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In hyperbolic geometry, squares with right angles do not exist. Rather, squares in hyperbolic geometry have angles of less than right angles.

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Unlike the square of plane geometry, the angles of such a square are larger than a right angle. Larger spherical squares have larger angles.

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In hyperbolic geometry, squares with right angles do not exist. Rather, squares in hyperbolic geometry have angles of less than right angles.

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Unlike the square of plane geometry, the angles of such a square are larger than a right angle. Larger spherical squares have larger angles.

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To take a trivial example, which of us ever undertakes laborious physical exercise, except to obtain some advantage from it? But who has any right to find fault with a man who chooses to enjoy a pleasure that has no annoying consequences, or one who avoids a pain that produces no resultant pleasure? But I must explain to you how all this mistaken idea of denouncing pleasure and praising pain was born and I will give you a complete account of the system.

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In non-Euclidean geometry, squares are more generally polygons with 4 equal sides and equal angles.In spherical geometry, a square is a polygon whose edges are great circle arcs of equal distance, which meet at equal angles. Unlike the square of plane geometry, the angles of such a square are larger than a right angle. Larger spherical squares have larger angles. In hyperbolic geometry, squares with right angles do not exist.

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