1. Euclid and Euclidian Geometry is still studied to this day because of its historical impact on mathematics. The Elements was a well laid-out book of a wide range of mathematical concepts like 2D/3D geometry and number theory. With this breadth of coverage, it was possible to be used in many curriculums. The structure of the book also made a big influence on how we structure our proofs, definitions, and mathematical ideas to this day.
2. Yes, I believe there is beauty in Euclidian Math that comes from its rigorous structure with simplicity, yet having enough clarity in the proofs and explanations. Here, beauty isn't the pretty things we add on to make it look nicer, nor is it the complexity of ideas that are introduced. Beauty is the clear and perfect arrangement of ideas in logical order, just like a cake without any decorations but with a perfectly baked sponge cake and balanced use of ingredients.
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