Rafael Araujo's 20 Mesmerizing Geometrical Masterpieces (2024)
abakcus.com
abakcus.com
Personal fav is "Dürer" that demonstrates Albrecht Dürers method of projecting a spiral.
Google: Rafael Araujo artist formula. Ahhhh! https://www.rafael-araujo.com/calculation
Now we are getting somewhere... and another that shows the process a bit better: https://hazelhomeartandantiques.blogspot.com/2015/04/the-cal...
Now I am trawling github to see if I can find some processing or similar libraries that I can play around with. Golden Ratio sketches, defining physical objects and shapes from purely mathematical constructions... I love rabbit holes!
A surface that exhibits very strong variability in curvature (like the spikes in the shell) is most likely a collage of different pieces. These would (at best) have only a locally valid mathematical formula. Achieving a visually convincing result through smooth patching introduces lots of ugly "numbers".
Most likely the "formula" concerns only some aspects of the drawing, like overall symmetry and relative sizes.
Does Donald Knuth have any metaprogramming for golden section/ratio?
About golden section in the universe there is a nice book by Scott Olsen - https://www.goodreads.com/book/show/316282.The_Golden_Sectio...
I recently heard the saying "a great artist knows when to stop" (it was Ben Afflek talking about AI art - I guess he was quoting someone?). I feel like in the case of these drawings, less detail would actually be better. More readable, perhaps.
Still, an impressive amount of effort for each one, given only straightedge and compass.
Removing the details removes the reference to the formula(e), which is the soul around which the beatiful pictures are created. In this case, the art is the process, more-so than the end result - which is a by-product.
Yikes. The golden ratio has limited significance, nothing to do with spirituality, and little presence in nature [1]. Araujo's pictures look great, but in almost any of them you could replace the golden ratio with 1.6, 1.7, or 1.5, and get something no less beautiful.
The Wikipedia page is fairly good on this, especially the "Disputed observations" section: https://en.wikipedia.org/wiki/Golden_ratio#Disputed_observat...
As a mathematician, fetishisation of the golden ratio bugs me.
[1] The main place is spiral arrangements of leaves, petals, etc. Vi Hart explains why (watch all three parts): https://www.youtube.com/watch?v=ahXIMUkSXX0
> nothing to do with spirituality
It clearly does have a lot to do with spirituality, for many people, as symbol. Much as the cross does for Christans. Neither of these symbols have spiritual meaning to me - a cross is just a cross, a spiral is just a spiral. I don't have much need for spiritual symbolism myself - when I meditate, I rather to focus on a simple sound or light source - but I'd consider it highly egotistical of myself if I was to start judging other people's use of symbols just because they don't understand maths, or whatever.
> fetishisation
I've yet to ever see this word used except to denigrate other people's beliefs, or as an attempt to make the user feel superior. I believe you did both here.
My advice, one mathematician to another: chill and let people have their symbols. Don't expect them to have a deep understanding of mathematics, much as we don't have a deep understanding of their need for spiritual symbolism. Nonetheless we can let each other be, and all get along.
Who knows, perhaps a fascination with this "sacred geometry" as they call it, might be a starting point for someone to have a genuine interest in mathematics.
The only people I’ve ever seen healthily walk the boundaries were from philosophy/physics/math to spirituality (whatever that means for individuals), not the other way round.
So basically, the same as all human language then?
If you're saying that geometric terms should only be allowed to be used in a strictly defined mathematical sense, even by non mathematicians, that's a kind of gatekeeping that doesn't make any logical sense to me.
Firstly, it completely misunderstands how humans use language, how we play with it, make puns, reuse terms from other social groupings (maths) in new ways that have meaning to another social group (new age spirituality), how we bend and twist the meanings of words over time.
Secondly, it's impossible, and unwarranted, to try and police this, so I hope you're good at dealing with being ignored.
I know, but hear me out: it's a decent hook for teaching people about Geometry, Recursion, and Dynamic Programming.
(Or is it just that the largest rectangle that inscribes a regular hexagon has the same ratio?)