Nice. I love the sense of humor of the motivational quotes. Immediately after inscribing a circle in a square: "You can't fit a round peg into a square hole. (American proverb)"
That is neat, I did not know this method of constructing a gold ratio. Once you have a golden ration it's easy to construct a pentagon (with straight-edge and compass).
I always like the equlateral triangle with the top half removed to for a rombus, the shape is used in the mosaic virus. now I understand my attraction to it, thanks!
The idea that the golden ratio is particularly aesthetically pleasing is 100% snake oil.
Sure, moving a heading slightly higher can make it look much better than if it was perfectly equidistant from the side and the top, but the precise amount depends on a million visual factors. The golden ratio might happen to work fine, but there's nothing magical about it.
Even temples that we thought followed the golden ratio for their dimensions have been measured better, and it turns out they don't. The civilizations back then knew enough so they could have made them very close to the golden ratio, but they didn't. Not always at least.
Edit: years of searches and minutes after I post this I found https://www.youtube.com/watch?v=CaasbfdJdJg thanks to using "continued fraction" in my search instead of "infinite series" X(
Original:
Tangentially, for a few years I've been looking for a Youtube video, I think by Mathologer [1], that explained (geometrically?) how the Golden Ratio was the limit of the continued fraction 1+1/(1+1/(1+1/(...))).
Anyone know what I'm talking about?
I know Mathologer had a conflict with his editor at one point that may have sown chaos on his channel.
Do any of you deliberately integrate the golden ratio into anything you create or do? For me it always seems more like an intellectual curiosity rather than an item in my regular toolkit for design, creative exploration, or problem solving. If I end up with a golden ratio in something I create it's more likely to be by accident or instinct rather than a deliberate choice. I keep thinking I must be missing out.
The closest thing I do related to the golden ratio is using the harmonic armature as a grid for my paintings.
I don't have the energy to delve into this shit again, I found another antique site + ancient measurement system combo where the same link between 1/5, 1, π and phi are intertwined: https://brill.com/view/journals/acar/83/1/article-p278_208.x... albeit in a different fashion. + it was used to square the circle on top of the same remarkable approximation of phi as
5/6π - 1
which preserves the algebraic property that defines phi
phi^2 = phi + 1
But only for 0.2:
0.2 * pseudo-phi^2 = 0.2 * (pseudo-phi + 1) = π/6
My take is that "conspiracy theories" about the origin of the meter predate the definition of the meter. You don't need to invoke a glorious altantean past to explain this, just a long series of coincidentalists puzzling over each other throughout time. It's something difficult to do, even on HN, where people don't want to see that indeed g ~= π^2 and it isn't a matter of coincidence. https://news.ycombinator.com/item?id=41208988
I'm depressed. I tried to sleep as long a possible, because when I woke up, within 3 seconds, I was back in hell. I want it to end, seriously, I can't stand it anymore.
Is there a computational advantage to constructing φ geometrically versus algebraically? In rendering or CAD, would you actually trace the circle/triangle intersections, or just compute (1 + sqrt(5)) / 2 directly?
I’m curious if the geometric approach has any edge-case benefits—like better numerical stability—or if it’s purely for elegance.
wow that is gorgeous. this is the kind of thing that convinces me that the golden ratio is a fundamental, natural construct, rather than merely a mathematical abstraction. not that the typical construction itself doesn’t make me think that— the way it is constructed absolutely lends itself to natural, physical explanation that is almost too natural to ignore.
20 comments
[ 0.16 ms ] story [ 42.5 ms ] threadAre we really upvoting this on HN? Truly the end times have come.
Sure, moving a heading slightly higher can make it look much better than if it was perfectly equidistant from the side and the top, but the precise amount depends on a million visual factors. The golden ratio might happen to work fine, but there's nothing magical about it.
Even temples that we thought followed the golden ratio for their dimensions have been measured better, and it turns out they don't. The civilizations back then knew enough so they could have made them very close to the golden ratio, but they didn't. Not always at least.
I sat down and worked it out. What do you know golden ratio.
Oh and this other number, -0.618. Anyone know what it's good for?
Original: Tangentially, for a few years I've been looking for a Youtube video, I think by Mathologer [1], that explained (geometrically?) how the Golden Ratio was the limit of the continued fraction 1+1/(1+1/(1+1/(...))).
Anyone know what I'm talking about?
I know Mathologer had a conflict with his editor at one point that may have sown chaos on his channel.
[1] https://www.youtube.com/c/Mathologer
https://youtu.be/ubHVK71F01M
This one actually has the geometric (rectangle subdivisions) animations I had in mind.
The closest thing I do related to the golden ratio is using the harmonic armature as a grid for my paintings.
https://en.wikipedia.org/wiki/Fibonacci_heap
https://news.ycombinator.com/item?id=44077741
I don't have the energy to delve into this shit again, I found another antique site + ancient measurement system combo where the same link between 1/5, 1, π and phi are intertwined: https://brill.com/view/journals/acar/83/1/article-p278_208.x... albeit in a different fashion. + it was used to square the circle on top of the same remarkable approximation of phi as
which preserves the algebraic property that defines phi But only for 0.2: My take is that "conspiracy theories" about the origin of the meter predate the definition of the meter. You don't need to invoke a glorious altantean past to explain this, just a long series of coincidentalists puzzling over each other throughout time. It's something difficult to do, even on HN, where people don't want to see that indeed g ~= π^2 and it isn't a matter of coincidence. https://news.ycombinator.com/item?id=41208988I'm depressed. I tried to sleep as long a possible, because when I woke up, within 3 seconds, I was back in hell. I want it to end, seriously, I can't stand it anymore.
I’m curious if the geometric approach has any edge-case benefits—like better numerical stability—or if it’s purely for elegance.