P.S. In your examples, if I were writing, I'd use the shorter word "geometric." Shorter words are stronger, punchier, and English--and probably all languages--evolves in the direction of using shorter words. Also, the dictionary I checked lists "geometric" as the entry and "geometrical" as alternative, so "geometric" is used more frequently.

I don't think there's any difference at all in your examples. They can be and often are used as synonyms. I think there's a very fine distinction, though. I'm going to say it first and then go check a U.S. dictionary. Oops. The dictionary doesn't confirm, it just says "geometric; also, geometrical," so they are just alternative forms of the same word. I'm going to go ahead anyway. I might be wrong. Other English speakers please comment. In the very strictest sense, I think that there is or once was a fine distinction. "Geometrical" should mean "related to the field of geometry" and thus would _includes_ the meaning, "looking like the diagrams and shapes that are studied in geometry." "Geometric" should mean just "looking like the diagrams and shapes that are studied in geometry." so it would have a narrower meaning. You could talk about a "geometrical design" or a "geometric design." You could talk about a "geometrical proof" or "geometrical reasoning." If I'm right, then it would not really be correct to say "geometric proof." That sounds to me like a proof that's written out in the shape of squares and triangles--or a proof that keeps getting longer and longer, like a geometric progression!