I have always had a sort-of fascination with mathematics, but at the same time never really enjoyed mathematics as it is taught in traditional grade school. I found that I enjoyed proofs more than someone just telling me a formula or equation exists and does something. When teachers would present something like “The volume of a sphere is 4⁄3×πr3” I would often wonder “Why? Why does this equation exist and how was it extracted?”. I then learned the word “proof” and my researching became much more interesting, I began learning both “why” and “how” whenever it came to a math equation/formula.

JMP

Geometry to the rescue

One thing I really liked when learning about integral calculus was when finding the area beneath a curve you could use primitive geometrical shapes to get an approximation. If you remember back to your integral days you may remember “Riemann sums” which is fancy wording for what is actually going on. I remember back in Geometry I would ask “Why does the area of a polygon interest me? What can I do that is useful with it?”. It still astounds me to this day how useful geometry is in our daily lives and most of us don’t even recognize it. The fact of the matter is that everything around us is tangible and 3-dimensional, everything has a sort of shape. Being that all these shapes exists, that would mean that many problems we come across in our lives in this universe will be related to these shapes, either directly or abstractly. The most beautiful thing about life is that shapes exist even when they don’t exist. Right triangles exist wherever there is a 90° anywhere, it is just that the hypotenuse is hidden to our eyes.

Alright, what is all this for? Well something that I loved when first learning integral caclulus was using the sums of primitive shapes to find the area underneath a curve. Using the area for a collection of rectangles, triangles, and trapazoids that approximate the area underneath a curve was just one of the coolest things to me. This same thing could also be used inversely to find the area of gaps in a graph, such as a line that temporarly lowers and rises back up to continue. Anyway, I know this isn’t anything mind-blowing for people who have gone through calculus or higher mathematical thinking, but sometimes it is nice to just stop and admire the beauty of how the world fits together like one big puzzle!

Games

On that note, if you find that you find the same delight I do in these kinds of things. One of my favorite games I like to play with on my tablet is Euclidea which is a really cool game about geometry and building a “toolbox” of Geometrical concepts to use to solve puzzles that are presented to you. If you haven’t already tried it, I would highly recommend it.