|
If you like to notice more around you, astound your friends, you should read such books, as there is more beauty around you than what you just see. Let us look at some examples in the book "The joy of mathematics": - earthquakes and logarithms- connection lies in the method to calculate earthquakes' magnitudes by means of Richter scale, which is logarithmic, - the catenary & the parabolic curves- who takes as an obvious phenomena- the Golden Gate Bridge in San Francisco- it looks gorgeous, but what it looks like is connected with construction equations, which contribute to the fundamental thing, that it really is invulnerable and cannot be destroyed by the mass itself, as well as additional natural forces.
These factors cannot be separated, as at first you have to do more than just look around, but you have to have a beautiful mind of a child and be an intellectualist at the same time, not just to take things for granted, but as a child be curious and ask questions and finally as an intellectualist and mathematician find answers to them.Yet, there is more to it. My appreciation for Theoni Pappas is enormous as for an observer and admirer of the world around her and mathematician.
Most people associate mathematics as calculating especially money, yet in mathematics the theory models or formula are created, and it occurs that they find application in our material world sometimes even centuries afterwards. It is so, as the author popularizes mathematics.
She answers the basic questions about role of mathematics in our lives. Even Galileo noticed the curve to be parabola, - Thales & the Great Pyramid- Egiptians' calculations of the height of a pyramid were based on shadows and similar triangles, -the Dome of Milan -Gothic plans incorporating the application of geometry and symmetry in architecture, and lots of stuff like that.
if the discoverable arithmetic of the everyday natural world interests you, try this; and then you may want to explore her other work along this line.
This book allows you to sample many, many ideas without feeling overwhelmed by details you may not understand. But the idea originated from the overview in the book.
It is meant to touch on many mathematical ideas, not to go into depth on any one idea. My son read this at age 8, then at 10, and again at 12 - getting something more out of it every time.
The widely divergent reviews reflect a lack of understanding of the purpose of this book. What I consistently found myself doing is researching from the internet and other print resources.
Many of the ideas intrigued and inspired him to seek out more information on his own, to research and understand more deeply. For that purpose, it deserves the highest rating.I did not give 5 stars because there are some instances where I did find errors, these do not detract from the purpose of the book, but they are annoying to those of us who try to delve deeper.
Many recreational mathematics books are inaccessible to beginners or math phobes. If you want details, you go explore the world opened up by the book.
It appears that the author could not make up her mind wether this was to be a "math tricks" book or a "popular mathematics" presentation substantiated by theory. Sorry to say but this book is a dud. There are many other excellent books that are more fulfilling. While the concept of presenting interesting mathematical facts is great the presentation is so brief, so wrought with errors, and so incomplete that the work is not worth perusing. Some of the "chapters" have answers at the back of the book and some do not. Journey Through Genius comes to mind. All in all a disappointing work.
This book gives the non-expert reader the impression that he or she is learning something, but a great deal of the time this is just the illusion of learning.I will list a few of the errors and illusory learning that I can readily find:________p. 18: It is mentioned that pi cannot be the solution of an algebraic equation with integral coefficients, but there is no discussion in the book of what such an equation is.__________p. (They can be constructed in 3 dimensions). 45: The Klein bottle is discussed and illustrated here, but there is no mention that a genuine Klein bottle cannot be constructed in ordinary 3-dimensional space. Twistors are mentioned but not defined, even in a rough, metaphoric way -- just not at all.________p.
(The familiar model of a Klein bottle depicted here is a self-intersecting version of the real Klein bottle, which does not intersect itself. All mathematical concepts are real within mathematics, and do not exist (except as approximations) in the real world.It's a worthwhile topic in the philosophy of mathematics, and could well have been introduced in this book, but it has nothing whatsoever to do with fractals per se.________p. 91: Here the author attempts to describe a model of hyperbolic geometry (in a circular disk) devised by Henri Poincaré. This phenomenon occurs for a bowl whose cross-section is an *inverted* cycloid, but that is omitted.________p.
7: It is stated that when marbles are released in a cycloid-shaped container, they will reach the bottom at the same time. All the illustrations appear to be low-quality xerographic copies from other books (clearly used without any permissions).But worst of all, the book is chock full of misstatements, misconceptions, and sentences that don't convey any meaning. The halves are erroneously shown as identical, but they should be mirror images of each other.________p. Sadly these are often not the case with this book.Rather, this book gives every sign of being essentially copied from bits of many dozens of other books. (The author neglects to mention that the faces of such a solid must be *regular* polygons).________p. 13: Both the "impossible tribar" and "Hyzer's optical illusion" are NOT mathematically impossible, contrary to what is written.
96: Here it is stated that it has been proved that knots cannot exist in more than 3 dimensions. Not only should the correct number be 6/(pi * pi), but the idea of randomly choosing an integer is left completely undiscussed, although there is no known way to do this. This book could have been good if the author had done a careful job of writing the text, and perhaps if the illustrations were original, and above all if the author had understood the material she was writing about. This is much like the fact that a picture of a knot drawn in the plane must appear as if the knot intersects itself, though it does not do so in space).________p. 46: The illustration at bottom purports to show what the model of the Klein bottle would look like if it were sliced in half.
78: The title of this page is "Fractals -- real or imaginary."This is an entirely misguided question that will only confuse the reader.
________p.
Apparently the author is unfamiliar with an extensive and thriving field of higher-dimensional knots.
6: The illustration of the cycloid curve should show it to be in a vertical direction where one arch meets another; instead it is at 45 degrees to the vertical.________p.
(For example, a sphere can be knotted in 4-dimensional space).________There are many, many more such gaffes, but I fear I have gone on too long.
19: Also, it is stated that the probability of two randomly chosen integers' being relatively prime is 6/pi.
38: The Platonic solids (aka regular polyhedra) are discussed here, but although they are defined twice, neither definition is correct.
However, she gets it exactly backwards, saying that objects get smaller as they approach the boundary of the disk.(She may have been well-aware of how this model works, but her prose is at best completely ambiguous).________p.
I just wanted to make it crystal-clear that this book is riddled with erroneous and vacuous statements.
|
