Last year, the inimitable Vi Hart made a Thanksgiving video series, describing how to imbue your holiday celebration with more mathematics. My favorite video is the one about Borromean onion rings, perhaps because I've been slightly obsessed with Borromean rings for a while.
Borromean rings are three circles that are connected so that if you remove any one of them, the other two are no longer connected.
I used the word "circles" in the sentence above, but that's not quite correct. Topologically, Borromean rings are made of circles, but geometrically they're not. When two shapes are the same topologically, you can stretch or squish one thing until it looks like the other one. Any shape you can make with a rubber band without cutting it is a topological circle. On the other hand, the geometric definition of circle requires that all points on the circle be equidistant from one center point. Three geometric circles can't be linked to make Borromean rings. The circles need to be able to wiggle a bit to get them all to connect the right way in the real world.
Now if there's a lull in the Thanksgiving dinner conversation, you can fill it with your knowledge of topology and geometry! If things get really dire, you can try to figure out what food on your plate is topologically equivalent to what other food. Unfortunately, unless you're having pretzels, this might be kind of boring. Most food is roughly blob-shaped, and blobs are all topologically equivalent. Perhaps instead, you can have a competition for who can create the most topologically interesting Thanksgiving plate. If anyone at your table creates a Klein quartic surface out of sweet potatoes, please send me pictures!
The other mathematically interesting thing about Thanksgiving this year is that it coincides with Hanukkah. This is an exceedingly rare event, and apparently it won't happen again until the year 79811. Jonathan Mizrahi has a nice blog post about what our portmanteau-crazed nation has dubbed "Thanksgivukkah" here.
Personally, I think it's a bit presumptuous to be making claims about what the dates of Thanksgiving and Hanukkah will be in over 77,000 years. Thanksgiving has been a federal holiday for 150 years, but it hasn't had the same date formula the entire time. Furthermore, we've only been using the Gregorian calendar for 431 years, and the Hebrew calendar, in which the current year is 5774, took its modern form only about 1300 years ago. As Mizrahi notes in his post, the Hebrew calendar is slightly out of sync with the solar calendar, and as it drifts away from the seasons, I assume it will be modified to get it back in sync. (Unlike the lunar Islamic calendar, which traipses through the calendar and seasons fairly quickly, the Jewish calendar has a solar fix that is intended to keep the Hebrew months and holidays in certain seasons.) If either the Hebrew or the Gregorian calendar is modified or replaced, all bets are off for the dates of Thanksgiving and Hanukkah.
But calendar reform might be the least of our worries. A lot can happen in 77,000 years! 77,000 years ago, our Homo sapiens ancestors were still making their way out of Africa, and Neandertals populated Europe. There's no reason to think things won't change just as much in the next 77,000 years. If humans are still around in 79811, it's very possible that none of them will even know what Thanksgiving or Hanukkah are. If that's a depressing thought, sorry. Maybe you can cheer yourself up with a green bean matherole and some perfectly spherical sufganiyot.