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Sink or Float? Thought Problems in Math and Physics

Keith Kendig
Mathematical Association of America
Publication Date: 
Number of Pages: 
Dolciani Mathematical Expositions 33
[Reviewed by
Sarah Boslaugh
, on

Sink or Float? is an entertaining collection of math and physics puzzlers with a serious aim: to encourage people to engage in a type of thinking characteristic of mathematicians working on a problem. These aren’t the kind of problems usually included in textbooks, and you don’t need much of a math or physics education to think productively about them (a high school education will suffice for most), but you do need to be willing to sit and think, and to adopt a mode of inquiry which is foreign to many people but common in mathematics.

My father, a career attorney and judge, said that most of what he learned in law school was not the substance of the law but how to engage in legal reasoning. The situation is the same in many professional fields: learning the content of the field is not the issue so much as learning to adopt those habits of thought which are characteristic of the profession. It is Kendig’s belief that mathematicians approach problems differently from most people, and that many students need help to find and exercise those habits.

A selection of problems from Sink or Float? would be a good addition to many high school or college physics courses (but only if the students are willing to think rather than memorize), and those who already enjoy math will find it a delight as well. The problems have been selected to shake up habitual thinking: their solutions require fresh thinking rather than memorized knowledge, often requiring abandonment of a common misconception or application of a well-known principle or technique in a novel way.

The problems are arranged in ten categories: geometry, numbers, astronomy, Archimedes’ Principle (displacement), probability, classical mechanics, electricity and magnetism, heat and wave phenomena, the leaking tank (problems about flow, whether of liquid, heat, or electrons), and linear algebra. There’s also an introductory section with problems drawn from many fields. The problems look simple but most are not: there’s no heavy-duty calculations required, but you do have to apply what you already know, frequently in a way you never expected. Fortunately, solutions and detailed explanations are supplied for all problems: many will leave you slapping your head and saying “Now why didn’t I think of that!”

Keith Kendig is Professor of Mathematics at Cleveland State University. His mathematical interests include classical algebraic geometry and applied math. He received the Lester R. Ford Prize of the Mathematical Association of America for his 2001 article "Is a 2000-Year-Old Formula Still Keeping Some Secrets?” His book on Conics was published in 2005 in the MAA's Dolciani series.

Sarah Boslaugh ( is a Performance Review Analyst for BJC HealthCare and an Adjunct Instructor in the Washington University School of Medicine, both in St. Louis, MO. Her books include An Intermediate Guide to SPSS Programming: Using Syntax for Data Management (Sage, 2004), Secondary Data Sources for Public Health: A Practical Guide (Cambridge, 2007), and Statistics in a Nutshell (O'Reilly, forthcoming), and she served as Editor-in-Chief for The Encyclopedia of Epidemiology (Sage, 2008).


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