**Comments:**

These articles deal with the visualization of mathematical equations, which turns out to be very powerful, as you will realize here and subsequent articles. The first article is about the Cartesian coordinate system, first introduced by and named after the great French philosopher René Descartes. (Yes, the one who famously said “I think, therefore I am.”) In the last article, we introduce the Cauchy-Schwarz inequality, which is essential to prove Heisenberg’s uncertainty principle in quantum mechanics. Heisenberg’s uncertainty principle says, the more precisely you know the postion of an object, the less precisely you can know its velocity and vice versa. Actually, proving the Cauchy-Schwarz inequality doesn’t require any visualization of mathematical equations, but it helps to understand it better.