For whatever reason, the words in question were "monogamy" and "gamete", which, in fact, DO stem from the same root. Shall we?
Monogamy: 1610s, from Fr. monogamie, from L.L. monogamia, from Gk. monogamia, from monogamos "marrying only once," from monos "single, alone" + gamos "marriage" (see gamete).
Gamete: "sexual protoplasmic body," 1886, name introduced in Mod.L. by Austrian biologist Gregor Mendel (1822-1884), from Gk. gamete "a wife," gametes "a husband," from gamein "to take to wife, to marry," from PIE base *gem(e)- "to marry" (cf. Gk. gambros "son-in-law, father-in-law, brother-in-law;" Skt. jamih "brother, sister," jama daughter-in-law;" Avestan zama-tar "son-in-law;" L. gener "son-in-law"). This also is the source of the suffix in monogamy, etc. The seventh month of the ancient Attic calendar (corresponding to late January and early February) was Gamelion, "Month of Marriages."
This one is actually pretty straightforward now that I'm in the know. Nice little tidbit about the month "Gamelion" there at the end, too.
And if you're both paper-folding enthusiasts, you can have an origamous relationship.