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In 1959, Josef Albers created a series of fairly boring paintings entitled 'Homage to the Square'. These aren't particularly satisfying to look at, and they aren't particularly tricky to create. I wouldn't buy these paintings except as an investment.
That said, I think Albers hit the Modern zeitgeist right on the nose (and when I say Modern, I don't mean modern as in contemporary, I mean Modern as in early 20th century to the early 1960s, sometimes edging into the 70s).
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This is what Modernism is all about. It is one massive homage to the square. Painting and sculpture are not all literally squares, but often are. To be a Modern painting is to care mainly about shape, color, and it doesn't hurt to be really, really flat.
Frank Stella and Jasper Johns are the giants of Modern Art, and it's all because of that square. Robert Rauschenberg got a lot of attention for painting canvases in all white (The "white paintings" contain no image at all. They are said to be "so exceptionally blank and reflective that their surfaces respond and change in sympathy with the ambient conditions in which they are shown". Hmmm... sounds like a white square to me).
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Minimalist sculpture generally contains a lot of repeated squares. This is quintessentially Modern. Donald Judd is my favorite minimalist (although I'd be hard pressed to even name another minimalist), and he's almost all squares, almost all day.
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But, where the square really comes into play, where you actually see almost nothing but square is in architecture. Go onto any college campus, any downtown, you'll know which buildings are built after 1950 and before 1975 because it's all straight, perpendicular lines.
To be post-modern is to add columns, circles, arches, and something, anything, besides a square.