When I was first introduced to polynomial arithmetic, my teacher said it's very similar to regular arithmetic. In fact, because you don't need to worry about carrying, performing addition, subtraction, and multiplication, is significantly easier. Are polynomials really that similar to numbers in base $x$? I felt compelled to find out, unaware of the fact that I was about to go down an unfathomably deep rabbit hole. This article will introduce you to various unusual approaches to dividing both polynomials and integers, and the algorithms we'll develop will serve as a foundation for many future explorations. more

Have you ever wondered how the magical cosine and sine buttons on your calculator work? If so, then this article will not only answer this question, but also develop most of trigonometry and rotation transformations along the way. The only prerequisites are a basic understanding of vectors, and general comfort with algebra. Let's roll up our sleeves and begin exploring the fascinating world of rotations! more