Nov 4: Euclid's Elements and beauty

Euclid and Euclidean geometry were concepts I first encountered during my undergraduate studies at UBC, particularly in my Euclidean Geometry and Discrete Mathematics courses. It was not until later that I realized how foundational Euclid's work had been to much of the mathematics I had studied for years. It is present in topics like trigonometry, geometry, algebra, number theory and calculus. As a result, Euclid and Euclidean geometry remain highly relevant in the mathematics domain. 

The Elements are also appealing for reasons outside of math applications. First, the framework of Euclidean geometry aligns with our natural intuition for visualizing space in one, two, and three dimensions using points and planes. Second, Euclid’s postulates form an axiomatic system that follows a clear and logical progression that mirrors how many of us reason today. Finally, Euclid's Elements have influenced many fields beyond mathematics, including art, architecture, astronomy, and music, highlighting their impact on daily life.

Many people may find the Euclidean postulates beautiful because they enable the derivation of profound theorems from simple, intuitive facts. The use of geometric shapes and symmetries in these theorems also adds to their visual appeal. Lastly, the logical flow of the proofs makes them easy to understand, further enhancing their charm.