We will explore the art of discretizing, a way of building something new from a familiar and well-understood mathematical object: For instance, the real number line can be “discretized” into the integers. Our discussion will center on mathematical objects drawn from my area of specialization: differential geometry. This area of math uses linear algebra and calculus to understand the geometry of objects like a ball or a cone. Our meandering discussion will include puzzle games, a ton of pictures, and questions for you to explore. We assume that the reader has had a full year of calculus (Calc. I and II) and possibly multivariable calculus (oft times called Calc. III) as well. Some examples and remarks will involve graph theory and topology; but familiarity with these subjects should not be necessary to follow the main idea.