### Teacher’s Summary

This essay creatively explores the philosophy of geometry by blending personal experiences with historical and mathematical inquiry. The author effectively demonstrates how ancient mathematical concepts continue to shape modern understanding by measuring the height of a pine tree using two different methods. The narrative emphasizes the significance of geometry as a tool for connecting past and present, while also reflecting on the challenges and discrepancies encountered in real-world applications. The essay successfully intertwines the study of history and mathematics, offering a thoughtful and engaging analysis.

**Grade:** A

## The Philosophy of Geometry: A Mathematical Adventure in My Backyard

As a history major with a minor in mathematics at Howard University, I often find myself drawing unexpected connections between the past and the present, the theoretical and the practical. This assignment on the philosophy of geometry wasn’t just about measuring a tree; it was about understanding how ancient mathematical concepts continue to shape our world today.

### Choosing My Subject: The Mighty Pine

When I was tasked with finding an object in my community to measure, I immediately thought of the towering pine tree in my grandmother’s backyard. This tree has been a constant presence in my life, its branches swaying with the weight of family memories. Who would have thought it would also become the subject of a mathematical inquiry?

## Method 1: Similar Triangles and the Homemade Hipsometer

Creating my own hipsometer brought back memories of my high school geometry class. As I crafted this simple device to measure the angle of elevation, I couldn’t help but think about the ancient Greek mathematicians who first developed these concepts. Thales of Miletus would have been proud!

## Method 2: Trigonometry and Shadows

Using trigonometry to measure the tree’s height felt like stepping into the shoes of ancient Egyptian surveyors. As I measured the shadows cast by the tree and myself, I was reminded of how these same principles were used to build the pyramids. My mom, helping me measure the shadows, joked that we were like a modern-day mother-daughter surveying team from ancient times.

### The Mathematical Process: Numbers Tell a Story

Converting measurements, cross-multiplying equations, and juggling formulas might seem tedious to some, but to me, it’s like decoding a historical document. Each step in the calculation process felt like peeling back layers of mathematical history.

## The Discrepancy: A Lesson in Real-World Applications

When I realized the two methods yielded different results, I was initially frustrated. But then it hit me – this discrepancy is exactly what makes mathematics so fascinating in real-world applications. It reminded me of the stories my calculus professor told about the challenges NASA faced in early space missions due to mathematical imprecisions.

### Reflections on Methodology

Pondering the pros and cons of each method, I couldn’t help but draw parallels to historical research methods. Just as historians must choose the right approach for different types of historical inquiry, mathematicians and scientists must select the appropriate mathematical tool for each unique situation.

## Conclusion: Geometry as a Bridge Between Past and Present

This assignment did more than teach me how to measure a tree. It showed me how mathematics, like history, is a living, breathing discipline that connects us to our past while helping us navigate our present and future. As I continue my studies, bridging the gap between history and mathematics, I’m excited to discover more ways in which these seemingly disparate fields intersect and inform each other.

Who knows? Maybe one day I’ll write a groundbreaking paper on the mathematical principles used in historical architecture or the historical development of geometric concepts. For now, I’ll never look at that old pine tree the same way again – it’s not just a family landmark, but a standing testament to the enduring power of mathematical thinking.

**References:**

• Cooke, Roger. *The History of Mathematics: A Brief Course*. Wiley-Interscience, 2005.

• National Institute of Standards and Technology. “The Use of Mathematics in Real-World Problems.” NIST.gov.

• Katz, Victor J. *A History of Mathematics: An Introduction*. 3rd ed., Addison-Wesley, 2008.

• “The Geometry of Surveying.” *Mathematics in School*, vol. 20, no. 5, 1991, pp. 22-24. JSTOR, JSTOR.org.