High School Mathematics-Physics SMILE Meeting
1997-2006 Academic Years
History of Science

16 March 1999: Bill Colson [Morgan Park HS]
He told a joke of a Y2K ["y" to "k"] solution where days changed from "day" to "dak" ie, Mondak instead of Monday. Should the year 2000 would be more appropriate as Y2M, instead of Y2K??

06 April 1999: Bill Shanks [Joliet Junior College; quasi-retired from Joliet Central HS]
Bill handed copies of an article entitled "Quantum Sound", which appeared in Electronic Magazine recently. It not only explained phonons as sound quanta, but introduced the concepts of the "photino" or "microphonon?, as well as "polyphonons", "telephonons", and the important work of the Bolognese residents Dr Leonardo Da Capo and Enrico Fermata, who finance their work by selling T-shirts with the slogan Hooked on Phonons. Bill then demonstrated his remarkable musical skills on a toy saxophone presumably purloined from a small child

12 October 1999: The final discussion took a non-phenomenological turn, addressing important matters such as the following:

 

06 April 1999: John Bozovsky [Bowen HS]
According to him, the seriousness of the fabled Y2K problem pales in comparison with the difficulties in facing the Y1K problem, as evidenced by an article from a London newspaper circa 999 AD/CE. [http://www.towson.edu/~duncan/Y1K.html] In fact, many people predicted the end of the world at the end of the first millennium. They may have been correct!

29 February 2000: Porter Johnson (IIT Physics)
told us of Birthdays on Today's Date (Leap Day!): Gioacchino Rossini http://en.wikipedia.org/wiki/Gioachino_Rossini in 1792 and Herman Hollerith http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Hollerith.html in 1860. The first being the composer (who wrote William Tell), and the latter the inventor of punched card computers. Interesting stuff!

02 May 2000: Arlyn van Ek (Illiana Christian HS)
showed us an interesting 50 minute video available from NOVA. See the website http://www.pbs.org/whatson/press/winspring/secrets_medsiege.html. Titled Medieval Siege, it sells for about $26 (1-800-949-8670). He uses it when he must be out of the classroom. He showed us some excerpts about the WARWOLF [the atom bomb of the 14th century] and the Trebucket (like a catapult with a sling on its end), and how a group of people experimented building several models, many to full-scale, to test whether they had the range and power to knock down the thick defensive walls of a medieval castle. They had some problems until they put wheels on it, like old engravings showed them to be built. The wheels, counter-intuitively, increased the range of the projectiles and stability of the trebucket! Most interesting physics involved. Thanks, Arlyn!

23 October 2000: Don Kanner (Lane Tech HS, Physics)  Inertia
Don
handed out selected portions of the authorized English translation of landmark book Philosophiae Naturalis Principia Mathematica by Sir Isaac Newton, which included explanations of the following definitions and laws: [For the Latin text see http://www.maths.tcd.ie/pub/HistMath/People/Newton/Principia/Bk1Sect1/].

    Definitions
  1. The quantity of matter is the measure of the same, arising from its density and bulk conjointly.
  2. The quantity of motion is the measure of the same, arising from the velocity and quantity of matter conjointly.
  3. The vis insita, or innate force of matter, is a power of resisting, by which every body, as much as in it lies, continues in its present state, whether it be of rest, or of moving uniformly forwards in a right line.
  4. An impressed force is an action exerted upon a body, in order to change its state, either or rest, or of uniform motion in a right line.
  5. A centripetal force is that by which bodies are drawn or impelled, or any way tend, towards a point as to a centre.
    Laws
  1. Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.
  2. The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.
  3. To every action there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

Curiously, Newton distinguishes an innate force of matter (inertia?)  in #3 from an impressed (applied) force in #4.

Porter Johnson commented that the question of whether Newton actually discovered his laws by himself has been hotly debated over the years. Consider this excerpt from a Newton Biography:  http://www.ing.iac.es/PR/int_info/intisaac.html

Isaac Newton was born at Wolsthorpe, Lincolnshire on 25 December 1642. Born into a farming family and first educated at Grantham, Isaac Newton was sent to Trinity College, Cambridge, where as an undergraduate, he came under the influence of Cartesian philosophy. When confined to his home at Woolsthorpe by the plague between 1665 and 1666 Newton carried through work in the analysis of the physical world which has profoundly influenced the whole of modern science.

On returning to Cambridge, Newton became a Fellow of Trinity College, and was then appointed to the Lucasian Chair of mathematics in succession to Isaac Barrow. In the 1670s lectures, demonstrations and theoretical investigations in optics occupied Newton.  In 1672 he constructed the reflecting telescope today named after him, but in the early years of the 1680s correspondence with Robert Hooke re-awakened his interest in dynamics. After Edmond Halley's visit to Cambridge to encourage him in this work, Newton laid the foundations of classical mechanics in the composition of his fundamental work Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), which was presented to the Royal Society in 1686, and its subsequent publication being paid for by his close friend Edmund Halley.

Consider also this excerpt from the Biography of Robert Hooke:  http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Hooke.html

In 1672 Hooke attempted to prove that the Earth moves in an ellipse round the Sun and six years later proposed the inverse square law of gravitation to explain planetary motions. Hooke wrote to Newton in 1679 asking for his opinion:-

... of compounding the celestiall motions of the planetts of a direct motion by the tangent (inertial motion) and an attractive motion towards the centrall body ... my supposition is that the Attraction always is in a duplicate proportion to the Distance from the Center Reciprocall...

Hooke seemed unable to give a mathematical proof of his conjectures. However he claimed priority over the inverse square law and this led to a bitter dispute with Newton who, as a consequence, removed all references to Hooke from the Principia.

For balance, look at the corresponding Newton Biography on the St Andrews website:  http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Newton.html.

Consider also the excerpt from this source: http://www.aps.org/units/fhp/FHPnews/reports.cfm

Michael Nauenberg, University of California, Santa Cruz, who organized the session, presented a paper entitled, "Newton's Early Computational Method for Dynamics." He began by observing that despite considerable historical research, very little is known about how Newton developed the mathematical theory of orbital dynamics which culminated in the Principia. A letter from Newton to Hooke, written on Dec. 13, 1679, reveals that Newton had made considerable more progress in understanding central force motion than had been previously realized. In particular a careful analysis of the original diagram which appears in this letter reveals that by then Newton understood by the fundamental symmetries of orbital motion for central forces. Moreover, the text of the letter indicates that he had developed a computational method to evaluate orbital motion for arbitrary central forces. Nauenberg went on to show that the early mathematical method Newton used to solve orbital motion for general central forces in his letter to Hooke was based on the calculus of curvature which he developed in the late 1660's. In correspondence with Newton in late 1679, Hooke suggested an alternative physical approach to which Newton gave a mathematical formulation without acknowledging Hooke (later in 1686 he wrote to Halley emphatically denying that Hooke had made any important contributions). This approach led Newton immediately to the discovery of the physical basis of Kepler's area law, which remained hidden in his earlier curvature method. The new approach is described in Proposition I, Theorem I of the Principia, and constitutes the cornerstone for the geometric methods in the book.

11 September 2001: Bill Colson (Morgan Park HS, Mathematics)
passed out copies of a page from Popular Science Flash Forward Summer 2001, entitled Famous Last Words.  It contained such entries as the following:

He also passed around a copy of the book Flatterland:  Like Flatland, only More So by Ian Stewart [Perseus Publishing 2001 ISBN 0 - 7382 - 04420].  This book stands as a sequel to the classic book Flatland by Edwin Abbott [Dover 1982 ISBN: 048627263X ].  Like its predecessor, it delves into travel from one dimension to another, including the "fractal forest", or the "Mandel Blot".  Porter Johnson pointed out that theories involving gravity in ten dimensional spacetime are currently under serious investigation.

20 January 2002 Bill Shanks (Joliet Central, retired):  Obituary of ISPP Participant Leo Seren
[originally published in the Los Angles times at http://www.latimes.com/news/obituaries/la-000002603jan11.story?coll=la%2Dnews%2Dobituaries]
Leo Seren, 83; Physicist on the Atomic Bomb Who Turned Pacifist. Leo Seren, 83, a University of Chicago physicist who called himself a war criminal for the role he played in the development of the atomic bomb, died of amyloidosis Jan. 3 at a hospital in Evanston, Ill. Seren had just earned his doctorate from the University of Chicago when he went to work with Enrico Fermi on the Manhattan Project in 1942. Seren was one of 51 people present in an abandoned squash court at the university's Stagg Field on Dec. 2, 1942, when the first nuclear reactor achieved critical mass. Seren's job was to measure the density of neutrons in piles of graphite, uranium and cadmium control rods used to build the reactor.  He worked on nuclear power until 1960, stopping when he reached the conclusion that there was no way to safely dispose of radioactive waste. He began to focus on renewable energy sources, such as solar, wind and water power. In a 1982 speech before anti-nuclear demonstrators at the University of Chicago, Seren spoke of his regret over his role in the Manhattan Project, which led to the devastation of Hiroshima and Nagasaki, Japan, in 1945 and the loss of tens of thousands of lives. He said that if he were tried for crimes against humanity, "I'd plead guilty. And I'd say for mitigating circumstances that at least I decided that I'd never work on nuclear weapons again."

06 May 2003
Hiroshima and Nagasaki for Physics Teachers:  A one-week workshop, 7-11 July , 2003:  Guide: Raymond G. Wilson, Ph.D., Emeritus Associate Professor, Physics Department, Illinois Wesleyan University, Bloomington, IL 61702.  He began teaching about the effects of nuclear war in 1959, and has spent seven summers of study in Hiroshima. For details see the website http://titan.iwu.edu/~physics/Hiroshima.html.

29 November 2005: Larry Alofs showed us the inside of a combination lock apparatus, which might once have been a locking door for a post office box. There are three round tumbler plates inside the lock, each having a notch. Each number of the combination rotates one of the plates so that the notch is aligned in a certain direction. The right sequence of numbers serves to align the three notches on the three plates, which allows the lock to be opened. Neat!  Thanks, Larry.

Porter Johnson then told us the story of how Richard Feynman, who, during his time at Los Alamos working on development of the  atomic bomb during WWII, devised a way to open combination locks. He first made these observations:

For a standard 40 number combination lock with 3 tumblers, it would take 403 = 64,000 trials to determine the correct combination. Feynman cleverly reduced the number of trials to 82 = 64, making it fairly easy to open an ordinary lock.

21 October 2003: Bill Blunk [Joliet Central HS, physics]        Columbus and the Telescope
In his unofficial capacity as guardian of public interest in historically accurate portrayal of science in the media, Bill was somewhat surprised to see an advertisement [from a furniture store] portraying Christopher Columbus looking out from his sailing vessel with a telescope.  This image was quite remarkable, since Columbus sailed in 1492, and the telescope was invented around 1608.  For more information on CC, the son of a wool merchant who found his way to the new world, see The Columbus Navigation Homepage [http://www.columbusnavigation.com].  Who really invented the telescope, and when? For insights, see http://www.mce.k12tn.net/renaissance/inventions.htm or http://www.ee.umd.edu/~taylor/optics3.htm, or perhaps even http://news.bbc.co.uk/1/hi/sci/tech/380186.stm.

It makes one wonder about the furniture, as well! Thanks for blowing the whistle on this one, Bill!

18 November 2003: John Scavo [Evergreen Park HS]        How Many Blades on a Propeller??
John
reminded us of two important anniversaries:

According to John, the Wright brothers had determined how to make the proper size and shape of propeller. They calculated that 90 pounds of force were required for the launch, and they measured a force of 160 pounds; thus they decided to fly! For more details see the NASA website Wright 1903 Flyer -- Propeller Propulsionhttp://wright.nasa.gov/airplane/propeller.html and the Nova:  http://www.pbs.org/wgbh/nova/wright/flye-nf.htmlJohn mentioned that the P-51 Mustang fighter plane, champion of the skies in World War II, could fire its guns at their maximum rate for only 15 seconds before running out of ammunition.

How many blades are optimal for a propeller?  The answer depends upon many factors, such as the pitch of the blades, their operating speed, their size and shape, the weight, shape, and cruising speed of the plane, etc.  The problem is different for a windmill, which converts wind energy into more useful forms.  For details see An Illustrated History of Wind Power Development: http://telosnet.com/wind/index.html .  See also the science project Number and Size of Blades on Wind Turbine vs Electrical Outputhttp://www.selah.k12.wa.us/SOAR/SciProj2000/JohnH.html.

Interesting questions, John!

24 February 2004: Carl Martikean [Crete Monee HS, Physics]           Galileo's Study of Motion (handout)
Carl pointed out that, in Galileo's time, the subject of algebra was very new to Europeans -- even the well-educated elite.  The scientists of his and Isaac Newton's time were more comfortable with geometrical arguments, since the study of Euclidean geometry was part of their education.  Thus, Galileo's analysis of Accelerated Motion [in effect, blocks sliding down inclined planes] was given in the language of geometry. Carl discussed Galileo's proof of the following proposition:

Theorem II, Proposition II
"The spaces described by a body falling down from rest with a uniformly accelerated motion are to each other as the squares of the time intervals employed in traversing these distances."
[Today we are more comfortable in describing such motions using algebra: d = vo t +1/2 a t2, with vo = 0 for starting from rest.]   Using spark timer data to describe uniform acceleration, Carl outlined the steps in analyzing the information in the style of Galileo.  We were struck with the difficulty we encountered in following Galileo's approach.  Carl also mentioned that it took only 3-4 generations for investigators to develop calculus, once they had learned about algebra.  Still, the scientists of the late renaissance considered themselves first and foremost as geometers.  When Sir Isaac Newton said that there was no royal path to learning geometry, he used the word "geometry" to mean what we call "physics" today. For more details on Galileo's life and discoveries, see the ST Andrews [UK] History of Mathematics website [http://www-groups.dcs.st-and.ac.uk/~history/Indexes/HistoryTopics.html], and especially their biographical information on  Galileo Galilei [http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Galileo.html].

Thanks for sharing this new insight, Carl.

04 May 2004: 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/sophie-germain-mathematical-genius.html], which appeared in the Program for the Goodman Theater production of the play Proof by David Auburn, which deals with a fragile young woman without formal mathematical training who makes an important discovery concerning prime numbers.  Sophie Germain (1776-1831) [http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Germain.html] --alias Monsieur Le Blanc -- obtained important results on Fermat's Last Theorem [http://www-groups.dcs.st-and.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 SurfacesSophia Germain was instrumental in saving the life of the most famous mathematician in the world, Carl Frederich Gauss [ http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Gauss.html], from the invading armies of Napoleon BonaparteGauss 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 SlinkyVery nice ideas, Ann.  Excellent!

14 September 2004: Porter Johnson and Don Kanner called attention to The Archimedes Palimpsist, which was discussed in a recent PBS program.  For details see http://www.pbs.org/wgbh/nova/archimedes/palimpsest.html on the PBS website, http://www.pbs.org/.  Note: a palimpsist is a parchment or tablet that has been written upon more than once, the previous text having been imperfectly erased and still visible.  This partial manuscript of The Method by Archimedes indicates that he used continuous summation (integral calculus) in calculating the volumes inside curved surfaces.

09 November 2004: Dianna Uchida [Morgan Park HS]           Neat Book
Dianna recently obtained the book Science Explorer [ISBN 0-7566-0430-3] for $12.97 at COSTCO.  This book, published in 2004 by DK Eyewitness Books [http://www.dk.com/], shows a beautifully illustrated and annotated variety of historical apparatus, and is rather wide-ranging.  She cited the example of development of bronze tools for axe blades, swords, and (ouch!) razors in primitive society. Thanks for the information, Dianna!

13 September 2005: Karlene Joseph (Lane Tech HS, physics)     Predicting Paths: Exercises for Critical Thinking
Karlene
has been searching for problems for her students that get away from "plug and chug" and more towards critical thinking. One she called "Predicting Paths". The first example was a hoop that was marked with a point on its circumference.  Karlene slowly rolled the hoop on the (flat, horizontal) table. She asked her students to visualize/determine the path traveled by the single point as the hoop rolls in one direction. Several of us commented that the curve is a cycloid -- the special case of a Brachistochrone is described below.

A similar question involves a hoop with the point rolling on the inside of a fixed circle. The curve here might be called an epicycloid.  A third one is like the second but now the outer (large) hoop rolls while the inner hoop is stationary -- like a point on the edge of a Hula Hoop. The next time around Karlene asked her students to design an apparatus to give a physical demonstration of the process and the results. One student represented the cycloid visually by taping a flashlight onto the inside edge of a coffee can, and rolling the can across the table.  Nifty! Thanks for the ideas, Karlene!

Porter had us consider an application, the Brachistochrone problem, posed by Johann Bernoulli in 1696 --- see Brachistochrone Problemhttp://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Brachistochrone.html. Here is a simple statement of the problem:

Let us connect two fixed points, A and B, by a wire that maintains its shape. What is the optimal shape of the wire, for a bead (of constant weight) to slide down the wire from A to B -- without friction  -- in the shortest time?
This question was the first one solved using The Calculus of Variations. For additional details see the website The Brachistochrone:  http://whistleralley.com/brachistochrone/brachistochrone.htm.

13 December 2005: Bill Colson [Morgan Park HS, mathematics]            Stamps
Bill called attention to a set of commemorative stamps that honor Richard Feynman and other scientists.  For details see the USPS website http://www.usps.com/communications/news/stamps/2004/sr04_076.htm and the Friends of Tuva website:  http://www.fotuva.org/online/frameload.htm?/online/stamp.html.  Be sure to obtain this stamp before 08 January 2006, when postage rates increase.

24 January 2006: Bill Colson (Morgan Park HS, math)               Handouts
Bill passed around the article Secret Science in Art by Josie Glausiusz, which appeared in the December 2005 issue of Discover Magazinehttp://www.discover.com/issues/dec-05/features/physics-art-matisse-seurat/.  The article contains the following introductory statement:

"Shakespeare, Seurat, and Matisse knew little about physics, but their work is awash in its principles."
Bill also showed us the 08 January 2006 Foxtrot cartoon by Bill Amend, Physicists always lose snowball fightshttp://yodha.livejournal.com/136964.html.  Thanks, Bill.

04 April 2006: Terri Donatello (retired)                          Newspaper Articles
Terri
brought in two recent newspaper articles. In one a team of MIT scientists tried to recreate Archimedes death ray: http://web.mit.edu/2.009/www//experiments/deathray/10_Mythbusters.html. While they did not disprove that it actually happened, they showed that it was unlikely to have worked. A second article was about the current neutrino project at Fermilab (in which IIT is significantly involved). It described a continuing experiment in which neutrinos made at Fermilab sre beamed 450 miles to a detector 0.5 mile below the surface in the Soudan Underground Iron Mine in northern Minnesota:  http://www.dnr.state.mn.us/state_parks/soudan_underground_mine/index.htmlThanks, Terri.

02 May 2006: Porter Johnson (IIT physics)                       Shroud of Turin Project
Porter
learned about a Shroud of Turin Project website from Steve Feld, Editor of  ThinkQuest NYC Newsletter: http://shroud2000.com/LatestNews.htm.  The site is featured on the Landmarks for Schools homepage http://landmark-project.com/index.php.  The website describes scientific investigations on the authenticity of The Shroud of Turin. It gives a link to various English and Greek Language versions of a Biblical eye-witness account in the Gospel of John, Chapter 20, verse 7, in which the shroud of Jesus is specifically mentioned [Online Parallel Biblehttp://bible.cc/john/20-7.htm]. Finally, it provides information to suggest that Leonardo DaVinci may actually have created the shroud, discussing his motivations as well as his capabilities.  A re-creation of a Shroud Image  has recently been done by Stephen Beckman, using a camera obscura -- along with other materials and technology available in Leonardo's era. This Shroud of Turin website is http://shroud2000.com/LatestNews.htm.  The website merely presents the information, allowing visitors to the website to express their own opinions on this subject.  The results of an online poll are presented.  The project provides an excellent example of Scientific Inquiry! Thanks.