Euclid

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?


Euclidean geometry is still being studied today in large part due to the fact that his work has been preserved. As stated in the reading, we were able to recover a vast amount of his works, and we were able to analyze and study perhaps his greatest accomplishment, Elements. Euclid was probably not the first person to discover or introduce many of the concepts in his books, but, as far as historians know, he was the first to compile all these findings inside the literature.

Another reason I believe it is still studied to this day is because Euclid really presented flawless arguments with each proposition. From the proposition of being able to construct an equilateral triangle, to the world renowned theory of the Pythagorean Theorem, Euclid was able to describe their proofs in precise detail.


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

I believe that the beauty in Euclid's works come from the simplicity of the concepts involved. We have advanced our mathematical abilities constantly throughout history, with newer and more difficult theories being discovered and developed as time progresses. These findings are usually difficult to decipher or understand without higher level mathematical schooling, but when it comes to Euclidean geometry and Elements, some complex geometrical patterns can be proved with axioms that even children can understand. It is beautiful, in my opinion, because so much of culture was affected by it. Whether it be Egyptian culture or Greek mathematics, Euclid was able to influence their society at the time. Even some notable characters in history such as Abraham Lincoln credited Elements with providing him the tools and thinking strategies to successfully argue against slavery.

Beauty is something that can be admired, regardless of the time and age an audience is in. With Elements, all who study it can agree upon the influence it had on ancient society and culture. It emphasized the importance of proof and structure, and that various postulates and propositions worked together to prove new theorems. For me, it made me realize that everything I learn can potentially help discover something new.

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