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© Copyright 1999, Jim Loy
"No straight lines," seems to be the rallying cry of people who make ugly, round, plastic (or concrete?), igloo-shaped houses. You may have seen some. I suppose that the idea is that straight lines, in architecture, are the result of "Western man's" warped sense of aesthetics.
Actually, straight lines come straight from nature and mathematics (which also comes from nature, in its way). The horizon looks very straight, when you stand in the right place. Light beams are used to define straight lines.
The real reason that straight lines are ever-present in western architecture and engineering is that it is easier and cheaper to use straight lines and right angles. When a boat is built, a great deal of effort goes into bending boards to just the right curvature. Carpenters are probably thankful that they don't have to do very much of that on a house. And a straight beam is usually much stronger than a curved beam.
So architectural aesthetics are dictated by practical concerns.
Also of practical concern is loss of heat. A sphere is the best shape to minimize heat loss with a given amount of interior volume. If a building rests on the ground, which more or less prevents heat from leaving through the floor, then a hemisphere is the best shape. So an igloo is mathematically efficient, in that respect.
Using straight lines and right angles, a semi-cube (square as seen from above, and half as high as it is wide) is the best shape, to minimize heat loss.
Another example of practical concerns dictating aesthetics is that a peaked roof is much less likely to leak than a flat roof.