It's a been a little while since I've last posted. As part of my calculus class, we end the year with an exploration into a calculus related topic that we present to the rest of the class. I and my partner chose to explore the origins behind the brachistochrone: the curve of fastest descent for a rolling ball. Below is the related write-up I did as part of this project, and thought it might make for a good posting. It helped refine my LaTeX skills and I think is a good introduction into the field and motivations of the calculus of variations. Now that summer is right around the corner, hopefully I'll be able to write more in the coming months. For now, I hope this will do.