The more you argue your case the worse your chance to -really- win the argument, convince the other side. More often they will admit defeat to get you off their neck and keep believing their falsehood even stronger.
Sounds to me like religion.
If you're looking for geometry learning, try to make an asteroids-like game.
It's not too challenging as to turn someone down, but lots of fun and you'll learn how to apply geometry. Specially sine and cossine, which my teachers did a terrible job in teaching what that was all about (only teached transformation formulae, never applying them). I only learnt what it was meant to do when I tried to do a subspace-like game.
Nice... Keep thinking that you're safe, and I won't tell you how I would have gotten a virus just today when I downloaded a basic app for my HP calculator, were it not for my AV software, which detected it just when I downloaded the installer from HP's official site.
I hope you never download anything from anywhere, including sites which should be safe and trustful, but just aren't.
Kleeneness is next to Godelness.