High School SMILE Meeting
07 March 2006
Information:
"As part of my duties as a Wright Fellow, I am giving workshops for physics teachers on my 'stuff' that I've been working on, and I am giving a set in Chicago. The place is IMSA, and the dates are April 5th and June 23rd. I know April 5th is a Wednesday, but it was necessary for scheduling. The workshops are absolutely free (and you even get fed!), so all the school district has to do is pay for a sub for the day. Participants are expected to attend both sessions, but let me know if there are special cases and we'll see what we can do. The title is "Relatively Physics", and I'll be sharing curricula in relativity, quantum mechanics, and cosmology for use with high school students. No previous background is required, and freshman physics teachers or physical science teachers are very welcome! Participants will also receive a CD of the workshop materials as well as some demonstrations to take home with them. Did I mention this is all for FREE? The workshop website is http://www.tufts.edu/as/wright_center/ and you can register here and find out more information."
Bud Schultz (Aurora Middle
School) Gonzo Gizmos
Bud
shared a book he bought at American Science and Surplus -- Gonzo
Gizmos: Projects & Devices to Channel Your Inner Geek by Simon
Field (http://www.kk.org/cooltools/archives/000667.php).
This book is full of great ideas, explanations, and projects -- it
contains a lot of interesting activities involving
electricity. Thanks for the Info, Bud!
Don Kanner (Lane Tech HS,
physics)
The Sound of Physics
Don suggested modifying the simple discussion of open ended and
closed ended
organ pipes, as made at the last meeting by Larry Alofs. The
equations l
= 4L (for a pipe with one end closed) and l =
2 L (for a pipe with both ends open) gives the fundamental
frequency only for
pipes under certain geometrical restrictions. In fact, it is an
oversimplified way of
describing the vibrations. It is not just the length of the pipe that
determines the pitch; we tested this for various
pipes, across which we blew
air to try to make standing waves. Another exercise involves
a Florence flask and an Erlenmeyer flask of equal
heights
and volumes. They produce sounds of rather different pitch when air is
blown
across them. The size of the neck and opening of the vessel
is also important in determining what tone is made in this
way. For additional information see The Resonance of Common
bottles and
Jugs by Don Kanner: http://www.iit.edu/~smart/kanndon/lessonb.htm.
Hermann Helmholtz actually found out that the ideal shape for
a resonating volume is a sphere. For additional discussion see
the
comments at the 25 February 2003 HS Math-Physics SMILE meeting:
http://www.iit.edu/~smile/weekly/mp022503.html.
Sounds good! Thanks, Don.
Fred Schaal (Lane Tech HS,
math)
Parabolic Points
In an extension of his presentation at the last meeting, Fred
used a
similar procedure to trace out the points on a parabola using
only his (chalk) compass, a meter stick and the blackboard. He chose a
focal
point (focus) at random above a horizontal line (directrix).
He used the compass to draw a portion of a circular arc with an
arbitrary radius, with the center at the focus . Two arcs are then made
with the compass held at
the same radius, with their centers on the line. A tangent to these two
arcs intersects
the first arc at two points, which lie on the parabola. The
process is repeated using the same focal point but different
radii, generating points to trace out a
parabola. For additional information see the interactive webpage The
Parabola by Alex Bogomolny: http://www.cut-the-knot.org/ctk/Parabola.shtml,
Neat, Fred!
Earl Zwicker (IIT
Physics)
Mr Angry is on the left, and Mrs Calm is on the right
Earl had gotten an e-mail from Rudy Keil, including the
remarkable
image shown here.
There are two images of a face, one with a calm look and
one
with an angry look. The two images seem to switch depending on whether
they are viewed from close in
(about 1 foot away) or far away (about 8 feet). It works
completely!! But no one knew the reason for this! We will
have to look for one!! One way to investigate it would be to
try to find out if there is a consistent distance (for the
members for the class) at which the transition occurs. We
tried this. Fred tried it and the transition (where the
images looked roughly the same) occurred at a distance of
about 6 floor tile widths and the switch was complete at about 10
tiles. Don tried it and got 8 and 10 for the same figures.
Walter got 8 and 10; Ed got 6 and 9. Fairly consistent
results which did not seem to depend upon whether or not the
observer was wearing glasses. For additional discussion see the
website
http://cvcl.mit.edu/gallery.htm#hsflsf,
from which the following has been excerpted:
"This impressive illusion created by Dr. Aude Oliva and Dr. Philippe G. Schyns, illustrates the ability of the visual system to separate information coming from different spatial frequency channels. In the right image, high Spatial Frequencies (HSF) represent a woman with a neutral facial expression, mixed with the low spatial frequency (LSF) information from the face of an angry man. On the left, the face of the angry man is represented in fine details whereas the underlying female face is made of blur only."Thanks, Earl!
Porter Johnson (IIT,
Physics) Sangaku-Followup
Porter continued the discussion of the “Circle Inscribing Sangaku”,
which was introduced at the last class by Walter McDonald. This
problem is
discussed on the Mathworld Website on the web page
http://mathworld.wolfram.com/CircleInscribing.html.
However, that discussion is incomplete, in that it does not prove that
the
inscribed circle centered at O_{3} is tangent to the
isosceles
triangle ACB.
(1 + r) y = r Ö[2 (1 - r)] .
Let the symbol j represent the angle ACD. Because the point C lies on the largest circle, its distance to the center O is 1/2. Furthermore, the right triangle ADC, has these side lengths:
Porter then told us about Morley’s Theorem. Start with any triangle and trisect all three angles. Pairs of the trisecting lines from adjacent angles will intersect to make three points inside the original triangle. Connection of these three points will always produce an equilateral triangle!! Fred then illustrated this by laying out a carefully drawn figure on the board. For more details see the website http://www.cut-the-knot.org/Curriculum/Geometry/Morley.shtml, which contains an adjustable triangle showing the result. See also http://www.jimloy.com/geometry/morley.htm, which contains the following comment:
"One of the interesting side results of some of the proofs is that the side of the equilateral triangle is equal to 8R sin(A/3) sin(B/3) sin(C/3), where A, B, and C are the angles of the larger triangle, and R is the radius of the circumcircle."Fascinating, Porter.
Lee Slick (Morgan Park HS,
retired)
Cricket Temperature
Lee
described how to estimate the temperature (in degrees
Fahrenheit) from the
frequency of cricket chirps. (handout by Tom Skilling,
Chicago
Tribune, February
5, 2006. http://wgntv.trb.com/news/weather/weblog/wgnweather/archives/ATW020506SUN.jpg
) Count the number of chirps a cricket makes during a 15
second interval, and add 39 to that number. You get
a remarkably accurate
reading. This works because crickets are “cold blooded” (poikilothermic),
so that their metabolism (and thus
frequency of chirping) will increase as the temperature
increases. For more details see the website Oecanthus: Pulse
Distribution and Temperature Effects: http://facstaff.unca.edu/tforrest/ASA
98 Seattle/sld005.htm.
Keep on chirping! Thanks, Lee!
Bill Colson (Morgan Park HS,
math)
Assorted Literature
Bill shared several items with us:
Thanks, Bill!
Our next SMILE meeting will be on Tuesday March 21, 2006. See you there!
Notes prepared by Ben Stark and Porter Johnson.