Divine Proportions: Rational Trigonometry to Universal Geometry

I discuss my book Divine Proportions: Rational Trigonometry to Universal Geometry, which gives a novel way of thinking not only about trigonometry, but also Euclidean geometry. It also lays the ground work for a more rational and logical approach to other geometries, including hyperbolic geometries.

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[adjoaadjavon]

Video Content:
00:00 Introduction Of Divine Proportions Rational Trignometry To Universal Geometry

[_GrayBear_]

Another 503 error.  I dare say the popularity of your book is overwhelming the site, njwildberger!

Thank you so much for sharing.  I'd stalled in my progress through your Rational Trigonometry videos.  This is exactly the kick in the pants that I've needed.

[Hythloday]

Many thanks for the book and all your YouTube videos.

[MarvinDHernandez]

Thanks Norm, the free download is much appreciated.

[georgeorourke]

I got the hard copy...recently some original prints of Einstein's 1905 papers were auctioned off and they fetched a very high price. If Rational Trig does end up impacting the mathematical world then the hard copy will equally become a very desired document to have (more than a PDF). So I suggest that if you enjoyed the Youtube series as much as I did you should do the same and give WildEgg Publishing some encouragement. The lexctures were all clear, the diagrams perfect and the style very enjoyable. I will now revert back to Hyperbolic Geometry and also listen to all the other great stuff Prof Wildberger is posting.

[QuarkStew]

Thank you Mr. Wildberger. Strangely I was planning on purchasing your book this evening, which I will still do, but now I don't have to wait for it to arrive before I take a look.

[davidkeirsey]

Thanks for the PDF version.  I have always wanted an electronic version.  I have a hard copy, but it is nice to be able to quote your work with ease now.

[repiv]

Have the book, best money I ever spent on a book of knowledge and understanding.

Glad to see you offer it in PDF from and hope this helps get it in more hands and 'minds'.

Did you correct the few errors found in the physical book in the current PDF file?

[robharwood]

Thank you for this contribution, Prof. Wildberger! I look forward to reading it.

[palmtoptigeri]

I'm looking for people to discuss some exercises and theorems of the book. Any takers?
Any forums where you guys lurk and discuss?

[postbodzapism]

Looking forward to a new, more advanced book as a sequel to this excellent book.

[Gauteamus]

Thanks for all your inspiring and provocative videos here on YouTube! Especially the series on hyperbolic geometry (why not intro more videos with some Bach? :)). I really look forward to reading your book.

[octaveoctopus]

Thanks this is awesome! Was not aware of ResearchGate so thanks for that as well. Looking forward to reading your book!

[ronancarroll]

Thanks Professor. Am an avid follower of your work. Great to have a pdf copy as well as the  printed one

[MarvinDHernandez]

@Karl Schultheisz : It opens fine with MuPDF 1.7a with no error messages (Windows 7).  Perhaps the download was corrupted?  Here are the hash signatures :

CRC32: AD6030F8
MD5:
SHA-1:

[mostafawaleedhashem]

Thanks for sharing the book. Your YouTube video has been a great source of information to my research. I will definitely read your book. Thanks again

[AnotherFkingidiot]

Hi Professor, I'm curious as to if this rational approach means you don't really believe in calculus? I mean that whole field is relying on infinitesimals and limits.

[palmtoptigeri]

I'm having trouble solving exercise 5.17 on page 69. My guess is that the exercise has something to do with theorem 28 (obviously), examplels 2.2 and 2.4 and maybe exercise 2.3. The last proving also troublesome for me. Can someone set me on the right path with exercise 5.17? Also, what is a relevant reading material to help me understand exemples 2.2 and 2.4 and exercise 2.3?

[myName-dgqm]

I tried the download link and I get "503 Service Temporarily Unavialable". I tried joining but apparetly I need an institutional email address.

I dont know if I need to be a member of Research Gate in order to download the book.

[pieinthsky]

Norman,
I guess you know this and you was told about it multiple times, but your trigonometry is obviously not rational, it's algebraic.

In the book your first comparison example gives irrational quadrances.

Also you starting point is pretty weak, because "classical trigonometry" is very vague term. It's usually presented as some hodge-podge of Euclidian geometry, Hilbert's and/or Birkhoff axiomatizations of Euclidian geometry, and therefore based on the theory of "real numbers".

As far as i know, there are much finer modern treatments of Euclidian geometry around, e.g. Tarski's axiomatization, which explore Euclidian geometry in terms of constructible numbers to the great extent.