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The Mathematics Behind Arcadia



 

Tom Stoppard weaves several exciting mathematical discoveries into his play Arcadia. The following multimedia tour of these discoveries—designed especially for non-mathematicians—is curated by mathematician and novelist Manil Suri.

 

 

Arcadia contains references to several mathematical discoveries such as Fermat’s last theorem, iterated algorithms, fractals, population dynamics, and chaos, together with the related Second Law of Thermodynamics. The links below provide some user-friendly, non-technical background on these topics, so that you can more fully appreciate the changing view of the universe limned by Stoppard in the play.

 

We suggest you start by watching the video  m(Arcadia) by Manil Suri, prepared especially for this production of Arcadia, which explains the mathematics behind the play.

 

 

Due to limited video resolution, some of the computer-generated action on populations shown in the video is best experienced through a higher-resolution PowerPoint presentation, which you can download here. (Microsoft PowerPoint required for viewing.)

 

The links that follow are the ones used by Manil Suri in his video. Visit them to further explore these topics on your own.

 

Fractal Generator
Generates a fern fractal when you press start, similar to what Thomasina might have been trying to do with her apple leaf. Changing the upper left hand box to “words and graphs” generates the “Coke” fractal shown in the video.

 

Fractal Landscapes
Website used in video to generate landscapes based on fractals.

 

Cobweb Plots 1  

First website used in video to explore Valentine’s grouse problem. Uses different models, whose formulas can be reset for you to experiment.

 

Cobweb Plots 2
Second website used in video to explore Valentine’s grouse problem. Uses different models (all done graphically). Emphasis is on where populations finally end up. Instructions available in downloadable PowerPoint presentation referenced above, or download here .

 

Coverly Set
Shows the kind of pictures that Valentine might have generated on his modern computer using Thomasina’s algorithm. Technically, this shows the Mandelbrot and Julia sets for the iterations described in the last part of the video.

 

Chaos, Fractals and Arcadia
A website by Robert Devaney for further reading.

 

 

Manil Suri, a mathematics professor at the University of Maryland Baltimore County, is the author of the novels The Death of Vishnu and The Age of Shiva. His mathematics outreach videos Taming Infinity and The Mathematics of Fiction can be accessed through his academic website or on YouTube .



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