11.4- Response-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 believe that Euclidean geometry remains relevant today for several reasons. First, its simplicity and clarity make its concepts easy to grasp. For instance, the statement "Things that are equal to the same thing are equal to each other" is both advanced and straightforward. Second, Euclid's work established a rigorous logical structure and method of reasoning that has deeply influenced not only mathematics but also our daily lives. His logical approach goes beyond mathematics, shaping the way we reason and prove ideas in everyday contexts, which gives this mode of thinking a timeless quality. Moreover, I feel that his writing holds a profound philosophical significance, as it explores the foundational nature of truth, equality, and logic in ways that resonate far beyond geometry alone.

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

  I do find beauty in the Euclidean postulates. His words are simple and philosophically rich, conveying ideas that are instantly understandable, yet with deeper meanings upon reflection. For example, “Things which coincide with one another are equal to one another” seems to hint at values like fairness or equality, as we understand them today. The principles for assessing proofs—Completeness, Consistency, Independence—can apply universally. Just as each of us is an independent individual, we still exist in harmony with the world, where everything has its own rhythm and balance. There’s no endless opposition; each element has its own role. These qualities reveal profound philosophical insights, which, to me, imbue Euclid's work with aesthetic meaning.

  To me, beauty is harmony, but not through suppression or uniformity. True beauty allows each part to have its own vitality. Each element stands on its own with its own life force, and when brought together, they create a shared beauty that is inclusive and enriching.