Geometrical Researches on the Theory of Parallels

by Nikolai Lobachevsky

This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.

Genres: Science, Mathematics, Classics, Nonfiction, Philosophy, Russia

55 pages, Paperback

First published January 1, 1914

Reviews

[Joshua Nomen-Mutatio · Rating 4 out of 5]

This shit blew my motherfucking mind. Yes, math that makes you curse like a sailor. I absolutely hated it at first and insisted that it was completely stupid and made absolutely no sense. "How can parallel lines continue to get closer to each other for infinity?? GODDAMMIT!!?!?" And this was in a classroom with people much calmer and more mathematically inclined than myself.

One day while venting about how little sense this kind of math made to me, someone somehow calmed me down by basically explaining that...well, actually now I can't even remember what they said, but somehow it soothed my confusion and totally indignant outrage.

I still don't understand things like this. Higher level mathematics (and by extension much of particle physics, namely quantum mechanics) is often so outrageously counter-intuitive that one has to wonder if those for whom these topics are bread and butter are just spinning an epic and elaborate joke. Part of me somewhat likes to imagine that behind closed doors it's all cackles and guffaws at mathematics and physics conferences.

I still don't understand Lobachevsky's wild mathematical models, but I now more or less dumbly marvel at them rather than get frothy with incredulous rage.

P.S. Cantor's ideas about multiple infinities also leave my jaw agape and the basic logic modules of my brain inflamed.

[Brian · Rating 5 out of 5]

Fascinating when compared to Book I of Euclid's Elements.

[Travis]

Existential crisis inducing.

[Adam C · Rating 3 out of 5]

to be honest, i skimmed it and didn't fact check his proofs (which obviously have been proven). he created hyperbolic geometry. that's big. i got the general gist of his paper without diving too deep into the trigonometry and proof following. fascinating, also over my head (in the sense that i'm not trying to get a math degree right now and studying it wouldn't improve my job).

[Mark Kreider · Rating 5 out of 5]

Read this book ... bend your brain.

[shanamadele · Rating 5 out of 5]

So, you think mathematics is really straightforward, and then you read this book and you find out that "paradigm shift" doesn't begin to cover the way the world changes.

[Lisa · Rating 4 out of 5]

parallel lines look like this /\

triangles >180 degrees

rectangles with angles like this |\ on top and like this |_ on the bottom?

This book will shatter your universe!

[Trey Kennedy · Rating 5 out of 5]

This is a great look at the start of non-Euclidean geometry. I enjoyed it almost as much as I enjoyed reading Euclid himself.

[Chase Waller · Rating 5 out of 5]

Wooooooooow what the hell.

[Val]

Everything u thought you knew, you don't