Geometry: A Journey Through School and Life

Everyone struggles with different aspects of math, but for me, one particular subject stood out as easier to grasp—geometry. In my high school days, I faced various challenges in math classes, but geometry was a refreshing exception. I found enjoyment and ease in understanding and proving concepts, which ultimately became my best math performance area.

My Initial Encounter with Geometry

My early introduction to geometry came in a very different form than what students experience today. In the 1960s, geometry was known as 'new math' or 'the Yale plan,' focusing on non-metric geometry and dealing with concepts like lines and forms. Without the need to manage arithmetic, I adapted well and achieved good results in my early years of the subject. However, as my sophomore year approached, the subject became more complex, involving theorems, axioms, and corollaries.

The Transition and Understanding

As the complexity increased, I encountered a significant challenge with arithmetic. Despite the difficulty, I found the abstract and logical nature of geometry more appealing. The clear structure of theorems and principles made sense and were easier for me to understand. Geometry remained my strongest subject, followed by algebra and then trigonometry. This experience taught me that depth of understanding and logical thinking are crucial in mastering mathematical subjects.

The Euclidean Approach in High School

During my time in New South Wales in the early 1860s, we were introduced to Euclidean deductive geometry. This method required learning theorems in a predetermined order. Interestingly, despite not needing to memorize theorems by number, it posed a significant challenge for me. Mastering the correct order of applying theorems was something I struggled with, leading to a significant number of lost marks in my grade 9 geometry exam. In all my other 18 math exams, combined, I lost fewer marks in geometry.

Reflecting on Past Lessons

Now, over 60 years later, I find it difficult to recall many specifics about geometry. However, certain concepts still linger, such as the nine-point circle, which I would like to explore again. There was a theorem whose name stuck with me—Menelaus Theorem. It’s exciting to mix nostalgia with current interests and delve deeper into these geometric concepts.

Geometry teaches us not just about spatial relationships and mathematical proofs but also about logical reasoning and problem-solving skills. Even if some of the concepts seem vague now, revisiting them can reignite the spark of curiosity and appreciation for the subject.