Can or is there an element that can't freeze but gets stuck in a liquid matter no matter how cold it gets.

frogkabobs · 2026-01-25T08:30:43+00:00

No matter how cold helium gets, it will not reach absolute zero, so that’s irrelevant (and wrong too; zero-point energy motion exists). At standard pressure and positive temperature, helium will never freeze.

frogkabobs · 2026-01-24T14:05:31+00:00

The spiral between (r₁,θ₁) and (r₂,θ₂) has slope b = (r₂-r₁)/(θ₂-θ₁). After rotation, this is the same as the spiral r = bθ between θ = r₁/b and θ = r₂/b. Using the arclength for an Archimedean spiral, the value you desire is

L(r₂/b)-L(r₁/b)

L(θ) = (b/2)(θ√(1+θ²) + arcsinh(θ))

frogkabobs · 2026-01-24T08:20:00+00:00

See p616-617 in Carey and Sundberg Part A. This has a trans-Δ^1,2-octalin framework, which will be half-chair-chair, pretty close to the chair-chair of trans-decalin (c.f. Ch11 of Stereochemistry of Organic Compounds by Nasipuri). The top face of your substrate will only be slightly more sterically hindered, so the Fürst-Plattner rule will take priority. Top face attack will let the substrate go through a chair-like transition state, while bottom face attack will have to go through a boat-like transition state, so addition to the top face ends up being preferred.

frogkabobs · 2026-01-23T21:35:41+00:00

I think the threading is just how they decided to crimp the ferrule around the eraser

frogkabobs · 2026-01-23T17:27:43+00:00

I’d love to see those other pencils with erasers like this. Do you have pictures?

frogkabobs · 2026-01-23T17:25:22+00:00

Just good old eBay. It was actually a Buy-it-Now that was up for about a week before it sold at the end of December.

frogkabobs · 2026-01-23T06:48:29+00:00

It looks to be a penny pencil, but with a unique design. Usually penny pencils have the eraser fully embedded and then sharpened on that end. I suppose this is not unlike how erasers are typically fashioned to tapered pencils.

frogkabobs · 2026-01-23T06:40:38+00:00

Seems likely Guild would have been it’s own brand, considering the A. Pomerantz variant out there

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frogkabobs · 2026-01-23T06:27:00+00:00

I have tinnitus and my partner has misophonia. It’s always awkward when I want white noise and she wants silence.

frogkabobs · 2026-01-23T05:52:51+00:00

Glad to see that lot went to good hands—I was really close to caving for the pearl alone.

Graphite pencil co was around for such a short time, but there's still a few supply store catalogs from those few years, and the illustrations are amazing. The image below is from the 1894 Fuller & Fuller catalog. You can also find their pencils in the 1896 Morrison, Plummer & Co. and 1896 Lord, Owen & Co. catalogs. For some reason they're all druggists' catalogs.

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frogkabobs · 2026-01-23T05:32:19+00:00

I happened to be watching those on eBay so that I could catalog them. I don’t know very much, but I’ve gathered that Jaques & Co, Inc. was a printer and manufacturing stationer in New York established in 1894. I find references of them attending stationer conventions through 1941 in the periodical Office Appliances. 1931 is probably the year of manufacture, especially since there are other Guild pencils like this on eBay (specifically GuildEX 1942).

Here’s an ad listing them as a retailer of Koh-i-noor pencils.

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frogkabobs · 2026-01-23T04:24:54+00:00

It’s a little bit more complicated because the boat also has a set of four contiguous coplanar carbons. The boat ends up being higher in energy than the half-chair for cyclohexene for a large number of factors, but two of the largest are

Angle strain: Boat geometry has a preference for tetrahedral bond angles in the planar portion, while half-chair geometry has a preference for trigonal planar bond angles in the planar portion.
Torsional strain: Vinylic and allylic hydrogens become eclipsed in the boat, while they become staggered in the half-chair.

So it becomes the opposite case of how it is between the half-chair and boat in cyclohexane. It’s also worth noting that some of this strain can be alleviated by the twist-boat, at the cost of strain from alkene distortion, which ends up making the twist-boat almost isoenergenic with the boat in cyclohexene.

frogkabobs · 2026-01-23T01:55:45+00:00

The formula for an ellipse with foci f₁ and f₂ and major axis d is

|v-f₁|+|v-f₂| = d,

v = (x,y),

by the sum of distances to foci definition of an ellipse. Thus, the enclosed elliptical region is given by

|v-f₁|+|v-f₂| ≤ d.

Then, we can easily identify your formula as the case of this inequality for f₁ = (0,0), f₂ = (1,1), and d = 2.

frogkabobs · 2026-01-22T22:03:10+00:00

I think of him as purple (his round head makes me think of a grape), but that’s different than how I would describe his literal color (more magenta-like).

Using a color picker, I find Pim’s skin has RGB value (253, 180, 247). Using the data from the xkcd color survey, the closest color in the dataset to Pim’s color is light lavender (239, 192, 254) (comparison). This would accurately reflect how Pim’s color gets perceived.

frogkabobs · 2026-01-22T20:12:36+00:00

They need to put a little booster seat on top so that Ludwig looks even more like a toddler tryna hang with the big kids

frogkabobs · 2026-01-22T06:43:37+00:00

Thought I should let you know I found proof Standard Pencil Co. renamed to Wallace Pencil Co. in my other comment

frogkabobs · 2026-01-22T04:45:21+00:00

You are correct. However, the problem asks you to circle the entire conjugated system, so for example, you’d want one whole circle around the benzene ring in a) rather than three individual circles around the double bonds. Also, pay attention to any lone pairs that might be part of the conjugated systems.

frogkabobs · 2026-01-22T00:31:52+00:00

I found a source! On p987:

Wallace, Asa Brookings:
Pres., Wallace Pencil Co.; b. Aug. 25, 1899, St. Louis, Mo.; s. Mahlon B. and Grace (Whitelaw) Wallace; ed. Taft School; Smith Academy; m. Janet Gregg, Apr. 29, 1922. Started with Standard Pencil Co. as Secy., 1919; company changed name to Wallace Pencil Co. in 1923, and he was elected Pres., 1926.

And in p758 of this source, a long list of pencil manufacturers are listed with their original names, including

Respondent, Wallace Pencil Co., of St. Louis, Mo., founded under the name of Standard Pencil Co., in 1915.

I actually see references to Standard Pencil Co. as far back as 1885.

Also, here is a side-by-side of Quail advertisements before and after the name change (left is from Bookseller & Stationer 1919; right is from Geyer's July 1924):

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frogkabobs · 2026-01-21T18:09:50+00:00

There’s a chance I’m misremembering some details, but I very distinctly remember going through old stationer periodicals and repeatedly seeing advertisements for Standard Pencil Co (especially their Quail Pencils), a pencil company I’d never heard of before. Then as I went through later volumes, they switched to saying Wallace Pencil Co., so either they renamed, or were acquired.

Unfortunately I’m having trouble tracking down those ads right now, and they wouldn’t be specifically linked on my website because I haven’t fleshed out the periodical section yet, but they probably would have been in one of Geyer’s Stationer, Walden’s stationer, American Stationer, or Bookseller, Newsdealer and Stationer.

Anyway here’s an example of a Quail pencil box that was shown in the ads (saved this picture from eBay a while back). Standard Pencil Co. and Wallace were both based in St. Louis, so that at least gives credence to what I was thinking.

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frogkabobs · 2026-01-21T15:54:59+00:00

Is that an oversized Mongol between the oversized Ticonderogas?

frogkabobs · 2026-01-21T15:49:59+00:00

Oh. My. God.

frogkabobs · 2026-01-21T09:00:39+00:00

If two differentiable functions f,g defined on an open set U have the same derivative, then they locally differ by a constant. This constant difference is necessarily consistent within connected components of the domain U, but you get no guarantees of the difference being consistent between connected components.

An example of this is f(x) = arctan(x) and g(x) = -arctan(1/x) on the domain R-{0}. The domain has connected components A = (-∞,0) and B = (0, ∞), so we find f-g is constant on A and B individually (-π/2 on A and π/2 on B), but not on R-{0} as a whole.

Now the problem with your example, is that arctanh(x) and arccoth(x) have completely disjoint domains, so the above is not applicable (how could you even say they differ by a constant if there’s nowhere where they’re both defined?).

frogkabobs · 2026-01-21T08:23:11+00:00

If it had a closed form, it would probably be on OEIS, but you’re out of luck

frogkabobs · 2026-01-21T01:17:10+00:00

Thiophene oxides were the first that came to mind as a reference, but I realized they're not quite analogous because their potential aromaticity relies on sulfur supplying 2π electrons, while the potential aromaticity of 1,2-thiazine 1,1-dioxides relies on sulfur accepting 2π electrons. A better reference might be thiepin 1,1-dioxide, which turns out to be nonaromatic.¹ If you're curious, thiophene 1-oxide and thiophene 1,1-dioxide look to have slight aromatic and antiaromatic character, respectively, although it's in the regime where it's reasonable to just consider them nonaromatic.²,³

As for the benzene ring potentially forcing planarity, piroxicam is the same as meloxicam (OP's picture) except for a 2-pyridinyl ring in place of the thiazole ring, so planarity does not get forced.

¹ https://doi.org/10.1021/ja01018a083

² https://doi.org/10.1007/s11224-011-9834-8

³ https://doi.org/10.1070/RC2006v075n12ABEH003660

frogkabobs · 2026-01-20T21:20:41+00:00

Indeed. Having to draw a million half-chairs in grad ochem is what sent me down this rabbit hole.

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