Volume 16, Number 8 Visit us at augsburg.edu/math/ February 12, 2003 Colloquium Series Dates for Spring, 2003 Puzzle & Problem... Colloquia are held on Wednesdays from 3:40 to 4:40 p.m. in Sci- PUZZLE SECTION: ence 108. Here is the tentative schedule for 2002-2003: Last week’s puzzle was solved by Wed. Feb. 12 David Molnar, St. Olaf College Augsburg students Patrick Martell Wed. Feb. 26 Tracy Bibelnieks, Augsburg College and Hung Nguyen. This week’s Wed. Mar. 12 Laura Chihara, Carleton College puzzle is limited to the 3-D puzzle Wed. Mar. 26 Nick Coult, Matt Haines, & Ken Kaminsky, on this page. Augsburg College PROBLEM SECTION: Wed. Apr. 9 Augsburg Students There have not been any solvers to Wed. Apr. 16 Augsburg Students last week’s “Creamer Game” prob- lem. But, we can wait. This week’s talk: To Infinity... and Beyond! Here is this week’s problem: by David Molnar, St. Olaf College If a chord (see the Figure) is selected at random* on a We normally think of there being just one in- chord finity. For example, when we speak of a limit fixed circle, what as n goes to infinity, there is no need to say is the probability that its length, l, radius which infinity n is going to. There are areas exceeds the radius, of mathematics in which a further distinction r, of the circle? needs to be made. The purpose of this talk is *Take ‘at random’ to mean that the end- to introduce you to the ordinal numbers, points of the chord are uniformly distrib- which include many funky varieties of infin- uted on the circle. David & daughter Ava ity. On the way, you will learn some strate- Send your solutions to the editor at gies which may help you win the game of Hackenbush. [email protected], or drop them in the P & P box just inside Puzzle of the week (3-D) the math suite, SCI 137. Last week’s 3-D puzzle was solved by Regina Hopingardner of the CLASS Of- fice. She found the order, farthest to nearest to be 5, 4, 1, 2, & 3. Below is is available on-line at Augarithms another 3-D puzzle. Your job is to find its hidden message by tricking your eyes augsburg.edu/math/augarithms/. Click on the into bringing the two images to one. The hidden message should then stand out. date you want to see. 3D3D PPuuzzlezzle 3D3D PuzzlePuzzle Mathcartoons.com is a website 3D3D PPuuzzlezzle 3D3D PuzzlePuzzle of old and new math and other cartoons by your editor. Visit at mathcartoons. com, and let us Mathematicians and other Mathematicians and other know what you think. scientists often gather at parties scientists often gather at parties to discuss their disciplines. to discuss their disciplines. Augarithms Short or tall , male or female, Short or tall , male or female, TheBi-weeklyNewsletterof people of science always like to people of science always like to theDepartmentof stand around and talk shop. stand around and talk shop. MathematicsatAugsburgCollege Regardless of how it turns out , Regardless of how it turns out , they in variably remain friends. they in variably remain friends. 2211RiversideAvenue Never a rowdy crowd , they just Never a rowdy crowd , they just Minneapolis,MN55454 like a good argument from time like a good argument from time Editor................................................KenKaminsky [email protected] to time. Kaminsky 2003 to time. Kaminsky 2003 From Dictionary of Mathematician Biography--William Feller Theories* Born July 7, 1906 in Zagreb, Croatia, William Feller was edu- Feigenbaum’s period-doubling cas- cated by private tutors and had no secondary schooling. He cade: Named after its discoverer, entered the University of Zagreb and was awarded his first American physicist Mitchell Jay degree in 1925. His Ph.D. was awarded by the University of Feigenbaum (1944- ), this is a theory Göttingen in 1926. He spent two more years at Göttingen be- about the onset of chaos. fore accepting an appointment from the University of Kiel It hypothesizes that when the forces act- where he worked until 1933. ing on a physical dynamical system are William Feller Because of his Jewish background, Hitler's policies forced changed, a periodic orbit is often re- Feller out of Germany in 1933. He went to Copenhagen until placed by another one close to it which 1934, then he moved to the University of Stockholm where he joined the prob- makes two turns before returning to its ability group. He moved to the USA in 1939 becoming professor of mathematics starting point. This action is repeated at Brown University. resulting in periodic orbits of periods 2, The Nazis had taken over the German mathematical reviewing journal and there 8, 16, 32, ... times as long as the origi- was a need for another such journal to be set up out of their control. Feller became nal. The places where the period the first executive editor of Mathematical Reviews which was set up at this time. doublings occur have successive ratios which are approximately equal to In 1945 Feller accepted a professorship at Cornell university, where he was to FEIGENBAUM’S CONSTANT (See work for five years until being appointed Eugene Professor of Mathematics at below). The Feigenbaum cascade has Princeton in 1950. been observed in hydrodynamic turbu- In addition to significant research in probability theory, Feller's most important lence experiments. work was Introduction to Probability Theory and its Applications (1950-61), a Feigenbaum’s constant: Feigenbaum two volume work which he frequently revised and improved with new approaches, discovered the constant numerically. new examples and new applications. Oscar Lanford later supplied a com- Joseph Doob wrote the following tribute to Feller: puter-assisted proof. Those who knew him personally remember Feller best for his gusto, the pleasure with A constant equal to approximately which he met life, and the excitement with which he drew on his endless fund of 4.6692016 occurring in the iteration of anecdotes about life and its absurdities, particularly the absurdities involving math- many one-dimensional maps. Systems ematics and mathematicians. To listen to him lecture was a unique experience, for no in which the constant appears include one else could lecture with such intense excitement. the logistic map and the Hénon map. Feller received many honours. He was president of the Institute of Mathematical Reference: I. Peterson, The Mathematical statistics and he was a member of the Royal Statistical Society in the UK. He was Tourist (New York, 1988) awarded the 1969 National Medal for Science but died before the presentation. Martha Limber His wife received the medal on his behalf. *Reprinted with permission from Dictionary of Theories, by Jennifer Bothamley, Visible William Feller died January 14, 1970 in New York. Ink, Detroit Article by J J O'Connor and E F Robertson, reprinted with permission Cartoon Corner.