Euclidean and non-Euclidean geometries
by Marvin J. Greenberg · first published 1974
4mentions
1recommended by
2HN commenters
2014–2020first – last mentioned
50% recommend50% neutral
Euclidean and Non-Euclidean Geometries presents the discovery of non-Euclidean geometry and the reformulation of the foundations of Euclidean geometry.
Affiliate links. As an Amazon Associate I earn from qualifying purchases.
…and see each piece build on the last! Now, over 15 years later, I'm still telling myself to read GEB, but I always wonder how much point there is. A very worthwhile book to read in parallel to N&N is Euclidean and Non-Euclidean Geometries, by Greenberg. It's more textbooky, but still short, and it will let you see how some of the same themes played out in geometry as well as arithmetic.
on “Ask HN: Is "Gödel, Escher, Bach" still worth reading?” ↗Sometimes this is called "the unreasonable effectiveness of mathematics"---if you want something to Google for. I feel like the order of the world is vaguely miraculous. You might also want to read about Euclidean and Non-Euclidean geometries and the history of the parallel postulate for how humans have grappled with this question in the past, and how our thinking has evolved in the last 150ish years. This is a fantastic book with a mix of…
on “A mysterious connection between number theory, algebra and string theory?” ↗I thought of a few others that are "fun": - The Annotated Turing by Charles Petzold - Quantum Computing since Democritus by Scott Aaronson - Euclidean and Non-Euclidean Geometries by Marvin Jay Greenberg (a textbook, but an easy one to read on your own) - Gödel's Proof by Nagel and Newman (best if he can read it with a partner and talk through the steps) - Prime Obsession by…
on “Ask HN: Recommend a maths book for a teenager?” ↗…consistent?" Gödel also answered this problem with his "incompleteness theorem," which states that all consistent axiomatic formulations include some undecidable propositions. For more, see the short history of Euclidean and non-Euclidean geometries. This is imprecise, and the last sentence is a non sequitur.
on “Math problems that challenge the world” ↗