Mathematical Guide to Arcadia
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While some may find it quite odd to have mathematics in a play, especially one as funny and interesting as Arcadia, it plays a very important role in this play's motif. Due to the fast paced nature of this play, this guide will help the viewer to further appreciate what is transpiring on stage. The viewer will be able to have a better understanding of the mathematical concepts being presented by reading this before the show as well as referring to it afterwards. There are three main mathematical ideas that are presented in this play. They are the theory of iterated algorithms and fractals, Fermat's Last Theorem, and chaos theory.
As the play progresses and slides into the modern time setting, Hannah discovers Thomasina's notebook and the following statement, "I, Thomasina Coverly, have found a truly wonderful method whereby all the forms of nature must give up their numerical secrets and draw themselves through number alone." What Thomasina had found was something known as an iterated algorithm. Hannah is confused as to what this is and asks Valentine to explain. Valentine explains to Hannah that an iterated algorithm is like a recipe, and if you knew the recipe to make a leaf you could then iterate the algorithm to produce this leaf. Explaining how this iterated algorithm works, he says:
The math isn't difficult...