"They say in space no one can hear you scream, but if you are falling into a black hole, you can't even hear yourself. According to the so-called asymptotic silence hypothesis, spacetime becomes so contorted that signals can't travel any significant distance -- not even from your mouth to your ear. ..."
In addition, Earl mentioned the article Motoring Oil Drops, which also appeared on the American Physical Society webpage: http://focus.aps.org/story/v15/st7.
Fred Schaal [Lane Tech HS,
mathematics]
RANDINT(1,14,4)+50
Fred used the Pseudo-random Number Generator RANDINT,
which is
programmed into the TI-83 calculator.
He generated a random, equally-distributed set of 200 integers from 1
through 14, and obtained the following
number-of-occurrences of the generated numbers:
Generated Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
Number-of-occurrences | 13 | 12 | 13 | 18 | 17 | 14 | 20 | 15 | 13 | 13 | 17 | 10 | 13 | 12 |
Porter Johnson mentioned that "everybody knows" that it is unlikely for a randomly flipped coin to come up H (Heads) ten times in a row. However, not everybody realizes that the alternating sequence H T H T H T H T H T is equally unlikely. Furthermore, it is quite unlikely that in 1000 coin flips, Heads will occur exactly 500 times.
For a general discussion of Pseudorandom Number Generators see the Wikipedia webpage: http://en.wikipedia.org/wiki/Pseudorandom_number_generator.
Fred also brought in his metal candy box, for which we had taken exterior measurements last time mp022205.html to determine a volume of about 910 cm^{3}. We took a graduated cylinder filled with water, from which we were able to pour about 800 cm^{3} of water before the box became full. Our estimated volume was too large by over 10%. Why?
Fred also pointed out that the planet Mercury would be visible next to the New Moon just after sunset in the next few days. Thanks for the ideas, Fred!
Bill Colson [Morgan Park HS,
mathematics]
Poetry
Bill read us these two poems that were used in connection with a
No Talent
Show at a weekend school event:
Bill Shanks [retired, Joliet New Lenox
environs]
Geometry
Bill reminded us of the Pythagorean Theorem for a right
triangle of sides (a, b, c = b +
d), where c is the hypotenuse:
/|
c = b + d / | b
/ |
/___|
a
a | b | c=b+1 |
3 | 4 | 5 |
5 | 12 | 13 |
7 | 24 | 25 |
9 | 40 | 41 |
11 | 60 | 61 |
13 | 84 | 85 |
25 | 312 | 313 |
35 | 612 | 613 |
999 | 499000 | 499001 |
a | b | c=b+2 |
4 | 3 | 5 |
6 | 8 | 10 |
8 | 15 | 17 |
10 | 24 | 26 |
12 | 35 | 37 |
100 | 2499 | 2501 |
1000 | 249999 | 250001 |
a | b | c=b+8 |
12 | 5 | 13 |
16 | 12 | 20 |
20 | 21 | 29 |
24 | 32 | 40 |
28 | 45 | 53 |
36 | 77 | 85 |
888 | 49280 | 48288 |
a | b | c=b+9 |
15 | 8 | 17 |
21 | 20 | 41 |
27 | 36 | 45 |
33 | 56 | 65 |
39 | 80 | 89 |
111 | 680 | 6893 |
999 | 55440 | 55449 |
I | I + 1 | J |
3 | 4 | 5 |
20 | 21 | 29 |
119 | 120 | 169 |
696 | 697 | 985 |
4059 | 4060 | 5741 |
23660 | 23661 | 33461 |
Note that the scale of subsequent triangles increases by a factor of about 6 each time. For discussion see the solution to Problem #152 on this website: http://www.dansmath.com/probofwk/probar16.html#anchor585356. For a general solution and a relation of these triangles to the Pell Equation, see the following PDF file: http://hometown.aol.com/jpr2718/pell.pdf.
Thanks for the ideas, Bill!
Ann Brandon [Joliet West,
physics]
Magnet Experiments
Ann
has a homebound student with MS this semester, so she developed a
number of "take-home" experimental setups involving magnetism. Ann
began by putting a bar magnet on the desk, and covered it with a large
sheet of
paper. She place a small "toy" compass on the paper near the
location of the magnet, and drew a short line on the paper to mark the
direction
of the compass needle (direction of the magnetic field). Ann
moved the
compass in the direction of the field, marking the direction at each
new
location, and repeated the process several times. She then
connected the
marks with a solid line, thus graphing a line of force of the magnetic
field. By starting at various positions, Ann traced out
several lines of
force for the magnetic field. Next, Ann sprinkled iron
filings out
of a "salt shaker" and onto the paper. The iron filings aligned
along the lines of force that she had previously drawn. As the amount
of
fillings increased, the lines of force became three-dimensional. Very
interesting visual patterns!
Ann then placed two Ring Magnets on a wooden rod. When the North (or South) poles of the magnets were adjacent to one another, the magnets repelled each another. However, when the magnets had opposite poles adjacent, they attracted each other. Ann then put several magnets on the wooden rod with the unlike poles adjacent, and held the rod vertically up. The magnets bobbed up and down slightly, coming to equilibrium positions. Interestingly, the spacing between the magnets was greatest at the top, and least at the bottom. (Why?) Neato!
Ann pointed out that it is often possible to get End Rolls of Newsprint from local newspaper offices: e.g.
South Holland/Dolton Star - 6901 West 159th Street, Tinley Park, IL, 60477-1602End rolls may or may not contain a lot of paper, depending upon what's left over after printing. The printers office will often give them gratis to school teachers, or else at minimal cost. Thanks, Ann!
Phone: 708-802-8800 Fax: 708-802-8088
http://www.starnewspapers.com.
Leticia Rodriguez [Peck Elementary
School]
Ceragem Thermal Acupuncture Massager
Leticia has been using a thermal massage bed, which is described
on the Ceragem
website: http://www.ceragem.com/.
The following is excerpted from that website:
What is Ceragem?
CERAGEM is a thermal massager that helps soothe body aches and pains associated with daily stress, pressure, and bad posture. It combines the benefits of alternative medicine derived from traditional Eastern medicine with advanced technology to provide the most effective healing and relaxation. Ceragem is easy to use and highly effective, as proven by the positive feedbacks we received from our customers. Ceragem is available for free trial at our distribution centers.
The device consists of a bed with rollers for spinal alignment, with an IR light source to stimulate circulation. Leticia asked that we each go to test this device (six times, without cost) to assess its effects on our health and happiness, at the following location:
5756 West Belmont Avenue, Chicago IL
(773) 205-1020
Notes prepared by Porter Johnson