pack (verb), packing (noun): a native English word with cognates in the Germanic and Romance languages, but of unknown prior origin. In its oldest English usage, a pack was a bundle or bale. From the noun came the verb to pack “to put things into a bundle.” When physical objects are put into a (back)pack, they can be pressed together but can't interpenetrate each other. Following that notion, in topology a packing is a set of non-overlapping sets. One mathematical challenge involves packing as many circles of different sizes as possible into a square of a certain size.

pair (noun, verb); parity (noun): pair is a French word, from Latin par “equal, even.” The Indo-European root underlying Latin par may be perə- “to grant, to allot,” which is possibly the same as perə- “to produce, procure.” A native English cognate is fair, which describes a situation in which things are equal. French pair also appears in an alternate form in peer “someone who is your equal.” Latin par is also used in English as a golf term; it is the number of strokes you must take to equal the average performance on a given hole. In mathematics when you pair things up, you form two equal groups. A pair means two things, with emphasis on the two-ness rather than on the even-ness of the original word. In contrast, a suffixed version of the word, parity, emphasizes the evenness (or oddness) of a number, rather than the twoness.