"Fair and Square"

Fair and (even or balanced).
OK. I understand what fair means. But square?
Why does square mean balanced (ie: square meal)
Is it because there are four basic food groups-- hence, four corners of a square. What if there were only three basic food groups -would it be "Fair and Triangle"
P.S. Is this the same square as the 1950's cliche for nerd?

Anything to do with a Masonic Connection perhaps? e.g. 'On the Square' 'On the Level etc..

Ade