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yes, a square can only exist on a plane in euclidean geometry.
Euclid just another Greek
true
Objects that exist in the real world usually have shapes (although they can also be shapeless) and those shapes will bear some resemblance, and in some cases a very close resemblance, to the theoretical shapes of plane and solid geometry, such as triangles, squares, circles, spheres, cubes, etc. But even aside from that, a deep understanding of our universe (and the laws of nature which describe the way it operates) would not be possible without a knowledge of plane and solid shapes. Geometry has implications for every area of mathematics, and mathematics is the language of science.
Two dimensional geometry is called "plane geometry" meaning that it occurs on a single surface or plane. The objects used in plane geometry are called plane figures.