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## Math in Theatre

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**Math in Theatre**Applications of Conics to the Building of Amphitheaters; and Theatrical Performances that use Math. Karina Wallrafen**What exactly is an ellipse?**• The textbook definition: the set of all points for which the sum of their distances to two fixed points, known as the foci, is constant Karina Wallrafen**Reflective Properties of Ellipses**Karina Wallrafen**Whispering Galleries**• Sound waves, like water and light rays, travel from one foci of a room with an elliptical cross-section (that is, its roof is a semi-ellipse) to the other • This creates a so-called „whispering gallery“, where a person at one focus can hear the person at the other focus whispering, despite the distance between them and/or any background noise • This effect can be achieved • in an elliptical chamber (preferably with a vaulted roof) • By placing the end caps of an ellipse (concave parabolas) with the correct distance between them Karina Wallrafen**Circular Whispering Galleries**• Sound from any point of the circumference of a circular whispering gallery travels along the wall to any other point • Examples are St. Paul‘s Cathedral in London, England and the Gol Gumbaz mausoleum in Bijapur, India Karina Wallrafen**Greek Amphitheatres**• The theatre in Epidaurus, Greece was designed by Polykleitos the Younger in the 4th century BC. • Scientists at the Georgia Institute of Technology have discovered that its remarkable acoustics are due to the limestone seats that hush low-frequency noises (background noise from the crowd) while reflecting high-frequency sounds (the performers‘ voices). Karina Wallrafen**Complicite**• A British theatre company originally known as Théâtre de Complicité uses extreme physical movement, dazzling technology and thought-provoking themes. • Their principle involves „seeing what is most alive, integrating text, music, image and action to create surprising, disruptive theatre“ • Their 2007 production „A Disappearing Number“, whose central characters are the mathematicians Ramanujan and G.H. Hardy, is about pure mathematics, string theory, and the idea of infinity. Karina Wallrafen**A Disappearing Number**• Tells the story of the mathematician Ramanujan and his Ramanujan summation, which assigns a sum to infinite series is part of the base of string theory • Its music involved chants of number sequences morphed into a more traditional score • Uses strong visual and physical imagery to portray patterns and sequences in mathematicians • Staging the play involved exercises for the cast to practice translating mathematics into stories and vice versa. These exercises explored the importance and effects of rhythm and the concept of reducing a story to its essential fragments. Karina Wallrafen**Sources**• www.complicite.org • Dawson, Stephen. "The Reflective Property of an Ellipse." The Reflective Property of an Ellipse. N.p., 2001. Web. 01 Aug. 2013. http://www.math.ubc.ca/~cass/courses/m309-01a/dawson/. • Derksen, Bryan. "Ellipse." Wikipedia. Wikimedia Foundation, 31 July 2013. Web. 22 Aug. 2002. <http://en.wikipedia.org/wiki/Ellipse>. • Georgia Institute of Technology (2007, April 6). AncientGreek Amphitheater: WhyYou Can HearFrom Back Row. ScienceDaily. Retrieved August 1, 2013, from http://www.sciencedaily.com /releases/2007/04/070404162237.htm • Gualteri, Chris. "A DisappearingNumber." Wikipedia. Wikimedia Foundation, 6 Nov. 2010. Web. 01 Aug. 2013. <http://en.wikipedia.org/wiki/A_Disappearing_Number>. • Jones, Aubrey. "Complicite." Wikipedia. Wikimedia Foundation, 17 July 2013. Web. 18 Oct. 2009. http://en.wikipedia.org/wiki/Complicite. • Krohn, Petri. "Whispering Gallery." Wikipedia. Wikimedia Foundation, 25 July 2013. Web. 31 July 2007. <http://en.wikipedia.org/wiki/Whispering_gallery>. Karina Wallrafen