A good teacher is always aware that there are things they can learn.
One of the ways in which I encourage students to connect mathematics to other topics is by showing how words and morphemes used in mathematics are used elsewhere. For instance, “median” in mathematics refers to a number in the middle of a list, while the median of a divided road refers to the strip of land in the middle.
In one such case, I asked the students in my Freshman Orientation Seminar this summer to come up with some words that started with “dia-“. The mathematical terms “diameter” and “diagonal” came to mind, naturally; non-mathematical terms included “diaphragm”, “diabetes”, and “diarrhea”, the last of which caused more than a few chuckles from the Freshmen.
I’ll confess: Probably based on its similarity to “bi-” and the fact that Romance words for “two” start with <d> (French “deux”, Spanish “dos”, English “duo”), I came into this conversation thinking that “dia-” meant “two”. This also makes sense with the mathematical terms, since the diameter joins two sides of a circle and the diagonal connects two corners.
So when I asked the class, based on this word list, what “dia-” meant, I was surprised when one of them said “through”. Looking back on the list now, I’m even more surprised: There’s nothing about the medical terms they came up with that superficially suggest “through”, either. I recall having had teachers who would have shook their head condescendingly at “through” because, darnit, they know the answer is “two”. Instead, I paused, mulled it over, and entertained the possibility that I was wrong.
Which I was, sort of.
I think the students were also expecting me to chide them for coming up with “diarrhea”. To an extent, I should have seen that one coming; when I do this sort of exercise, I avoid using “circum-” because of the giggling that comes with “circumcise” or “circumcision”. Instead, I was more curious about “diabetes”, so I took a few moments to look it up. The word means “to come through”, and refers to frequent urination as a common symptom (“diarrhea”, meanwhile, means “to flow through”). “Diaphragm”, meanwhile, means “a barricade across”.
Pretty much every word that starts dia- in English started with this sense of “through” or “across” (“dialog”, “diaphanous”, “diaspora”), although some (such as “diabolical” and “diagnostic”) have lost the obvious connection. The only apparent exceptions I can find are “diary” (which comes from the Latin for “day”, and is related to “diurnal”) and “diamond” (which originally lacked the “i”).
By the way, the Online Etymology Dictionary says I was not entirely wrong: While “dia-” in Greek meant “through” or “across”, it was most likely because of the sense of joining two sides or points.