Curves: the history and development of solutions and applications of higher order polynominals

The purpose of this thesis is to explore algebraic curves, from definition and origination to development and technological / scientific application. A broad and oft-underappreciated topic, I will begin by exploring algebraic curves based on their degrees. Each chapter of my paper will be dedicated to an algebraic degree, beginning with 1st degree and concluding with 5th degree polynomials. In each chapter, we will look at the history and timeline of mathematical methods associated with that particular degree, along with a biography of major players in its discovery and subsequent achievements. The treatment of each degree will finalize with a look at technological and scientific achievements that can be, at least in part, attributed to the mathematics behind it. We will even observe that the rate of change of our technological growth almost seems to model the numeric growth of our topic; i.e., what began as a slow, almost constant rate of change (degree 1) with ancient societies has accelerated through the centuries (and indeed, millennia) to an exponential rate (degree 3). My work will conclude with a look at what potentially lies before us if our technology continues to grow at this rate.