A simple trick to decorate Theorem-like environments with poker suits QED symbols.
I did not come up with this theorem decoration style (I've first seen it here) nor with the whole code (I salvaged it from TeX StackExchange and other sources over the years). This is just my current implementation of the code.
"(Infinite) series are the invention of the devil, by using them, on
may draw any conclusion he pleases, and that is why these series
have produced so many fallacies and so many paradoxes."
-Neils Hendrik Abel
Based on the paper Sometimes Newton's Method Cycles, we first asked ourselves if there were any Newtonian Method Cycle functions which have non-trivial guesses. We encountered a way to create functions that cycle between a set number of points with any initial, non-trivial guesses when Newton's Method is applied. We exercised these possibilities through the methods of 2-cycles, 3-cycles and 4-cycles. We then generalized these cycles into k-cycles. After generalizing Newton's Method, we found the conditions that skew the cycles into a spiral pattern which will either converge, diverge or become a near-cycle. Once we obtained all this information, we explored additional questions that rose up from our initial exploration of Newton's Method.