Talk:3041: Unit Circle

First 162.158.175.72 23:00, 22 January 2025 (UTC)

This would actually be so helpful for my geometry class right now 42.book.addict^{Talk to me!} 23:06, 22 January 2025 (UTC)

Are you saying you have problem with abstract thinking? Why should matter if the unit circle had radius 1 yard, 1 foot, 1 meter or 1 lightsecond? -- Hkmaly (talk) 23:12, 22 January 2025 (UTC)

I don’t like having things defined as “x” and like to have exact measurements. The diagram just looks cleaner to me that way 42.book.addict^{Talk to me!} 23:38, 22 January 2025 (UTC)

There's nothing stopping you from considering non-dimensional lengths to be whatever unit you want. If you just write in, for example, "cm" after any linear dimensions, and corresponding units for areas and volumes, that's fine.162.158.158.169 14:24, 23 January 2025 (UTC)

I prefer units of light-nanoseconds or the metric version parnsecs (don't think about it too hard :P) -- SammyChips (talk) (please sign your comments with ~~~~) SammyChips 23:58, 22 January 2025 (UTC)

I like square acrminutes per steradian 42.book.addict^{Talk to me!} 02:38, 23 January 2025 (UTC)

Please sign off with ~~~~, or change your signature to include a link to either your talk page or user page. Thank you! 42.book.addict^{Talk to me!} 01:25, 23 January 2025 (UTC)

I did sign with ~~~~, but the option for treating my signature as plain text was enabled. SammyChips (talk) 15:57, 23 January 2025 (UTC)

SammyChips, if that is supposed to be Parallax nano-seconds, you should understand that that is probably more like a Giga-Parsec. The parsec is the distance at which an object appears to move one second of arc when the Earth moves halfway around its orbit. (though I'm not sure which orientation.) Divad27182 (talk) 03:34, 23 January 2025 (UTC)

I told you not to think too hard for that very reason :P It's actually parsec-nanosecond per year, but in a nod to the recent comics dealing with unit cancelation and making up personal scientific jargon, I collapsed it into its own unit. For those who didn't get it, a light-nanosecond is pretty close to a foot, and the "parnsec" is pretty close to a meter. SammyChips 15:50, 23 January 2025 (UTC)

You Americans will use anything but the metric system!172.70.58.45 16:30, 23 January 2025 (UTC)

parallax giga-seconds?Lordpishky (talk) 19:20, 23 January 2025 (UTC)

My Millennium Falcon gets 14 parsecs to the Kessel Run, and that’s the way I likes it! 172.68.186.34 06:26, 23 January 2025 (UTC)

I'm going to take all these desires for weird units with a barn-megaparsec of nackle. 172.69.195.160 07:00, 23 January 2025 (UTC)

yo Tori, this might help you with geometry too ;) Caliban (talk) 11:14, 23 January 2025 (UTC)

I’ve watched that video before-it’s really cool and it’s one of my favorite videos ever 42.book.addict^{Talk to me!} 16:10, 23 January 2025 (UTC)

Are "they" also searching for Apollo's doubled altar? Divad27182 (talk) 03:22, 23 January 2025 (UTC)

I guess the correct wording is that $\pi$ is a trancendent number. Some irrational numbers e.g. $\sqrt{2}$ can be constructed by compass and ruler. 172.68.185.165 (talk) 07:12, 23 January 2025 (please sign your comments with ~~~~)

To be more precise, constructable irrational numbers are those that can be obtained through taking square roots, even repeatedly. Transcendental numbers are out, but so are things like cube roots. Note also that the fact that there are no "absolute units" of length is a quirk of Euclidean geometry -- in, say, hyperbolic world, a unit circle like this could actually work. 172.68.213.153 09:10, 23 January 2025 (UTC)

Watch out you don't make that unit circle too big, or the square's vertices might stretch out to infinity and ignite the atmosphere! SammyChips (talk) 16:14, 23 January 2025 (UTC)

Didn't the unit kilogram lose some of it's mass? It may be working if something similar happened to this unit circle. 172.69.214.117 15:43, 23 January 2025 (UTC)

It probably gains mass. (Hard to tell, when the reference mass is the mass that may be changing... But it's what tends to be observed from how the IPK copies change. Could be the addition of small amounts of hydrogen onto the surface, or even mercury vapour escaping from the themometers/etc that tend to be around the reference masses. 172.70.58.6 21:43, 23 January 2025 (UTC)

The unit circle has a diameter of 2 units by definition, as a circle's diameter is twice its radius. In this comic, the diameter of the circle is 89 pixels, measured from the center of the outline on one side to the center of the outline on the other side. This implies that at the scale of this scene, the "unit" is 44.5 pixels. Cueball is 201 pixels tall, making him 4.5 "units" tall. Are characters' relative heights consistent enough in xkcd for this to be meaningful? --Tepples (talk) 18:22, 23 January 2025 (UTC)

The only true unit of length is ~1.616*10^(-35) meters. Whether you want that to be the circle's radius or diameter would be a matter of convention, although it might help to point out that the Schwarzchild "radius" of a unit mass is two length units, which makes me think of a diameter instead. 172.68.245.206 20:00, 23 January 2025 (UTC)

I'm surprised that this explanation doesn't cover the joke inherent in "dimensional analysts": This is obviously a reference to dimensional analysis, the process of cancelling out units in long chains (and the topic of 3038: Uncanceled Units). Trimeta (talk) 01:52, 24 January 2025 (UTC)

That all goes back to (at least!) 687: Dimensional Analysis, and has been covered since several times (I think at least one What If? mentions it), mildly surprised to see that there is not yet a Dimensional Analysis category.

Though, if there was, I'm not sure I would add this to that. It would cover, in my view, all the cases where unit-type cancellations/uncancellations/recombinings are used for surprising(/blatantly incorrect) purposes, or as a comment on how they could/should (as per 3038). The dimensional analysts in this comic aren't changing how length is used (i.e. suddenly using it for for a surprising <length*weight unit>/<weight unit> reduction), and seem to be styled as ultra-practical mathematicians (getting their hands dirty with expeditions to find mythical objects) rather than ultra-theoretic ones (darned be what the real world is like, to experience, they'll imagine the world how they want — or even try to make it work that way, though that probably involves getting one's hands dirty in a different way). One incarnation of the edit even had them as practically Indianna Joneses (named them as (action-)archeologists, having dug this object up, which I was glad to be changed, as there's little sign it was excavated and not just found in plain sight), which puts me at odds with them being actually called "dimensional analysts" in the aforementioned Dimensional Analysis sense, as they're not messing with the dimensional qualities. They're "arbitrarily de-abitrising" in a completely different way, setting up a single (non-compound) measurement unit in terms of all other similar units, under the (mis?)impression that their newly considered one is fundamentally more 'true', not "having fun with units(-plural)".

I'm sure the Explanation could cover Dimensional Analysis (perhaps try to explain their group-profession name to me, I'd have perhaps called them "practical mathemologists", or something like that), and you're free to do so if you think you have a handle on it, but I (for one) never saw a useful link between the two (even, tenuously, as being entirely opposite ends of the actual practical/theoretical spectrum), so didn't even start to think to link it up with an additional bit of explanation in this direction. Can't speak for anyone else, though, and perhaps your comment (and a complete disagreement with my own voiced interpretations) will inspire something of what you initially sought in vain... That's the beauty of the collaborative wikidocumentation process. ;) 172.69.195.200 09:42, 24 January 2025 (UTC)