squareness n the property of being shaped like a square Usage(s) The cast of The Producers' singing God Bless America on Broadway was all the more defiant for its squareness. Such houses looked simple to build, serene and solid, but their blocky squareness, their squatness, aroused comment more hostile than surprised. Richard Nixon was the very prototype of squareness, yet his rival, John Kennedy, whose amorous adventures infuriated Nixon, defeated him.