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Some shapes have angles and so they are important in defining the shapes. And angles are absolutely critical for angles. They are the very essence of their existence: if it were not for angles then there would be no angles.
Line segments are incredibly useful, and they essentially shape our world. Without them, there would be no edges and no shapes!
Porportion- Is a measurement of the size and quantity of elements within a composition. In ancient arts,porportions of form were enlarged to show importance.
Historically, it is because we live on a planet which is approximately spherical. 2-dimensional trigonometry was adequate for relatively small shapes where the curvature of the earth had negligible effect. For larger shapes the spherical nature of the earth was important and therefore, so was spherical trigonometry.
There are infinitely many such shapes. There are infinitely many such shapes. There are infinitely many such shapes. There are infinitely many such shapes.