My thoughts on Euclid of Alexandria

After reading a brief history on Euclid's biography and his publication, I was surprised by how little I know about Euclid despite using 'Euclidean Geometry' for most of my life.

In my opinion, the popularity of Euclidean's Geometry comes from the beauty of its simplicity. The simplicity only refers to the nature of this work as well as how humans can imagine and observe Euclidean's Geometry. Math as a human construct implies there aren't many inventions, most are called discoveries. In the case of Elements, the author(s) offers a theorem and axioms which are are still used until this day. Due to its wide range of application and tangibility, it is applied to many facade of our modern lives.

Beauty is subjective. I see beauty in Euclidean postulates, common notions and principles for proofs. The discussion of beauty in Euclid's work is mostly by audiences or disciples familiar with the subject of Mathematics. Per Lockhart's lament, high school trigonometry has ruined the imaginative and artistic nature of Mathematics. The insistence of having standard symbols and definitions when dealing with angles and triangle have made make students frown in classroom. Hence, I would argue having nations of students learning to conform to standardization of symbols for geometry may have driven Euclid's intention to another direction. It is important as Math educator to help students appreciate past work from Euclid, Pythagoras, Descartes etc.

Comments

  1. Erica HuangNovember 5, 2024 at 6:54 PM

    Great reflection, Raymond. It’s indeed amazing how starting with simple, intuitive axioms can lead to complex and even mind-bending discoveries through logical reasoning and proofs. Also, nice connection to the Lockhart reading. For those of us who love math, we see beauty in its elegance and strong logical framework. The challenge for us as a community is to find ways to help our students experience and appreciate that beauty, too. And I hope your list expand beyond just Western mathematicians like Euclid, Pythagoras, Descartes!

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