Sacred Geometry people are my math heretics— The mad with power inquisition version of me would want them burned at the stake. As it is? I just seethe at their “incorrect appreciation of geometry”
They worship wrong.
I bought a book of geometric constructions — (not reading about it too carefully...) Just cracked it open. It cheerfully gives instructions for constructing a triangle, square, pentagon, hexagon, and heptagon…
A footnote begrudgingly admits the heptagon is only 98.25% correct. 1/
I almost thought that footnote wouldn’t even be there! This book is that glib. The footnote contains the most interesting fact presented in the entire book.
I must compulsively check all these constructions to see if they are “real” they probably are— but still.
I wonder how the heptagon approximation was created— I get the desire to just know how to make a serviceable regular solid— but to talk of heptagons but not unconstructability ? heresy I say!
I wonder how the heptagon approximation was created
💯 I'm wondering too. Answering this would probably require to extend approximation theory, i.e. continued fractions, to arbitrary algebraic fields. Not sure if that should be done ... (or has been done).
@helge @futurebird I doubt Heron of Alexandria (or whomever he copied his homework from) had access to any of those though.
[monthly mention that I regret losing the bookmark to a math professor's YT channel that was dedicated to doing math proofs known to ancient Greeks using only the techniques that were known to them]
@helge @futurebird wait, I think it's this guy?
https://www.youtube.com/@njwildberger/playlists
Weird how YT search gave me nothing for years and now he just pops up again.
Mind you, I never got around to really sitting down to listen to his lectures (until now) so I'm not sure how good his material is - I just loved the idea of old, now overlooked math techniques being kept alive the same way some people keep medieval craftsmanship alive or something.
This channel aims to explain a lot of interesting mathematics to a broad audience, to introduce exciting new research directions, and to fix some of the logical weaknesses that beset the subject.. You'll find playlists on Rational Trigonometry (much simpler, more powerful), Linear Algebra, Algebraic Topology, History of Mathematics, Universal Hyperbolic Geometry (a complete new treatment of this subject), the Foundations of Mathematics (it needs fixing), the Sociology of Pure Maths, Playing Go, Mathematics and Music, Differential Geometry, The Algebra of Boole and even an elementary introduction to K-6 mathematics. I (N J Wildberger) am a professional mathematician, BSc U. Toronto 1979, PhD Yale 1984 and Honorary Prof at UNSW, Sydney with over 50 papers, one or two books, and a love of teaching. And hundreds of math videos. Also, please check out the Wild Egg Maths channel, where Members have access to dozens of Research Maths videos over a wide range of topics.
@helge @futurebird So I just did a pre-emptive milkshake duck check and I find:
"DIVINE PROPORTIONS : Rational Trigonometry to Universal Geometry by N J Wildberger"
https://web.maths.unsw.edu.au/~norman/
Please tell me that that's not the same as sacred geometry? 😅 I mean he's still a maths professor so his stuff is still subject to peer review right? Right?
(also could find no information regarding milkshake-duckness so probably ok?)
No, this just seems to be normal math with an over excited title-- that's the whole problem with the "sacred" crowd-- they are hard to distinguish!
@futurebird @helge Yeah, it makes me wonder how many potential readers he lost because of the title.
The wikipedia page about the book says he's a finitist and came up with these proofs basically just to get rid of limits and actual infinity, so still a little quirky. But that's more of a philosophy-of-maths thing that one may agree or disagree with - plus the proofs apparently were still novel and correct, so something good has come out of it either way :)
https://en.wikipedia.org/wiki/Divine_Proportions:_Rational_Trigonometry_to_Universal_Geometry
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