When you were a wee little child, your parents would take you to the neighborhood park to play. You'd swing and slide and climb on the jungle gym. Once in a blue moon, you brought colored chalk with you and played tic-tac-toe with your friends on the sidewalk. That was the closest you ever got to merging logic and fun.
We aren't going to claim that the logic in geometry is as fun as a playground. Very few things in life beat the sheer joy of making it to the other side of the monkey bars. What we will claim is that logic can be fun. Just ask any member of the United States Chess Federation.
In fact, the logic we use in geometry is like a Vulcan kid's playground. It's reasonable, but not overly complex. It gets us piecing together logical statements and eventually building arguments in the form of proofs. And it's fun…for Vulcans, anyway.