Definitions: Arch has two major root meanings: “upside-down U” and “superior.” The first stems from the Latin arcus, from which we get the somewhat similar arc. The second comes from the Greek arkh- or arkhi-, meaning “first,” “greatest,” “primeval.” That prefix passed through Latin as well.
The arch shape has applications in biology and art. A cat can arch its back, a foot can have an arch, a skeptical reader can arch an eyebrow. But arches show up most in architecture—yet the word architecture springs from that second meaning, not the first! (The tecture part comes from tekton, builder, or teks, to weave or fabricate.) Arches come in many styles: Gothic, Roman, Tudor, Moorish, semicircular, and horseshoe, for a start. Some are natural formations. A few examples of the most famous arches are below.
The second meaning often implies a cold superiority: an arch remark is clever at others’ expense, and you’re more likely to hear about an arch-nemesis or arch-villain than an arch-hero.
It’s not cut and dried: archbishops can be fine, depending on your feelings about Catholicism, and an archmage is sometimes good, sometimes evil. But those terms also sound a little archaic—and yes, the word archaic comes from the same root as that second meaning of arch, too. You can look that up in any etymological archive.
The Greek term αρχη, related to that second meaning, is best translated as “first principle.” Some philosophers considered αρχη the stuff of which the universe is made, but Plato and Aristotle thought of it more like a first law of thermodynamics.
Arch has a few other meanings. In statistics, ARCH stands for autoregressive conditional heteroskedasticity. Autoregressive means the value of each variable relies on earlier values, and heteroskedastic means that error ranges can increase or decrease. ARCH models can help estimate important things like how volatile a financial market is.
If you see a dot after arch, as in arch., then it could stand for archaism, architecture, architect…or archery or archipelago.
Arch can be a nickname for Archie, which itself is a nickname for Archibald or Archer. So the nerdy question “Who is the greatest archvillain in comics history?” could be answered, “Reggie Mantle.” (But that’s kind of an arch answer.)
(Not that I mind a good sight gag, but…there’s no visible writing on Reggie’s shirt in panel 2. Is that just an error, or did he run into the bathroom during panel 4 and change his shirt so he could model it for Archie? Either scenario seems like it’d be in character for him.)
Anagrams: Arch has one common anagram, char, and one not-so-common one, rach, a dog that hunts by scent. The rach ran up to the arch, sniffing the char on its wall. Would a really good hunting dog be an arch-rach?
In trigonometry, h can stand for height or hypotenuse, so the term arc h can be shorthand for the height of an arc.

Sorry today’s installment has run late: I’m only just back home and getting ready for another trip this weekend! I have a few other fronts to catch up on, including my all-too-usual correspondence delays. But also, I had to rewrite this piece once it became clear that there’s way more one can do with “arch” than I realized at first.
Or to put it another way, the narrative arc of this “Theming Arch” feature is rising a bit higher than I expected!
So tomorrow will feature the usual micross and this idea will continue…Thursday!