monstr

The root monstr hides a surprising connection between a classroom demonstration and a horror-movie monster. It all starts with the Latin verb monēre, "to warn" — the same root that gives us monitor (one who warns) and admonish (to warn earnestly).

From monēre the Romans built monstrāre, "to show, to point out." Literally, showing something is a kind of warning — you point so the other person takes notice. This "showing" verb is the calm, rational branch of the family:

- de- (fully, completely) + monstrāre → demonstrate: to show something fully — how a machine works, that a theorem is true, or, in the streets, that the public is angry. One verb, three modern senses: demonstrate a product (show how), demonstrate a proof (show that), demonstrate against a law (show feeling publicly).
- demonstration is just the noun of that act, and demonstrative the adjective — in grammar a demonstrative word (this, that) literally points; about a person, demonstrative means openly showing emotion.
- re- (back, in return) + monstrāre → remonstrate: to point something out back at someone — to object, to protest, to argue against. Its noun is remonstrance, a formal protest.

Now the eerie branch. The related noun monstrum did not mean an animal at all — it meant a sign sent by the gods, an unnatural event shown to mortals as a warning of disaster: a two-headed calf, a comet, a strange birth. Because these omens were so often grotesque and frightening, monstrum slid from "divine warning" to "unnatural, terrifying creature":

- monster — once an omen, now the thing in the dark. The warning faded; the horror stayed.
- monstrous / monstrously — "like a monster," which split into two everyday meanings: morally shocking (a monstrous crime) and abnormally huge (a monstrous wave).

So the same root that asks a teacher to show the class how something works also names the monster under the bed. The thread connecting them is older than both: the idea of something being shown — whether to teach, to protest, or to warn.