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

3.87 of 5 stars 3.87  ·  rating details  ·  661 ratings  ·  85 reviews
Through Euclid's Window Leonard Mlodinow brilliantly and delightfully leads us on a journey through five revolutions in geometry, from the Greek concept of parallel lines to the latest notions of hyperspace. Here is an altogether new, refreshing, alternative history of math revealing how simple questions anyone might ask about space -- in the living room or in some other g...more
Paperback, 308 pages
Published April 9th 2002 by Free Press (first published 2001)
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I’ve done what I never do – before starting this review I’ve read some of the other reviews on this site. I’m quite surprised at the negative reviews this book has received. Someone has even complained that this is quite an ‘anti-Christian’ book. I guess this is because the author was clearly less than impressed with the ‘Dark Ages’ which he introduces by discussing Hypatia. So, yes, I can understand why that might annoy a Christian. But this would be like a Marxist complaining when people menti...more
Euclid's Window is an unremarkable tour of a very specific line of reasoning that is neither refreshing nor fleshed out. The narrative is supposed to span the progress of ideas coming from the advent of space as a notion to modern multidimensional brane theory but the path drawn by the author is not clear.

Writing - The writing itself is fine. The prose is concise, the jokes are acceptable, and the anecdotes are quaint. Definitions are usually good with periodic reminders.

Organization - Strictly...more
History of math more than actualfacts math, with a minimally annoying authorial voice as these things go. Except for the teeny weeny culture/race centrism problem – I’m neither a historian nor a mathematician, but even I know it’s pretty freaking suspect when your history doesn’t include the advancements of, um, the Arab world, the South/Central American empires, or, you know, Asia, except for that one paragraph that one time. I mean, write a history of European geometry, by all means, I did lik...more
An extremely poor approach to the historical development of mathematics. The book is replete with historical inaccuracies and a clear anti-Christian bias throughout. Try Kline's "Mathematics for the Nonmathematician" instead.
Interesting discussion of history of geometry from the time of the ancient Greeks through geometry's role today in String Theory and M-Theory. It covers what it considers to be the major events of the history of geometry, starting with Euclid's organizing Greek knowledge of geometry into the Elements, Descartes bringing the coordinate system to geometry, Gauss and Riemann moving geometry beyond Euclidean space, Einstein with his theory of relativity, and finally Ed Witten and his contributions t...more
Book was great from the beginning with small stories that engage and keep you interested. When the book goes further on it takes too much time to describe Einstein and String Theory and moves too slowly. Half the book is the history of geometry, the other half is Einstein. It turned me off at the end.
Firstly, a disclaimer: as the author was a writer for "Star Trek: The Next Generation" (which I totally loved), I am naturally inclined to give a favourable review to whatever he writes :).

Back to the book: basically, this book is a history of our understanding of the structure of space (dimensions, curvature etc., in other words its "geometric" properties) starting from the Ancients (usual culprits, Pythagoras and Euclid) up to the latest scientific developments.
This book provides beautifully s...more
Mlodinow tackles what some people would think would be a dry topic and manages to infuse some wit into it. You can tell that he really loves his topic and wants the reader to as well. He explains the math and gives you examples to help you understand. And they are very helpful (although I must say that his examples using his sons start to get a little annoying after a while.) He explains the beginnings of geometry and how it progressed and reasons why it was, at times, held back due to politics...more
Nach dem Drunkard's Walk war das eine herbe Enttäuschung. Keine überraschenden Erkenntnisse, mehr Kurzbiographien als Erläuterungen der wissenschagtlichen Fortschritte selbst und ziemlich viel aufdringliche Beispiele, in denen Alexej und sein Bruder vorkommen. Ich hatte nicht die Illusion, dass ich diesmal Einsteins Theorien verstehen würde (das wird mir sicher nie gelingen), aber von diesem Ziel bin ich jetzt eher weiter entfernt als näher dran. Ich habe nichts dagegen, wenn Wissenschaft locker...more
Murph Hutson
Very mixed bag. The mathematics was quite interesting. I'm a math teacher; thus, the subject fascinates me. However, Mlodinow is an atheist and just can't stop ridiculing the Bible and Christianity. If I was interested in that view, I would have read the book he authored with Stephen Hawking. I was looking for a history of Geometry. What I got was a man's take on why mathematics could disprove the existence of God. Yet, I'm more in line with Galileo who said, "mathematics is the language with wh...more
I read Mlodinow’s The Drunkard’s Walk and thought this would be a great book on the history of mathematics. It started out good and then just fizzled out for me toward the end. His explanations were sometimes a little hokey and sometimes confusing. I think if you worked hard you could probably make sense of what he was trying to explain, but I’ve read better explanations of relativity, quantum mechanics, and string theory so I skimmed through the last half of the book pretty fast. It just didn’t...more
I kept reading this book because the subject matter is so fascinating. The writing, however, was awful. First, it makes no sense to me to have a book about geometry with so few diagrams included. To make things worse, the author lets a jocular tone stand in for clear, concise explanations. It is apparently not self-evident that these two things are NOT the same. A joke -- usually a bad one -- every paragraph. SERIOUSLY. This is the God's honest truth: I found myself telling the book to "Shut the...more
I listened to this as an audiobook, and thought it was fascinating. All of the historical anecdotes were relevant to the mathematical topics. Though geometry may seem objective and unquestionable, I learned a lot about how the development of this field has been very contentious and intimately tied to changing paradigms of reality in european/western thinking. As some other reviewers state, this book unapologetically leaves out mention of the development of geometry in other parts of the world. H...more
Sasha Zbarskaya
charming, inspite of sometimes a little bit too much of unceremoniousness.
and yes, it makes the brain work and get amazed. and excited.
and all in all: a person loving his|her subject just can't possibly write a vapid book, i believe.
Murali Behara
if you have a background in math and science, it sure would move you. human stories of extraordinary individuals and their insights. made me laugh and cry.
I enjoy Mlodinow's style of narration and wasn't disappointed. Although billed as the "story of geometry" it's really about man's ability to explain the physical world from macro to micro, from universe (or multi-verse) to the subatomic. Mlodinow takes us through the age of the Greeks to modern day explaining how Euclid's historical postulates set the stage for men of math and science across the ages to advance our knowledge of and our ability to shape the physical world. Mlodinow highlights the...more
Well, I loved this book (reading it as a layman who knows very little about geometry, physics and mathematics in general!)

It broadened my horizons - I want to read books about physics now. I want to read about Feynman and Gauss and string theory.

I loved how the author interwove other parts of history with the discoveries in geometry. I appreciated the way in which he explained complex mathematical concepts in an almost anecdotal style.

I noticed how when describing theoretically what a physicist...more
Overall, an excellent book that covers geometry all the way from Pythagoras (so not just Euclid) to modern day String Theory. It's probably not a good choice for a pop science book, but for someone interested in the history of mathematics/science, it's very well done.

There's a lot in this book. He covers early geometry by Pythagoras and Euclid, on to others like Descartes (and his predecessors), then on to people like Gauss and Riemann. He then discusses the impact of their work on Einstein whic...more
Nathan Glenn
This book was a completely fascinating read! It follows the history of mathematics and particularly geometry from the very beginning all the way to modern research in physics (which is heavily tied to geometry). It gives an account of the time before anyone thought of numbers by themselves, divorced from the length of a rope or a country's boundary. It recounts the revolutionary idea of Descartes that numbers can be drawn on a graph, with up being a bigger number and down being lower. These are...more
I've read a number of 'science for the layman' which work through the discoveries of quantum mechanics, special and general relativity, and string theory. This offering covers that ground as well but starts much farther back with the foundational discoveries within mathematics, which I enjoyed.

Looking at the development of mathematics and physics through the lens of geometry is a novel approach and led me to some better understanding of the subject matter than I brought in to the book.

I've been...more
Amazon review:

Through Euclid's Window Leonard Mlodinow brilliantly and delightfully leads us on a journey through five revolutions in geometry, from the Greek concept of parallel lines to the latest notions of hyperspace. Here is an altogether new, refreshing, alternative history of math revealing how simple questions anyone might ask about space -- in the living room or in some other galaxy -- have been the hidden engine of the highest achievements in science and technology.
Based on Mlodinow's...more
Ziqi Wang
Incredibly funny and cheeky; Mlodinow gives a broad overview of (a very Eurocentric) history of geometry, profiling 5 major figures: Euclid, Descartes, Gauss, Einstein and Witten. Truth be told, the biographies fell short and were very spotty. The author is very easily distracted and feels the need to insert a joke at every turn.

The Witten chapter was extremely disappointing; we only get a sliver of his work (M-theory is mentioned, like, twice), and it is corrupted by Mlodinow's own personal pe...more
This is a cute piece of pop-science that takes us through the history of the human understanding of space, from the Ancient Greeks to modern theories of quantums, strings and numerous dimensions that sound mysterious and strange. And mysterious and strange remained even after reading the book, since the author doesn't do a great job at putting the "popular" in "popular science" as the things he's talking about grow more and more complex (and seem to focus more on physics than math or geometry as...more
Euclid started out his hobby by lining up stones to represent numbers in order to find patterns. From there, the narrator goes through the historical developments of geometry. It combines biographical anecdotes and snippets of theory. As in art, many thinkers took pieces of a previous theoretical approach and gave new interpretation. Humanity would have more research to use if religion had not come around to kill people, torture people, and sometimes burn works of original thinkers. I love that...more
Euclid's Window is a book tracing the evolution of Geometry over thousands of year; the story of the people, the brilliant mathematicians who developed it and the resistance that they faced, first from the church and then from within their own small mathematical community itself.
This book brings to life the names we have heard during our school days and some that we have not; Thales, Pythagoras, Euclid, Archimedes, Galileo, Descartes, Gauss, Riemann, Einstein, Feynman and many others. Their live...more
The problem I have with this book is that the author adds in a lot of made up speculative stories about times and people that are not only extraneous and misleading; they are also detrimental to the book in that they are fictious and along the lines of mean-spirited, snarky humor that doesn't work. They don't help hold the story or transition to the next part making them mentally jarring to read through.
Noah Sandford
This book did a good job of explaining many complicated mathematical principles without getting to technical. It also described the lives of mathematicians nicely. I especially liked the chapter on the life of Gauss, mainly because it was a story of sheer genius overcoming social class, which is always nice.
The book goes off-topic.

The premise is excellent and the book starts off well. However, the standard tendency of such books of the era to bring everything to relativity, quantum physics and superstring theory - may be because of far easier availability of topics in the space - means the book loses its interesting and unique subject quite quickly.

As a result, when it is compared with other books on either history of maths/science or that try to explain cosmology theoretically, it comes up with...more
Fantastic book. Understandable and well-defined history of mathematics/ geometry. Author has a wry sense of humor as well.
I read this despite tepid reviews because I so liked Drunkard's Walk. Turns out the reviews were correct. This was not nearly as good as Drunkard's Walk. The story was more familiar to me, so not as compelling and there were several examples I had just read in DW. I expected to learn more toward the end of the book: relativity and string theory. I've seen better overviews of relativity. (Lillian Lieber for example.) The string theory part was nearly all new to me, but by then... Sigh. The book a...more
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Leonard Mlodinow is a physicist and author.

Mlodinow was born in Chicago, Illinois, in 1959, of parents who were both Holocaust survivors. His father, who spent more than a year in the Buchenwald death camp, had been a leader in the Jewish resistance under Nazi rule in his hometown of Częstochowa, Poland. As a child, Mlodinow was interested in both mathematics and chemistry, and while in high schoo...more
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