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1.
That intense inner feeling of "Yes! I did it! Fuck you!" when you irrevocably prove someone wrong in reasoned debate.

So much more satisfying than winning by ad baculum.
Dude: "Man, I just won that argument so badly! Think I might have a syllogasm right now."
by Snackajack August 28, 2009
 
2.
The orgasmic, ahh moment when you correctly do any form of geometry, or when you find out you have no geometry homework.
*In Geometry class while taking new notes*
Guy: "Ahh!!! FUCK YES!! I totally did this right!!!"
Girl: "Was that a syllogasm I just heard?"
Guy: " Hell yeah! I syllogasmed all over these notes!"
Girl: " Maybe we can do some Geometry work together. And you can teach me something."
by McDothes September 18, 2013