Euclidean geometry as a starting point would blow their minds.
Proving sqrt(2) is irrational might get you martyred though, be careful.
The problem with that is that this predictive power only manifests itself when you can make precision measurements of celestial objects, and the Greeks could not because they didn't have telescopes. (Hm, inventing the telescope might be an answer. Did the Greeks have lens-making technology?)
> Euclidean geometry as a starting point would blow their minds.
Sure, but that wouldn't prove you were from the future any more than it proved that Euclid was from the future.
By that standard it doesn't seem like any scientific or technological knowledge could prove you're from the future, either.
The only way to show you're from the future that can't also be explained by being from the present and having great knowledge/intelligence is to predict the unpredictable. But, you've narrowed the time constraint (a few weeks) and widened the range (a few years) so that predicting the immediate and unknowable isn't an option. Seems to be what you're going for also. So, I don't think you're left with anything.
Even if you loosen some of the constraints it’s hard. You could show up with a Jeep and some people would think you’re from the future and some would think you’re just from somewhere else. Even if your predict their future that may not convince someone! Predict an eclipse and they might say eclipses are predictable (of course, they’re right), predict the outcome of a battle and they’ll say you can see the future but that doesn’t mean you’ve been there.
Glassmaking would be a good one because the chemistry is based on available materials and with sufficient knowledge you would walk them through the history of glassmaking up to a simple lens and make eyeglasses.