Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace

This is a very good book, much better than I expected. I thought it would be more like a college mathematics text book. Instead it is more like a novel. It is very readable and the subjects flow smoothly from one to another. I found the reading enjoyable and it kept my interest from one chapter to the next. Most of it is not too technical or abstract so it should be understandable to the general public. There are, however, a few sections on math and physics theory that are difficult to comprehend. Those sections kept me alert and added interest to the book. I have a BS degree in mathematics and now I have a new perspective on the classes I took in college. The title of the book is OK, but it does not describe all of the content. There is much more such as the role of prominent men and women and their influence on geometry and mathematics on world history. The Epilogue at the end is very, very good, the best I have ever read.

"Euclid's Window" traces the roots of particle physics, from the initial geometric work of the ancient Greeks, to Descartes attaching algebra to geometry, to Gauss and Riemann realizing that space need not be flat, to Einstein applying these ideas in the theories of relativity, to the particle physics and string theory as we know it today. These are just a few of the mathematicians and scientists discussed. The book is not a history of geometry as the subtitle suggests, as Mlodinow only takes the parts that are relevant to the current physics-based explanation of the world (membrane theory) and the quest for a grand unified theory and how geometry fits into it. The story along the way is very engaging and entertaining, revealing both the life and times of the people that invented the various theories we use today, as well as lucidly explaining the theories themselves (even string theory). I highly recommend the book for both entertainment value and educational value, though I must qualify this statement: Mlodinow makes a few blunders along the way with dates, fills in some details with his own imagination, and interjects his opinion quite frequently. You might walk away from the book thinking that Ed Witten is the next Einstein (not to discredit Professor Witten, as he has made very important contributions). Mlodinow most noticeably leaves out contributions from the ancient Indians and Chinese, and only briefly mentions the Arabs- basically taking a very Europe- and American-centric point of view...take it or leave it, but I can't help but agree that these are the people that took us from the parallel postulate to quarks, gravitons, and so on. Historical context is cherry-picked to support the anti-Christian and anti-antisemite (basically pro-Jewish) opinions of the author, which isn't to say the points aren't valid. As you will discover in reading the book, Christianity killed (literally) the ancient Greek science, and has impeded the return of logical thought and science ever since.So we don't have complete historic rigor here- I say who cares. Mlodinow has written a story with few geometric sketches and even fewer equations, not a textbook. If you want the usual dry history of "and on April 12, 1652, Hermann von German discovered this phenomena while rowing a boat across a lake," or page after page of equations, then I'm sure there are many other books out there to satisfy your needs. So, take the finer points with a grain of salt (if it sounds too good to be true, it probably is- except for C.F. Gauss) and enjoy the ride of learning about the people behind the math and physics. This is still a great book that I would recommend to those interested in math and/or physics.

I loved this book. This book provides an understanding of the importance of the Greeks in the history of human thought that goes far beyond a mere historical description of what they did. I've known for more than thirty years that the Greeks were the fathers of rational and scientific thought (and answered exam questions with a suitably expanded discourse on that theme). But I now have a concrete appreciation for what that means. Mlodinow not only reveals the content of what they thought but also connects their discoveries and theories to later events. He shows how the foundation is connected to the top story (still under construction). Mlodinow is especially adept at presenting theoretical constructs in a way that is accessible to the non-scientist. His portrayal of the individuals who were responsible for the major steps along the way is characterized by a wry outlook that is effective and that contributes to the story he is telling. This is popular science at its best. A specialist might debate a point or two, but the story that is told here is clear and compelling. tThe author's frequent humorous touches add a note of grace to the subject. Simply put, it's fun to read this book.I highly recommend the book. I think it would be particularly useful as a text for a course in the history of Western thought.

The book is entertaining, and explains science concepts for a everyday life people with a simple language.I am not a science person, but I have a little bit of curiosity to understand some Physics concepts with out the deep knowledge of math.

This is a history of the development of geometric thought. It focuses on key figures like Euclid, Descartes, Gauss, Reimann and Einstein. It shows how Gauss's realization that Euclid's model of space was only one possible model and how that insight changed mathematics and then physics. Einstein couldn't have explained relativity if Reimann hadn't already created an appropriate geometry for extratresteral space. I wish there were a few more illustrations, but that's a nit. The author, Mlodinow, was trained as a mathematician and then evolved into a Hollywood writer (Startrek, etc) and this shows in his lively writing style. A very good read for someone who want's to know about the role of modern geomentry in today's intellectual world. (No real math background is required to read this book -- its history book, not mathematics text.)

Interesting breakdown of the history

ho detto tutto nel titolo sopra scritto

Fascinating!

Fantastic exposition of the progress of geometry over the centuries.

Fantastic Read !! Worth buying !!I kept this book in my Amazon wish list for almost 3 months and then purchase. I wanted to be absolutely sure what I am buying and whether I really know the background of it. For lay man, it is great; no mathematical equations into it. For physicist it just a read, I won't say it is a disappointment. The book concentrates on 4 areas: (1) Euclidean development of geometry (2) Cartesian thought on the development of co-ordinate geometry and analytical geometry (3) Einstein's idea of spacetime and the geometry of curvature, including Gauss and Riemann (4) The story of Edward Witten and string theory, geometry of CalbiYau manifold.If you consider the last phase, which is string theory, it was not required as the structure of geometry in string theory is not much explained as we even now do not have a very clear idea on the topology of string theory.The first development of geometry from Thales of Miletus to Pythagoras and then to Euclid's "Elements" are great.(1) You won't feel bored(2) The characters are living(3) Lucid and clear information on the scientific theoriesObviously, this kind of a book is devoid of any equations except g11 or such things...............Well, that make things tougher for us. Anyway, the author has used humor very effectively and some great stories. The development of Cartesian thought has been explained in details. The short life of Gauss and Riemann's contribution in making the metric tensor. Well, for this kind of complex mathematics, English words fall short of that. You cannot understand internal and extrinsic curvature, Gaussian curvature with just reading...............No, that is not possible. Truly speaking, from "Story of Einstein", things become really tough, if you are really looking for a better understanding. These are topic of topology and tensor analysis.The last part was not really worth mentioning. I think the author has mentioned it just to keep the reader updated with topics like String and M-Theory.As a whole, the book remains focused in the central topic -- The evolution of geometry through the history.For me it is a good read, but not much into the intricate details as the mathematical concepts remain vague. Indeed that is not the objective of the author.I would suggest, to go through the book of E.T. Bell's "Men of mathematics". It covers much more into Poincare, Riemann, Gauss and dedicates exclusive chapter to it - both life and their works.I would strongly recommend to buy this book and go through this journey of the development of geometry through ages.