Five Equations that Changed the World: The Power and Poetry of Mathematics [Paperback]

Michael Guillen (Author)

Book Description

ISBN-10: 0786881879 | ISBN-13: 978-0786881871 | Publication Date: August 29, 1996

The science expert on Good Morning America offers an entertaining and informative survey of the five mathematical equations with the greatest impact on modern times. Reprint. PW.

Editorial Reviews

From Publishers Weekly

Harvard mathematician Guillen looks at five mathematical breakthroughs and the theorists behind them, among them Isaac Newton and Albert Einstein.
Copyright 1996 Reed Business Information, Inc.

From Library Journal

Guillen, an instructor in physics and mathematics at Harvard, devotes this work to discussions of five significant equations in physics and the individuals who developed them. The individuals are Issac Newton (universal gravitation), Daniel Bernoulli (hydrodynamic pressure), Michael Faraday (thermodynamics), Rudolf Clausius (thermodynamics), and Albert Einstein (special relativity). Guillen sets their work in the context of the science of their times with accounts that are obviously fictionalized, containing many purported conversations and private thoughts of the physicists in question. The prose is quite purplish in places, and the matters of fact and interpretation are often questionable if not outright wrong. Not recommended for most libraries.?Jack W. Weigel, Univ. of Michigan Lib., Ann Arbor
Copyright 1995 Reed Business Information, Inc. --This text refers to an out of print or unavailable edition of this title.

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Product Details

• Paperback: 288 pages
• Publisher: Hyperion (August 29, 1996)
• Language: English
• ISBN-10: 0786881879
• ISBN-13: 978-0786881871
• Product Dimensions: 9.2 x 6.7 x 0.7 inches
• Shipping Weight: 10.4 ounces (View shipping rates and policies)
• Average Customer Review: 3.9 out of 5 stars  See all reviews (43 customer reviews)
• Amazon Best Sellers Rank: #132,331 in Books (See Top 100 in Books)

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44 of 47 people found the following review helpful:

4.0 out of 5 stars The poetry of equations --, February 15, 2002

By 

V. N. Dvornychenko (Rockville, MD) - See all my reviews
(REAL NAME)   

This review is from: Five Equations that Changed the World: The Power and Poetry of Mathematics (Paperback)

You might characterize this book along the lines of "an opera book for people who think they don't like opera." The author, Dr. Michael Guillen, sets himself the formidable task of instilling into non-mathematicians an appreciation of the beauty and glory of mathematical equations. His approach is to take five historical figures, give a brief biography of each, select an equation best encapsulating their accomplishments, and explain this equation's relevance for contemporary society. The figures selected are Isaac Newton, Daniel Bernoulli, Michael Faraday, Rudolph Clausius, and Albert Einstein.

Is his format a good choice? Yes, perhaps among the best. Are the historical figures good choices? Yes again; but here one might quibble a bit: all the figures selected are male physicists who lived during the approximately 300-year time-span, 1640-1950. Were there no important equations prior to this? What about the Pythagorean theorem? Euclid's proof of the infinity of primes? Archimedes's formula for pi? The delFerro-Tartaglia-Cardano equations for the cubic? What about women?

Is his approach successful? Generally speaking, yes. It is not clear what readership Guillen has in mind. At first I though it might be your typical Scientific American reader. But the biographies tend toward a Horatio-Alger style, suggesting a younger audience.

Dr. Guillen's unique talent is his understanding of the relationship between religion and science. Although he treats the subject only briefly, I have never seen a better exposition in readily accessible material. As Guillen points out, this relationship has not always been favorable to religion. A comparison with the proverbial ingrate camel comes to mind: having inveigled its nose into the tent, the camel proceeds to evict the original tenants. This process began with Plato's plea that science be allowed to investigate the celestial realm (at that time considered the province of the gods), and ended with Laplace's claim he had no need of the "God hypothesis."

Although I liked the book as a whole and applaud Dr. Guillan's effort, the book is unfortunately marred by some careless and misleading passages. I cite some in the hope these might be corrected in a future edition.

Page 58: "...a giant titanium bullet" - the Apollo capsule was made mainly of aluminum, not titanium.

Page 61: "As the rocket thundered its way to the clouds it began to spin like a bullet" - not so! Small rockets are sometimes "spin stabilized," but never large rockets like Apollo.

Page 61: "... the spaceship started to speed up ...the astronaut's had reached the point at which the moon's gravity was stronger than the earth's" - because the moon is a moving target, the minimum spacecraft speed along the trajectory does not occur at the point where the two gravities cancel.

Page 137: "He discovered that the force between [two magnets] diminished with the square of their separation" - Magnets always have two poles, so the force between them is complicated. For large separations the force diminished with the fourth-power of the separation.

Page 259: " ... letting out a hundred billion times more energy than one could ever get from ordinary, old-fashioned combustion" - the ratio is more like ten million.

26 of 26 people found the following review helpful:

5.0 out of 5 stars masterfully presented, February 15, 2008

By 

Michael R. Chernick "statman31147" (Holland PA) - See all my reviews
(REAL NAME)   

This review is from: Five Equations That Changed the World: The Power and Poetry of Mathematics (Hardcover)

Michael Guillen has chosen five famous mathematician to describe. The theme for discussing the particular person is that he discovered an equation that changed the world. Each deals with a result in Physics. One could argue that others could be added to the list but there is no question that these are certainly all contenders for the top five. Guillen is a science editor for ABC and is a professor of physics and methematics. This combination makes him well suited to choose the equations and to describe the results and the men behind them to a layman. The five equations and their authors are 1) F=GxMxm/d^2 Newton and the Law of Universal Gravitation, 2) P+rhox 1/2 nu^2 =CONSTANT, Daniel Bernoulli and the Law of Hydrodynamic Pressure, 3)DelXE=-dB/dt, Michael Faraday and the law of electromagnetic induction, 4) Delta S universe > 0, Rudoph Clausius and the second law of thermodynamics and 5) E=mxC^2, Einstein and the special theory of relativity. I am sure we all expected 1 and 5 and depending on your knowledge of physics, the others may or may not be a bit of a surprise. Guillen spends a lot of pages describing the nature of the equation, the character of the inventor and the impact of the results on society (sometimes centuries later). Newton's laws were instrumental in developing guidance and tracking systems for artificial satellites, space shuttles and other objects launched into space in the 20th Century. Our landing on the moon would not have been possible without Newton's laws. This makes for interesting reading for anyone interested in mathematics or science. A good book for teenagers to read to develop motivation to study math and science and to aspire for a career as a scientist.

47 of 51 people found the following review helpful:

3.0 out of 5 stars Engaging, Optimistic and Sloppy, March 13, 2003

By 

Joel M. Kauffman (Berwyn, PA United States) - See all my reviews
(REAL NAME)   

This review is from: Five Equations That Changed the World: The Power and Poetry of Mathematics (Hardcover)

Delightfully written, easy to follow, Guillen describes the personal situations and scientific context of Newton's Law of Gravitation, Bernoulli's Law of Hydrodynamic Pressure, Faraday's Law of Electromagnetic Induction, Clausius's Second Law of Thermodynamics, and Einstein's Theory of Special Relativity (the equivalence of mass and energy).

As is the recent custom outside of textbooks, Guillen has given an exceptional amount of personal detail, letting us be amazed once more about how much these five scientists achieved despite personal situations that varied from ordinary to awful. Furthermore, the resistance from other scientists of their times is still surprising to some of us, while the resistance of the Catholic Church is not.

Guillen's efforts to provide clear explanations for the discoveries mostly succeed, least well for Clausius's Second Law of Thermodynamics, in my opinion. Many clever similes are used. A better explanation of the inverted delta in Clerk-Maxwell's equation on Faraday's Law of Electromagnetic Induction is needed. Guillen defines it as "the amount of" (p158), while "the rate of change" might be better. The math does not go beyond high school algebra, with that one exception, so the mathematically challenged such as this reviewer need not fear.

What is very disappointing is the number of errors:

1. On p27 globes are said to 2-dimensional, when they are actually 3-dimensional; circles are 2-dimensional.

2. On p36 et seq planetary motion around the sun is said to follow oval paths, when the paths are actually elliptical. These are different shapes.

3. On p137 the Leyden jar was said to be the forerunner of the modern battery. In fact is was the ancestor of the modern capacitor.

4. On p139 Volta's piles were said to provide more current the higher the pile, meaning the more plates). In fact, more plates gave more voltage, not more current. The two terms are not interchangeable. The piles were said to be the ancestor of today's storage batteries, while, in fact, they were the precursor of today's "dry" cells, which are not rechargeable.

5. On p158 the general term "electricity" was used instead of the proper term "voltage" (E).

6. On p162 a perpetual motion machine seems to be described inadvertently by the supposed possibility of using an electric motor to spin a dynamo that, in turn, powers the motor. This is not possible, of course.

7. On p163 the term "current" is used instead of "voltage"; these have never been interchangeable. The current is the number of electrons passing a certain point per second, while voltage is the unit of electrical pressure.

8. On p163 the term "heat" is used instead of "temperature". Thermometers measure temperature; calorimeters measure heat.

9. On p187 there seems to be total confusion between heat capacity and conduction. The apple filling in a pie is mostly water which has high heat capacity and good conduction, so it is easy to be burned on hot filling. The crust is mostly carbohydrate with air pockets, almost a foam, and the combination of low heat content at a given temperature and poor conduction makes it harder to be burned by the hot crust.

10. On p246 the speed of light was said to be constant. This should have been qualified from the start as being in a vacuum, as was done from p248 et seq.

11. The gross structure of the atom was worked out by Ernest Rutherford et al. in 1911 by bombarding gold foil with a beam of alpha particles from radium, not in the 1930s with "atom smashers" (particle accelerators), p258.

12. Einstein's 1921 Nobel Prize in Physics was for his discovery of the photoelectric effect, not for quantum mechanics (p259), which Einstein never even accepted!

Other Amazon.com reviewers found other mistakes as well.