The book of numbers

What Hacker News says

1. root_of_unityMar 2021
   Really wonderful work, and wonderful article. As someone interested in more intuitive digital tools for exploring, understanding and articulating pure mathematics, this methodical breakdown of representations of algebraic numbers is an absolute delight.

   Folks interested in another angle on the field of algebraic numbers, which the author begins to enumerate in this article, might enjoy these two visualizations of the field, along with the C that was written to generate them.

   https://commons.m.wikimedia.org/wiki/File:Algebraicszoom.png

   https://en.m.wikipedia.org/wiki/File:Leadingcoeff.png

   It would be quite a fun project to make either of these visualizations “explorable” a la Bret Victor as an application of Frederik’s work. Since the set of algebraic numbers is countable, it seems to me to a scrubbing UI across the points in the color visualizations, joined to the enumeration that Calcium seems to be able to output, and rendered dynamically as the cursor moved around the image, would be a neat demo.

   Also Conway and Guy’s “The Book of Numbers” has an extraordinarily playful, intuitive and focused introduction to algebraic numbers that doesn’t require even an undergraduate math background to grok, for folks coming to this post wondering what algebraic numbers are.

   https://www.amazon.com/Book-Numbers-John-H-Conway/dp/0387979...

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2. noriudayJul 2020
   1) "The Science of Programming", by David Gries, is an excellent book dealing with mathematical proof based approach to programming.

   2) "The Book of Numbers", by John H. Conway and Richard Guy is a beautiful book which discusses about figurative numbers amoung several other beautiful topics.

   3) "Stories About Maxima and Minima", V. M. Tikhomirov has some beautiful anecdotes and interesting applications of calculus.

   4) "Contemporary Abstract Algebra", by Joseph Gallian is an algebra textbook that goes beyond just teaching material. It has quotations, biographies, puzzles and interesting applications of algebra.

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3. GuiAJun 2020
   Been going through Conway's (and Conway related) books since his unfortunate passing. His biography by Siobhan Roberts was a great starting point to ease into it (lots of direct quotes from Conway, which makes it a very easy read that still touches on the important concepts in his work, in his own words; also highly recommend all the Numberphile videos featuring him for that)- then:

   Winning Ways for your Mathematical Plays is really fun to thumb through.

   The Book of Numbers is fantastic and something I would gift to any mathematically curious, somewhat independent, child.

   Knuth's Surreal Numbers is also a great read.

   Got On Numbers and Games coming in the mail, and am trying to track down a reasonably priced copy of The Symmetries of Things.

   I'm tempted to get the Atlas for my collection, but I don't think I'd actually get much from reading it (:

   In non-Conway recommendations, The Princeton Companion to Mathematics is a huge brick of a volume, but is a very complete math encyclopedia that I love to keep on my desk and thumb through when I feel distracted. You always end up learning something new.

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4. oklFeb 2019
   Would also recommend 'Surreal Numbers' by Don Knut hand 'The Book of Numbers' by Conway and Guy.
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5. OscarCunninghamAug 2018
   I think Conway and Guy's "The Book of Numbers" might be a better source. It's more focused on infinities as different types of number, and certainly at a more suitable level. ONAG is quite a technical book; children don't really need to know that the surreals are the universally embedding real-closed field.
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6. mathgeniusDec 2017
   > so if there is another book that does the same thing with better exposition

   Have a look at Conway's "Book of numbers". He has a nice description of the complex numbers there. Conway can be terse aswell, but at least he is funny!

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