The chord through the midpoints of two sides of an inscribed equilateral triangle cuts a diameter in the golden ratio. This interesting method gives a purely geometric construction of positive Phi without using Fibonacci numbers.
> This interesting method gives a purely geometric construction of positive Phi without using Fibonacci numbers.
There's nothing particularly interesting about that; phi is (1 + √5)/2. All numbers composed of integers, addition, subtraction, multiplication, division, and square roots can be constructed by compass and straightedge.
I was somewhat surprised to learn that phi is _merely_ (1 + √5)/2, I didn't have a good conception of what it was at all but I didn't think it was algebraic.
Suppose you have a rectangle whose side length ratio is ϕ. You draw a line across the rectangle which divides it into a square and another rectangle.
Then the side length ratio of the new, smaller rectangle is also ϕ.
If you substitute b = φa into the other one, you get
ϕ(ϕa) = a + ϕa
And since a is just an arbitrary scaling factor, we have no problem dividing it out:
ϕ² = 1 + ϕ
Since we defined φ by reference to the length of a line, we know that it is the positive solution to this equation and not the negative solution.
(Side note: there are two styles of lowercase phi, fancy φ and plain ϕ. They have their own Unicode points.
HN's text input panel displays ϕ as fancy and φ as plain. This is reversed in ordinary text display (a published comment, as opposed to a comment you are currently composing). And it's reversed again in the monospace formatting. (Which matches the input display.)
HN's text input panel displays ϕ as fancy and φ as plain. This is reversed in ordinary text display (a published comment, as opposed to a comment you are currently composing). And it's reversed again in the monospace formatting. (Which matches the input display.)
I'm glad you posted this. I'm not a unicode expert and have always assumed these weird dichotomies were some sort of user/configuration error on my part. Realizing the unicode glitches are actaully at the website end instead of between my ears is quite a relief.
To be more specific, that usage note strongly suggests that the problem is in the font used by HN. The font is what complies or doesn't comply with the Unicode standard. We can also say that HN has a problem, but HN's problem is "they're using a noncompliant font for monospaced text".
(On further investigation, I got the characters backwards, and HN's ordinary display is correct while the monospaced display isn't.)
More competitionis better. If you take the market share and revenue off the table and spread that around in a competitive market you'd be in a much more interesting spot with respect to technology advancements. Instead we continue to stagnate with bullshit like Windows 10 --> Windows 11. Windows 11 was never supposed to exist, but $$$$$. There's literally nothing worth paying for in that upgrade. But Microsoft knows it can milk businesses and schools out of ridiculous profits for, essentially, the same garbage and also collude with hardware manufacturers to sell more PCs.
> There's literally nothing worth paying for in that upgrade.
Well there is the violations of Fitts law with the movement of the start button to the centre of the bar?
But it does make it look slightly more Mac! They should make sure the next upgrade moves the corner to grab away from the actual corner, and that the cursor change for grabbing it doesn't always trigger if they want to really rip it off.
I think Windows 11 in particular is a confluence of two other problems with respect to competition:
1. Subscriptions instead of discrete paid versions removes the incentive to put out a good product. In the past, if the new version was bad it was a direct financial hit. But now there's no direct financial feedback loop, as long as it's not so terrible that you leave the subscription entirely
2. I think Windows 11 is the first time there's no other version of Windows still in support you can use to "ride it out"
You might want to look into using cephadm to setup CEPH. Use Erasure coding as data pool for very efficient data storage and protection (8+2). From that export large RBD to be used as zpool with dedup. Scales to Petabytes and has lots of failure protection options.
Thank you for that recommendation. I think I'm probably too small time for the moment for Ceph considering that. I don't have multi-petabytes (yet or perhaps ever).
Hmmm, is there a native virt-manager build on Windows? Though I suppose running it in WSL and connecting with an external SPICE client would work just as well. (I’m wondering if there’s a way to just run SPICE server in WSL.)
Switch to Debian and i3wm and never be bothered again by this type of nonsense. PC = Personal Computer. Make other choices and regain your sovereignty and privacy.
I switched to Mac 20 years ago out of sheer frustration over the total lack of coordination between hardware and software, the frothing at the mouth obsession over excessive backwards compatibility over good design, privacy and security, and hardware that isn't total rainbow blinky light horseshit.
But I try to keep abreast of whats happening on the other side of the fence and I am often recoiling in horror and wondering why the fuck Windows users tolerate any of this.
Windows 11 is not performant, it's sluggish in a lot of places and everything got slower on the same or even better hardware. And I will never not laugh about having two context menus. Windows 8 was way faster even on low-end hardware thanks to DirectUI.
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