Individual Presentation Reflection

Pure mathematics has always been the branch of math that I have found most intriguing. I don't think I discovered the name for it until my proofs class in my first year of undergraduate studies. It's like, math from scratch. You have nothing, now create. You have this concept, now prove it. Although I'm awful at it, I find that it is the only thing that I have no problems being stuck at. Which is interesting now that I think about it. 

I feel like I rediscovered this while researching on the history of geometric constructions. It may be the purest of the purest forms of mathematics. When I realized that these mathematicians were creating theorems, proofs and conjectures based solely on concepts and not facts, I was amazed. They were creating factual experiments solely through proofs and conjectures. Euclid does not define a right angle as an angle that is ninety-degrees. He defines it as the two angles created by one line intersecting another line being equal - or "right". I had written a question for potential future students of mine in how I would incorporate this into my classroom where I asked "draw me a square without using a ruler or compass and prove that it is a square". I sat on this question for a long time thinking about how I would answer it and I still have not come up with an answer. But there's beauty in that, right? Why do I need to have the answer to this question - it's meant as an exploratory introduction to geometric construction and it would be informative regarding student thinking.