The Thirteen Books of the Elements, Vol. 1: Books 1-2 Review

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(More customer reviews)At the time of this writing, the sales summary points out "Vol. 1", but it does not point out that it is "Volume 1 of 3". Volume 1 provides a historical summary of work that followed _Elements_, along with a detailed translation of Book I and Book II. Heath includes bracketed references to justify each critical step of each proof. The text surrounding each Euclidean statement is detailed, but often very lengthy; at times, this detracts from the reading of the _Elements_ itself. This set is for the scholar of the history of _Elements_, and not the best source for a first-time reading of Euclid. Even with these minor quibbles, however, my copy of Volume I is a well-worn, beloved volume with frequently-annotated margins. All of the major "players" in the development of Geometry are detailed within, as well as their contributions.
I recommend it highly for any scholar that wishes to understand _Elements_ thoroughly, through a close reading of a detailed text.

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Volume 1 of 3-volume set containing complete English text of all 13 books of the Elements plus critical apparatus analyzing each definition, postulate, and proposition in great detail. Covers textual and linguistic matters; mathematical analyses of Euclid's ideas; commentators; refutations, supports, extrapolations, reinterpretations and historical notes. Vol. 1 includes Introduction, Books 1-2: Triangles, rectangles.

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A Beginner's Guide to Constructing the Universe: Mathematical Archetypes of Nature, Art, and Science Review

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(More customer reviews)This is a very well written book that relates some basic concepts in geometry to science, architecture and life. Each of the ten chapters is about a geometric shape and Mr. Schneider shows how to construct it using only compass and straight-edge. The author begins every construction from a circle, and every line is shown as the intersection of two or more circles. This is consistent with his assertion in Chapter One that the circle is Unity, but I believe it is also more accurate geometrically.
Mr. Schneider gets into the Platonic Solids, explains the golden section and its use in architecture and nature, shows the regularity in nature and a lot more. This is a very educational book that covers a lot of ground, and does so in an entertaining way.
What I really like about the book is the author's ability to bring geometry to life. There are many diagrams, drawings and pictures which make it easy to follow the text.
The book is written for the layman, not the mathematician. If you are looking for a more rigorous introduction to geometry, try reading H.M.S. Coxeter (if you can!).
This book would be a nice companion to "The Power of Limits" by Doczi, 'The Geometry of Art and Life" by Ghyka, and "The Divine Proportion" by Huntley.
If I had to recommend only one book about geometry for the average reader, this book would be my first choice.

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Zero: The Biography of a Dangerous Idea Review

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(More customer reviews)I've recently read both Charles Seife's "Zero:The Biography of a Dangerous Idea" and Robert Kaplan's "The Nothing That Is: A Natural History of Zero." They are at the same time very similar and very different. They each follow an almost identical line, presenting the evolution of zero chronologically, and they each make almost identical stops along the way. The difference is in how they treat the steps in zero's evolution which is conditioned by their differing metaphysical views. An illuminating example is how they each treat Aristotle's role in zero's history.
Charles Seife, from the beginning, reifies zero: the author accepts the misconception that zero is some sort of actually existing mystical force resting at the center of black holes. He doesn't step back to take a look at the concept as concept. Nor does he appear to keep in mind that mathematics is the science of measurement, or that time is not a force or dimension, but merely a measurement of motion. This distorts his perspective, from which he attempts to refute Aristotle's refutation of the existence of the void: for Seife, zero exists and is a force in and of itself. In Seife's hands, zero certainly is a dangerous idea!
Robert Kaplan, on the other hand, delves deeper. His work is informed by an obvious love for history and classic literature, and while this results in many obscure literary asides, one feels that this book takes part in the Great Conversation. As a result he steps back and takes a critical look at the true meaning and usefulness of the concept as a concept. Is zero a number? Is it noun, adjective, or verb? Does it actually exist outside of conceptual consciousness or is it exclusively a tool of the mind?
Both authors follow zero's role in the development of algebra and the calculus. As a math "infant", this reader, having read Seife's book first, found that the explanations of these two developments by Kaplan cleared away the haze, which Seife's book was unable to do. I found both books to be illuminating. Seife's book contains much valuable historical information. He did his homework. If one were to read only this book on the subject, one would have learned a great deal about the history of mathematics. But if I were to have to choose one to recommend, it would be Kaplan's book. It is more informed, more seasoned, more honestly inductive in its approach.

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