Euclid and Beauty

Why is Euclid and Euclidean geometry still studied to this day? Why do you think this book has been so important (and incredibly popular) over centuries?

I think that Euclid is still studied, in part, because of his contributions to mathematics. He really came up with these solid, foundational ideas and proofs that are important to how the world fundamentally works. When I think about why Euclidean geometry is still studied to this day, I think that the same question could be asked for a variety of other areas of mathematics. I suppose that at least the first couple books of Euclid's Elements do not have clear practical applications, but I think that they could. Especially the later books regarding number theory could be very useful in a variety of computer algorithms. 

I think that this book has been so popular because of its elegance in proving and constructing these ideas, such as constructing an equilateral triangle. When I took a Euclidean geometry course at UBC, I remember being mesmerized by the ideas that the constructions and proofs used. It wasn't like math I have ever seen before, but it still held the logic and reasoning that I am fond of. I want to believe that similar ideas contribute to the general popularity of these books.

Is there beauty in the Euclidean postulates, common notions and principles for proofs? How can we define beauty if these are considered beautiful? 

I think there is definitely beauty in these things. I think that watching someone draw the proofs by hand is quite beautiful. You start with simple things like a point and line and end up with complex drawings resulting in an interesting proof. 

If these are consider beautiful, I suppose beauty is defined closely to elegance, and possibly rigour. I actually think the completeness is what makes these things untraditionally beautiful. The Euclidean work takes ideas that may seem obvious and break them down so small to show how they hold up and are constructed. It is comparable to creating brilliant and beautiful ideas with virtually nothing.