Euclid and Beauty Response (Nov. 4 Reading)

I remember learning knot theory during my undergraduate, and oftentimes I marvelled at how deeply interconnected geometry is with calculus. Geometry is useful and applicable because it provides the foundation for solving complex mathematical problems. For experts in the fields such as engineering, science, and even art, it offers a way to interpret abstract concepts tangibly. 

Similarly, Euclid simplifies complex geometric ideas into understandable patterns, such as  Elements. For instance, Euclid’s fifth postulate, the "parallel postulate," very much laid the foundation for understanding spatial relationships. The beauty of these postulates lies in their simplicity and showcases the elegance of math. This attracts experts and their interest in the development of geometries. Euclid’s work on geometry is also a shared mathematical language, as it removes cultural and linguistic barriers. Different math experts all over the world are able to unite their shared passion for math. 

For high school students, learning Euclid’s principles is extremely useful for learning trigonometry, because it helps students develop the reasoning skills needed to understand relationships between angles and sides. I can use this in the unit circle or the sine and cosine functions. Studying Euclid can enrich their understanding of mathematics, but also foster critical thinking. Specifically, one of Euclid’s common notions, "things that are equal to the same thing are equal to each other," is in my opinion a very useful teaching tool in high school geometry, where students learn to apply it in, for instance, solving equations.