy of Rudy Keil]:

John Scavo [Evergreen Park Community HS]        Alka-Seltzer® Rocket
constructed a rocket, complete with nose cone, by wrapping a sheet of paper around an empty film canister to form a rocket, according to the instructions given in one of his lessons on the SMART website, Film Canister Rocket: http://www.iit.edu/~smart/scavjoh1/lesson2.htm.As explained there, the film canister is at the base of the rocket, and its cap is at the very bottom.  Having assembled the rocket, complete with nose cone, he put 1/4 tablet of Alka-Seltzer®, then added water, then put the cap back on, and put the rocket on the launch pad (table top).  The cap popped off within a few seconds, and the rocket shot upwards to the ceiling.  In fact, it was hard to avoid premature 'ignition'.  He 'fired' the rocket several times, and used an alternative fuel --- baking soda and vinegar.

John has made the transition from teaching science to teaching web design classes in the business department.  He was able to make this transition because of his experiences as a student and then as a staff member in our SMART program [http://www.iit.edu/~smart/].  He said that, unlike in his "former life" as a science teacher, he routinely runs into students who know more than he does about web design.  After some adjustment, he has learned to get them to share their knowledge with him.  He said that "hands on" teaching is called "quantum learning" in his new department.  John recounted his childhood experiences with the Estes Rocket, [http://www.estesrockets.com/rockets/engines] which involves using a pressurized can (then filled with Freon®) for the launch.  He also explained the meaning of an (apocryphal?) remark allegedly made by Neil Armstrong while he was on the moon in 1969. Finally, he mentioned matchstick rockets:http://www.matchstickrockets.com/howto.html.

John, your rocket really hit the spot--on the ceiling! Cubs Rule! [at least temporarily].  We enjoyed your lesson -- and thanks for reminding us of our own childhood adventures!

Walter McDonald  [CPS Substitute and VA Hospital Technician]        Fibonacci Numbers
began by writing some of the Fibonacci Numbers on the board:

0,  1,  1,  2,  3,  5,  8, 13,  21,  34,  55,  89 , ...
These numbers are generated from the seeds, f0 = 0 and f1 = 1 by using the recursive formula
fn+1  =  f +  fn-1
For example
f2 = f1 + f0 = 1 + 0 = 1
f3 = f2 + f1 = 1 + 1 = 2
f4 = f3 + f2 = 2 + 1 = 3
f5 = f4 + f3 = 3 + 2 = 5
He then calculated the ratios of adjacent Fibonacci numbers:
f4/f5  3/5  0.600 000 000
f5/f6 5/8 0.625 000 000
f6/f7 8 / 13 0.615 538 615 ...
f7/f8 13 / 21     0.619 047 619 ...
f8/f9 21 / 34 0.617 647 058 ...
f9/f10 34 / 55 0.618 181 818 ...
f10/f11 55 / 89 0.617 977 258
 . . .  .      .     .  .           .        .
Limit     - - - 0.618 033 988 ...
Walter pointed out that, although all these ratios of Fibonacci  integers are rational numbers (repeating decimals), the limiting value of the ratio is the irrational number x = [ Ö 5 - 1 ] /2 = 0.618 033 988 ... . The reciprocal of this number is 1 + x = [Ö 5 + 1] /2= 1.618 033 988.  The number x, which is the positive solution of the quadratic equation x2 + x - 1 = 0, is observed in nature in spiral growth patterns of certain leaves, and it is related to the Golden Section.  For more details see the website The Fibonacci Numbers and Naturehttp://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html.

Porter Johnson pointed out that the the number x, the limit of the ratio of adjacent Fibonacci numbers, is the "simplest" non-rational number --- all "1's" in its continued fraction representation.. For more information as well as additional references, see his comments at  the Math-Physics SMILE meeting of 10 April 2001: mp041001.htm.

Biographical information about Leonardo Pisano (sobriquet "Fibonacci") [1170-1250??] can be found at the ST Andrews University History of Mathematics website [http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Fibonacci.html], from which the following is excerpted:

"Fibonacci was born in Italy but was educated in North Africa where his father, Guilielmo, held a diplomatic post. His father's job was to represent the merchants of the Republic of Pisa who were trading in Bugia, later called Bougie and now called Bejaia. ... Fibonacci was taught mathematics in Bugia and travelled widely with his father, recognising ... the enormous advantages of the mathematical systems used in the countries they visited."

Fascinating topic.  Good job, Walter!

Jane Shields [Calumet Academy,  science]        Why is the Sky Blue?
took a glass of water and added a small piece of hand soap to it, and stirred the water.  As the soap dissolved, the water turned cloudy (milky). Jane then lit a candle, and we darkened the room.  It was quite evident that, when we looked at the candle through the water, the candle itself appeared to be reddish (yellow-orange, actually), whereas when we held the candle in front of the glass the water behind it seemed to be blue. This is one manifestation of Tyndall Effect, which explains that small particles suspended in water scatter blue light more efficiently than blue light.  Lord Rayleigh showed that  particles much smaller than the wavelength of light [0.5 microns, say] scatter light according to the inverse fourth power of their wavelength, so that blue light is scattered around 10 times as much as red light.

Bill Shanks used his new LED light sources [described below] to show that blue light is indeed scattered significantly more than either red or green light.

But now, is the sky blue because of dust in the atmosphere, or is that explanation incomplete?  For additional Information see the article Why is the Sky Blue? [http://math.ucr.edu/home/baez/physics/General/BlueSky/blue_sky.html], on the website of  USENET  Frequently Asked Questions in Physics, http://math.ucr.edu/home/baez/physics/, from which the following has been excerpted:

"A clear cloudless day-time sky is blue because molecules in the air scatter blue light from the sun more than they scatter red light.  When we look towards the sun at sunset, we see red and orange colours because the blue light has been scattered out and away from the line of sight." ...

"The first steps towards correctly explaining the colour of the sky were taken by John Tyndall in 1859.  He discovered that when light passes through a clear fluid holding small particles in suspension, the shorter blue wavelengths are scattered more strongly than the red.  This can be demonstrated by shining a beam of white light through a tank of water with a little milk or soap mixed in.  From the side, the beam can be seen by the blue light it scatters; but the light seen directly from the end is reddened after it has passed through the tank".  ...

"Tyndall and Rayleigh thought that the blue colour of the sky must be due to small particles of dust and droplets of water vapour in the atmosphere.  Even today, people sometimes incorrectly say that this is the case.  Later scientists realised that if this were true, there would be more variation of sky colour with humidity or haze conditions than was actually observed, so they supposed correctly that the molecules of oxygen and nitrogen in the air are sufficient to account for the scattering." ...

We see the light now!  Thanks, Jane!

Roy Coleman [Morgan Park HS, physics]        Pulling on a Spool with a String
brought in a very large wire spool [rough dimensions: outer diameter 40 cm, inner diameter of 15 cm, height 40 cm]. He wrapped a heavy cord around the inner portion, and went through the classic demonstration of pulling the cord, as described on the websites SMU Physics Demonstrations: http://www.ap.smu.ca/demos/index.php?option=com_content&view=article&id=167%3Aspoolin-around&catid=46&Itemid=80  and Julien C Sprott: Physics Demonstattions: Motion [http://sprott.physics.wisc.edu/demobook/chapter1.htm, item 1.12].  He made the spool come toward him, go away from him, stand still and slip, and slide toward him, just by pulling with various orientations of the cord. Roy then rolled the gigantic spool on the chalk tray of the board, attaching a marker to the edge.  The marker traced a cycloid on the board -- Beautiful! 

Bigger spools are better, definitely!  Neat, Roy!

Roy also called our attention to the American Association Physics Teachers [AAPT] High School Photo Contest, as described in the Fall 2003 issue of the AAPT Announcer [Vol 33, No 3].  [also, see the website http://www.aapt.org/Contests/pc03.cfm]  The First Place winner by Jared Hill of Durham NC, is shown on its front cover.  It  shows a hard-boiled egg spinning in a thin layer of water.  The water is creeping up the side of the egg until it is thrown outward, creating a fountain effect. See the journal article "Fluid flow up the Wall of a Spinning Egg" by Gutiérrez, Fehr, Calzadilla, and Figueroa, American Journal of Physics 66, 442-445 (May 1998).  Our own Ann Brandon is a guiding spirit of this contest!

Bill Shanks [Shanks Math-Science Academy, lifetime student]        Miraculous Battery Recharger
showed his latest toy, a novel Nickel Hydride battery charger made by Rayovac Corporationhttp://www.rayovac.com/. The following information is excerpted from a more complete description.

"Rayovac’s I-C3 Technology Makes 15-Minute Charger the First of its Kind.
New rechargeable system allows for battery charging in 15 minutes or less and up to 1,000 times.
Recharged batteries last up to up four times longer than alkaline in certain devices.
No other battery recharging system is faster"

The charger appeared to work as claimed, but Bill noticed a problem with the specifications on the package.  It required a power source with an E.M.F. of 14.5 Volts DC and a current of 4.5 Ampères, and yet it produced 2 Amp hours of charge in 15 minutes.  It seems to produce 8 Amps of charging current, and yet it requires only 4.5 Amps from the power source. Very odd!   After all, a battery, like a water pump, merely lifts the potential of the circulating fluid, and is not itself the source of the fluid. Does anybody understand whether their specifications are correct?  If so, how can they be?

Bill also showed his latest Ultra-bright High Intensity LED's from L.E.D. CLUB:  http://www.ledclub.com/products.htm, in Green, Blue, and White [two 3-Volt batteries required], as well as Red and Yellow [one 3-Volt battery required].  They were quite powerful, and he used them to show us color addition in the darkened room.

That was intense, man! Thanks for sharing your physics gadgets with us, Bill!

We ran out of time before Bill Blunk [Joliet Central HS, physics] could make a presentation-- on Siegerschnecke?  He will be first in line for our next meeting, 07 October.  See you there!

Notes taken by Porter Johnson