Lion Hunting and Other Mathematical Pursuits: A Collection of Mathematics, Verse, and Stories by the Late Ralph P. Boas, Jr

Overview

Memorabilia, mathematical articles, poems, and reflections by a distinguished mathematical expositor.

In the famous paper of 1938, "A Contribution to the Mathematical Theory of Big Game Hunting," written by Ralph Boas along with Frank Smithies, using the pseudonym H.W.O. Pétard, Boas describes sixteen methods for hunting a lion. This marvelous collection of Boas memorabilia contains not only the original article, but also several additional articles, as late as 1985, giving many...

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Overview

Memorabilia, mathematical articles, poems, and reflections by a distinguished mathematical expositor.

In the famous paper of 1938, "A Contribution to the Mathematical Theory of Big Game Hunting," written by Ralph Boas along with Frank Smithies, using the pseudonym H.W.O. Pétard, Boas describes sixteen methods for hunting a lion. This marvelous collection of Boas memorabilia contains not only the original article, but also several additional articles, as late as 1985, giving many further methods. This collection covers a range of topics. It includes articles on infinite series, the mean value theorem, indeterminate forms, complex variables, inverse functions, extremal problems for polynomials, and more.

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Editorial Reviews

The Mathematics Teacher
"If you are one who believes that all mathematicians are off in a world by themselves and not regular people-read this book.
If you enjoy reading light, humorous vignettes about famous people-read this book.
If you like the short, humorous poetry of Ogden Nash or the snappy observations of Dorothy Parker-read this book.
If you just plain like mathematics- read this book!
This tribute to Ralph Philip Boas, a fine mathematician, also shares with the reader a much broader profile of a man who contributed to the mathematics community as editor, teacher, administrator, and insightful humorist. Included are many of his lighter mathematical papers, along with verse, stories, anecdotes, and recollections of his interactions with the most prominent mathematicians of 1930 to 1985. Perhaps the most important feature of this books is how it subtly makes the reader aware of the nature of mathematics... I highly recommend Lion Hunting and Other Mathematical Pursuits to high school mathematics clubs, mathematics teachers of all levels, and anyone interested in mathematics. The reader will want to red the book to find out what lion hunting has to do with mathematics!"
Booknews
Light mathematical papers, poems, stories, and anecdotes written by the late Boas during his long career as an author, editor, teacher, administrator, and lover of literature. Also includes many photographs of him and people and places he touches on. Of interest to students and teachers of mathematics. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780883853238
  • Publisher: Mathematical Association of America
  • Publication date: 9/28/1996
  • Series: Dolciani Mathematical Expositions Series , #15
  • Pages: 320
  • Product dimensions: 6.20 (w) x 9.20 (h) x 0.60 (d)

Read an Excerpt

Section 1
Lion Hunting
As explained in the reminiscence of Frank Smithies earlier and in the autobiographical essay by Boas himself, the collection of methods for catching a lion that they published under the pseudonym, H. Petard, appeared in the American Mathematical Monthly in 1938. As is evident from the other articles in this section, the idea prompted a good many others to add to this literature. We include those articles of which we are aware- we make no claim that this is a complete compendium of contributions to this area of mathematics. A Contribution to the Mathematical Theory of Big Game Hunting*
H. Petard

Princeton, New Jersey

   This little known mathematical discipline has not, of recent years, received in the literature the attention which, in our opinion, it deserves. In the present paper we present some algorithms which, it is hoped, may be of interest to other workers in the field. Neglecting the more obviously trivial methods, we shall confine our attention to those which involve significant applications of ideas familiar to mathematicians and physicists.
   The present time is particularly fitting for the preparation of an account of the subject, since recent advances both in pure mathematics and in theoretical physics have made available powerful tools whose very existence was unsuspected by earlier investigators. At the same time, some of the more elegant classical methods acquire new significance in the light of modern discoveries. Like many other branches of knowledge to which mathematical techniques have been applied in recent years, the Mathematical Theory of Big Game Hunting has a singularly happy unifying effect on the most diverse branches of the exact sciences.
   For the sake of simplicity of statement, we shall confine our attention to Lions (Felis leo) whose habitat is the Sahara Desert. The methods which we shall enumerate will easily be seen to be applicable, with obvious formal modifications, to other carnivores and to other portions of the globe. The paper is divided into three parts, which draw their material respectively from mathematics, theoretical physics, and experimental physics.
   The author desires to acknowledge his indebtedness to the Trival Club of St. John's College, Cambridge, England; to the M.I.T. chapter of the Society for Useless Research; to the F.o.P., of Princeton University; and to numerous individual contributors, known and unknown, conscious and unconscious. 1. Mathematical Methods
The Hilbert, or Axiomatic Method. We place a locked cage at a given point of the desert. We then introduce the following logical system.
Axiom I. The class of lions in the Sahara Desert is non-void.
Axiom II. If there is a lion in the Sahara Desert, there is a lion in the cage.
Rule of Procedure. If p is a theorem, and "p implies q" is a theorem, then q is a theorem.
Theorem 1. There is a lion in the cage.

2. The Method of Inversive Geometry. We place a spherical cage in the desert, enter it, and lock it. We perform an inversion with respect to the cage. The lion is then in the interior of the cage, and we are outside. 3. The Method of Projective Geometry. Without loss of generality, we may regard the Sahara Desert as a plane. Project the plane into a line, and then project the line into an interior point of the cage. The lion is projected into the same point. 4. The Bolxano-Weierstrass Method. Bisect the desert by a line running N-S. The line is either in the E portion or the W portion; let us suppose him to be in the W portion. Bisect this portion by a line running E-W. The lion is either in the N portion or the S portion; let us suppose him to be in the N portion. We continue this process indefinitely, constructing a sufficiently strong fence about the chosen portion at each step. The diameter of the chosen portions approaches zero, so that the lion is ultimately surrounded by a fence of arbitrarily small perimeter. 5. The "Mengentheoretisch" Method. We observe that the desert is a separable space. It therefore contains an enumerable dense set of points, from which can be extracted a sequence having the lion as limit. We then approach the lion stealthily along this sequence, bearing with us suitable equipment. 6. The Peano Method. Construct, by standard methods, a continuous curve passing through every point of the desert. It has been remarked* that it is possible to traverse such a curve in an arbitrarily short time. Armed with a spear, we traverse the curve in a time shorter than that in which a lion can move his own length. 7. A Topological Method. We observe that a lion has at least the connectivity of the torus. We transport the desert into four-space. It is then possible ** to carry out such a deformation that the lion can be returned to three-space in a knotted condition. He is then helpless.
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Table of Contents

Introduction
Autobiographical Essay by Ralph P. Boas, Jr.

Reminiscences
By Frank Smithies, Harold P. Boas, Deborah Tepper Haimo, and Philip J. Davis

1. Lion Hunting
A Contribution to the Mathematical Theory of Big Game Hunting, by H. Petard
A New Method of Catching a Lion, by I.J. Good
On a Theorem of H. Petard, by Christian Roselius,
Some Modern Mathematical Methods in the Theory of Lion Hunting, by Otto Morphy
Further Techniques in the Theory of Big Game Hunting, by Patricia l. Dudley et al
New Ways to Catch a Lion, by John Barrington
Lion Hunting with Logic, by Houston Euler
A Brief Dictionary of Phrases Used in Mathematical Writing, by H. Petard

2. Infinite Series
Cantilevered Books
Snowfalls and Elephants, Pop Bottles and [Pi]
Distribution of Digits in Integers
Tannery's Theorem
Power Series for Practical Purposes
The Rose Acacia

3. Recollections and Verse I
Anecdotes
Echolalia
Time's Revenges
Prerequisites
Algorithms
Calculators
Limericks
Clerihews

4. The Mean Value Theorem
Travers' Surprises
Who Needs Those Mean-Value Theorems Anyway?

5. Recollections and Verse II
Anecdotes
Announcement of Trivia Mathematica
Nonsense (I. Cloudy Weather on the Increase (News Item), II. Cape Code Song, III Roadside Signs)
The Row Reduction Song
It Couldn't Happen Here (with H.P. Boas)
The Way

6. Indeterminate Forms
Lhospital's Rule without Mean0Value Theorems
Counterexamples to L'Hopital's Rule
Indeterminate Forms Revisited

7. Recollections and Verse III
Anecdotes
Inflation
Editorial Policy
Dialog
The Author and the Editors
Colloquium Lecture
Triolet
Please Fee the Archives
Manuscript Found in a Page Proof

8. Complex Variables
Yet Another Proof of the Fundamental Theorem of Algebra
When Is a C[to the power of x] Function Analytic?
Simplification of Some Contour Integrations (with M.L. Boas)

9. Recollections and Verse IV
Anecdotes
Excelsior!
Pereant
The Assistant Professor Blues
Indignation
An Appreciation of Deans
Computers Are Icumen In
Contempoary Love Song
The BASIC Blues
Hints for Programmers

10. Inverse Functions
Inverse Functions
Inverse Functions and Integration by Parts (with m. Marcus)

11. Recollections and Verse V
Anecdotes
Graffiti Anyone?
Ballade of Old Mathematics
Envoy
Getting Even (I. Dorsenia: The Indirect Insult II. Magic Word)
Spelling Lesson
Naming Things

12. Bourbaki
Bourbaki and Me
Letter to Scientific American
Bourbaki
Sonnet
Game Adjourned

13. The Teaching of Mathematics
"If This Be Treason...,"
Calculus as an Experimental Science
Can We Make Mathematics Intelligible?
Boxing the Chain Rule
Names of Functions: The Problems of Trying for Precision
Does "Holds Water" Hold Water?

14. Polynomials
Extremal Problems for Polynomials
Periodic Entire Functions

15. Literature and Mathematics
1724 Lilliputians
Shakespeare's Twelfth Night II, iii, 25-27 (with R.P. Boas)
What St. Augustine Didn't Say about Mathematicians
The Temptation of Professor McShohat
Sleeper
A Translation of Mayakovsky's "Hymn to Learning"
Camp Butner (1940)
Poets

16. Reviews and Miscellaneous Articles
Are Mathematicians Unnecessary?
Review of The World of Mathematics
Review of The Mathematics of Physics and Chemistry
Review of Printing of Mathematics and Mathematics in Type

Reminiscences by Students
Dale H. Mugler, Carl L. Prather, Antoinette M. Trembinska
Ralph P. Boas, Jr.- Bibliography
Index
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