Euclid Alone has Looked on Beauty Bare

Three characters are mentioned in Millay’s poem, Euclid, “Beauty” and “Praters.” In the first line of the poem, “Euclid alone has looked on Beauty bare” while other praters are still pondering the secret of Beauty. It is tempting to think that “Beauty” is mathematics, meanwhile the word “bare” is equivalent to the word “pure,” “intrinsic” or “minimalistic.” Even though the beauty people see is “in shapes of shifting lineage,” meaning mathematics is being discovered, perceived and interpreted differently by different people, Euclid is the only person who saw the very cardinal rationale of mathematics; he “anatomized” mathematical problems and proved them based on the postulates and axioms. In his work The Elements, He did not only discover the beauty of mathematics, but also proved them beautifully with the simplest mathematical language.     

After walking through the biography of Euclid and analysis of his work, I begin to understand why his work has been so popular for many centuries. The Element is a valuable attempt to prove mathematical problems with simply definitions, postulates and axioms. For instance, in our class, we tried to reproduce Euclid’s proof of creating a line which is the same as the given line through a point by only using axiom III and postulates II & III in The Elements. By dissecting his proof step by step, we gradually saw the rationale behind it. I believe that teaching The Elements could also be a good idea to help student discover the beauty of mathematics and establish their logic competencies. Euclid’s work also prompts us to think on whether we can use those fundamental postulates and axioms to prove other propositions, and to think on whether those postulates are tenable in other circumstances, leading to further studies in both Euclidean and non-Euclidean geometries.   

Comments

  1. Amanda FritzlanDecember 19, 2022 at 4:27 PM

    I continue to find the way in which Euclid uses visual logic and not numbers for his proofs. This could be appealing to students who can see the simple beauty. There are so many versions of the book The Elements - mathematicians and artists have been drawn to the representations.

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