200 Puzzling Physics Problems is a beautiful collection that provides challenges to every physics or mathematics lover, from the very capable high school student to the curious professor. Some of the problems of this book were invented for Hungarian high school and college-level competitions or for the Cambridge Colleges entrance examination, others were inspired by International Physics Olympiad problems. However, the majority of the problems are the evolutionary products of the works and influences of the "international ideas-market," where the authors played an active role for decades. Peter Gnädig and Gyula Honyek have trained physicists and physics teachers at Roland Eötvös University in Budapest, lead the Hungarian team in International Physics Olympiads, and edited the physics section of the prestigious 100-year-old Hungarian Mathematical and Physical Journal for Secondary Schools. Currently Dr. Honyek teaches at one of the strongest college preparatory demonstration schools in Hungary. Ken Riley has lectured in Cavendish Laboratory, Cambridge, worked as researcher at the Rutherford Laboratory and Stanford, and has served on many committees concerned with physics and mathematics education at various levels. He is currently a Senior Tutor at Clare College.
Why should a mathematician care to read this book? Mainly, because it is rich in creative and inspiring approaches, following the best traditions of the problem solving literature. The solutions are elegant and pleasing. Even for problems that could be solved via routine techniques, insightful new approaches are suggested, emphasizing the fundamental concepts both in physics and mathematics. Many of these solutions are what Paul Erdös might have characterized as the "Book proofs." For example, the use of symmetry and reasonable estimations, the appropriate choice of variables or coordinates, and the investigation of extreme values are common tools. There are seamless transitions between the basic principles of mathematics and physics.
Just to give a taste of the delights awaiting the readers, here are a few topics of investigation:
- How far below ground must the water cavity that feeds Old Faithful be?
- What is the shape of the water bell in an ornamental fountain?
- What would be the high-jump record on the Moon?
- How long would it take to defrost an 8-ton Siberian mammoth?
- What is the minimum take-off speed of a grasshopper that jumps over a tree trunk?
- If all the sides of an n-dimensional cube are made of 1- resistors, what is the equivalent resistance of the cube between the two endpoints of one of its body diagonals?
- How 'deep' is an electron lying in a box?
These problems can provide excellent context for the investigation and use of conic sections, exponential and trigonometric functions, vectors, continued fractions, differentiation, integration, characterization of curves, and to many more mathematical ideas.
The book should be an essential reading for mathematics and physics competitors and their trainers from high school-level competitions to advanced mathematical modeling, and should be available in the libraries of all people who enjoy mental challenges and have curious minds.
Agnes Tuska (firstname.lastname@example.org) is associate professor of mathematics at California State University, Fresno. Her special interests are teacher education and the history of mathematics.