# Review of How to Fall Slower Than Gravity: And Other Everyday (and Not So Everyday) Uses of Mathematics and Physical Reasoning

Princeton University Press, Princeton, NJ, 2018

320 pp., illus. 62 b/w and 4 tables. Trade, $27.95

ISBN: 9780691185026.

The first thing to clear up is the title. As Paul Nahin would know, gravity is an acceleration and not a speed, so strictly one cannot fall slower than it as the adjective “slow” refers to speed and not the rate of change of speed. Now, catchy titles are there to sell books of course and accuracy takes second place, so “How to fall at a slower speed than one would under gravity” although more precise is obviously a clumsy title. However, the book is not all about falling objects. The title springs from one problem about the accretion of a falling mass through moisture that does so with decreased acceleration due its mass increasing. The author is very surprised at this, but this reviewer thinks it follows that if the mass increases by taking on motionless water it will, by the conservation of momentum, accelerate less. An acceleration that is even less if drag is taken into account. Here, the conservation of momentum is another way of saying Newton’s second law of motion, not the kind of momentum conservation found in the collision of balls as here the momentum changes continuously and not through impulse.

Normally, a reviewer will now address the contents and order of the book, but this cannot be done here. The whole book is a rather randomly organised sequence of problems in mathematics and physics. It is a follow up to the book “In Praise of Simple Physics” by the same author that has a similar format. In days of yore, books of mathematical puzzles were very popular and some such as *The Canterbury Puzzles* by Henry Ernest Dudeney published in 1907, or one of the many books by Martin Gardner like *Fads and Fallacies* published in 1952, are now legendary in recreational mathematics circles. These older books only demand a knowledge of very elementary geometry and algebra or even just counting in order to understand the problems and their solution. Paul Nahin’s book needs calculus a lot of the time as well as trigonometry and this restricts the readership. Having myself carefully followed the solutions through, stamina and facility with algebraic calculation is also essential.

Paul Nahin seems to have been stung into action by a *Boston Globe* newspaper article that said “knowing how to solve quadratic equations has no practical value” arguing it was a waste of a child’s time to learn such stuff. References refuting this occur throughout the book; in fact, one could say that the whole book is a successful campaign for the usefulness of all kinds of different mathematics.

Now a word about the writing style. This sometimes lapses into the first person, which is poor and always assumes that the reader is keen to trot along with the train of thought, a train can be long and tortuous and sometimes difficult. This reviewer sometimes found this annoying and over presumptuous. One has to conclude that the book is targeted at the undergraduate physics, mathematics or engineering student who likes solving practical problems, the solution of which involve the usually surprising use of mathematics, and in some sense is happy to be herded along the path dictated by the author. Having said this, no doubt Paul Nahin has put a lot of hard work into this book. Some of the problems are difficult, yet the solutions are always meticulously derived and clearly presented.

In summary, this is a collection of problems with commentary and detailed solution provided in every case. This reviewer is still not clear what the target audience is for this book, and it does in a few places come across as a little self-indulgent. Obviously, the problems here are those enjoyed by the author, perhaps there are enough like-minded individuals out there to enjoy them too. On balance, this reviewer counts himself amongst them.