Euclid geometry reflection

 

  • 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?
  • 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 that Euclid geometry has become popular over centuries due to it's capacity to touch of several key components of mathematics.

For example, element 5 states that one and only one line can be drawn through a point parallel to a given line. I believe that many structures that were built in the old times and even today are built aesthetically and parallel structures are not uncommon. Therefore, these basic geometric ideas are essential and this is why the book is so incredibly popular.

Moreover, determining the GCF as indicated in book 7 would have been very useful in ancient times as it would be important when trying to divide quantities among people. Many civilizations such as the Greeks, Egyptians, and Arabs engaged in trade so the application is particularly relevant.

For me, I think their is beauty in complexity coupled with conciseness. Many of Euclid's propositions are beautiful in the sense that they compare 2 or more quantities and show the relationship between them. For example proposition 4 stating that "If there are two pyramids of the same height with triangular bases, and each of them is divided into two pyramids equal and similar to one another and similar to the whole, and into two equal prisms, then the base of the one pyramid is to the base of the other pyramid as all the prisms in the one pyramid are to all the prisms, being equal in multitude, in the other pyramid."  t This principle would apply for all types of pyramids as well yet it seems quite specific and for me their is beauty in that. The complexity yet the conciseness of it makes it an attractive book for years to come.

Comments

  1. Erica HuangNovember 5, 2024 at 7:02 PM

    Thanks for sharing, Zain! For those of us who love math, there’s indeed something extraordinary about complexity yet the conciseness in Elements. The challenge for us as educators is to share this appreciation in ways that resonate with our students, helping them find their own sense of beauty in math!

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