The Works of Euclid

                                                      

The Euclidean theorem serves as a significant tool in teaching students logical and systematic thinking. I recall my secondary school days when we diligently explored how various theorems were developed and how we applied them when solving geometry-related questions. We learned important principles, such as the fact that the sum of angles in a triangle totals 180 degrees, that angles on a straight line must also total 180 degrees, and we delved into theorems surrounding congruency and cyclic quadrilaterals, etc. Grasping these theorems provided us with a strong foundational understanding, enabling us to further expand our comprehension of geometric concepts, which made their application very easy. The elements continue to make an impact to date because they model how knowledge can be built from basic postulates, thereby shaping mathematics, philosophy, and scientific thinking.

Additionally, the article presents an interesting perspective by comparing the relevance of Euclidean theorems today to the significance of the Bible for Christians. To be called a true Christian, one must apply the teachings and instructions of the Lord Jesus in life dealings, with these teachings rooted in the word of God, known as the Bible. Just as Christians view the Bible as a guiding force for their daily lives, believing every word to be the absolute truth, the principles of Euclidean theorems serve as fundamental truths in mathematics, guiding logical reasoning and problem-solving related to geometry. These elements remain a vital area of study today. They form the foundation for understanding shapes, space, and logic, much like how the foundation of a building supports a house. Furthermore, they represent one of the earliest and most lucid examples of deductive reasoning.

After reading the article, I decided to do more research and discovered that Euclid was considered the "father of geometry," and he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. In other words, Euclid’s work established the system of geometry, now called Euclidean geometry, that is still taught in schools today. This includes the principles regarding points, lines, angles, and shapes that are fundamental to our understanding of space. Its rigorous approach of starting with basic definitions and axioms and using deductive reasoning to prove theorems sets the standard for logical thinking and scientific reasoning. Like I stated earlier in the first paragraph, in our senior secondary mathematics textbook, there were steps we had to follow when proving any theorems before applying them. They are usually presented with clarity and structure as they usually come in this order: definition, given, to prove, construction, proof, deduction and finally application. This approach mirrors Euclid’s systematic reasoning and continues to teach students how to think logically and systematically. The video link below gives a vivid idea of how these theorems are presented. https://www.youtube.com/watch?v=SZrpP2JUbMY.Teachers could use it across cultures and centuries, and they are now fundamental to modern fields like engineering, computer science, navigation, and everyday physical measurements.

Usually, when we talk about beauty, we naturally attribute it to aesthetic things or objects that are appreciated for their beauty. These include art, architecture, design, crafts, and other elements of human creative expression. The elements in Euclid's theory are not beautiful because of their aesthetic value of beauty, but because of the intellectual beauty they possess, which entails a harmony of thought, logic, and order. From the article, Euclid’s Elements stands as one of the most enduring works of reasoned thought in human history. Its beauty lies in its simplicity and structure. By beginning with clear definitions and five postulates, Euclid constructs an entire world of geometric truths through deductive reasoning. His first postulate, for example, “A straight line can be drawn joining any two points,” is both simple and universal, capturing a deep truth about space in a few words. This intellectual beauty comes from the way complex truths are built systematically from self-evident principles, depicting how humans can organize their thoughts from the abstract nature they see to what they understand. Personally, while teaching mathematics, I have seen how students unfold the rigid theorems by following the steps, enabling them to understand their beauty.

Finally, if we say that Euclid's theory is beautifully ascribed because of their intellectual importance, then beauty itself has to do with the harmony that arises from clarity, order, and truth, since it is not about appearance but entails coherence, which implies the way ideas fit together perfectly to reveal something universal.