I love mathematics! Unfortunately, I don't know as much about it as I would like to. I honestly spend a large portion of my free time reading further in my Calculus textbook, and it's very interesting. The world of mathematics is truly beautiful - but unfortunately, for me, it's incomplete.
I'd like to learn more about real mathematics. When I say "real", I don't mean that parts of math aren't real; I just mean to say that mathematics in it of itself can present really puzzling challenges. Like, for example, the paradox of filling Gabriel's Horn with paint. Or perhaps, finding equations to analyze probability matrices for Markov Chains. Or even something as simple as using differential equations to describe pursuit curves.
Mathematics is all around us - but what books are there that can truly capture its meaning? What books should a high school calculus student read to learn about truly beautiful math?