Mathematics and Theatre

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• Mathematics and Theatre

By Caitlin Johnson Claire Dickson
Niyanta Acharya
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Mathematics and Acoustics
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Vocabulary

• Acoustics Of or relating to sound, the sense of
  hearing, or the science of sound, transmission,
  and reception.
• Reverberation- The persistence of a sound after
  its source has stopped and echo like force or
  effect
• Incident Sound- A sound wave that strikes a
  surface
• Resonate- A natural frequency pertaining to the
  materials or device

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Sound Absorbing Materials and
Devices

• Foam and Fiberglass
• Flat or curved panels
• Movable cedar baffles
• Acoustical curtains
• Buffer zones of moving air between double walls

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Simulated residual interior noise insulated by
the wall of gypsum boards filled with mineral
fiber and cellulose mixed spray.
Measured interior residual noise with the
existing bare corrugate metal wall.
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Acoustic Masters

• Vitruvious was a Roman architect and engineer. He
  created the term resonate (sound bouncing back
  and forth). He showed that by placing pots along
  the wall and ceiling, you could enhance sound.

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The scientist who pioneered the developments on
acoustics was Manfred R. Shroeder of the
University of Gottingen in Germany. In the 1970s
Shroeder and his team undertook a major
acoustical study of more than 20 famous European
Venues.
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• He found that listeners preferred long, narrow
  halls over wide halls because wide halls produce
  sounds that first reflect from the ceiling which
  creates the same sound in both ears. Narrow
  halls, however reflect from opposite walls,
  giving the listener two different sounds at the
  same time.

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• To solve this problem, he discovered a number
  theory to determine the ideal depth of the
  notches on the ceilings which redirect the sound
  back to the walls.
• This system is a quadratic-residue sequence.

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Set Design
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Forces and Strains

• Force- A push or pull.
• Newton's Second Law- translation
• Magnitude- Quantity of force

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Calculations Involving Forces

• Trigonometry lets us resolve diagonal force into
  vertical and horizontal components.
• Sin opposite/hypotenuse
• Cos adjacent/hypotenuse
• Tan opposite/adjacent

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Equilibrium

• Sum of vertical and horizontal forces must equal
  zero
• Stresses

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Stress

• Direct Stress Formula
• f P/A
• f is actual stress
• P is applied external force, lbs
• A is cross-sectional area of the member, in2

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Hooke's Law

• Stress is directly proportional to strain.
• Elastic Limit
• elastic region
• plastic region
• ultimate strength

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Mathematics in Plays
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Plot

• Catherine and Robert
• Play starts off after Robert dies
• His ghost constantly visits Catherine
• Catherine is a college drop-out
• After her father dies, they discover a bunch of
  theorems
• Hal appears
• He wants to examine her fathers work
• Catherine reveals that she had written the proof
• Happily ever-after

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David Auburn

• Born in Chicago
• Attended the University of Chicago
• Majored in English Literature

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• "I think there is some connection between
  extremely prodigious mathematical ability and
  craziness. I don't think that math drives people
  crazy, but those with edgy or slightly irrational
  personalities are drawn to it."
• David Auburn (NY Times)

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Reasons for using Math

• Passion
• Intellectuality
• Abnormal daily life
• Both Catherine and her father, Robert have an
  attractive personality
• Roberts character is based on John Nash

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Numbers

• Catherine 1729 weeks.
• Robert 1729. Great number. The smallest number
  expressible-
• Catherine -expressible as the sum of two cubes
  in two different ways.
• Robert 12 cubed plus 1 cubed equals 1729
• Catherine And 10 cubed plus 9 cubed equals 1729.
• Robert You see? Even your depression is
  mathematical.

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Ramanujans 1729

• Littlewood visits him in the hospital and says
  that the number of the cab he took was 1729.
• Ramanujan replies with an interesting comment
  about the number that is repeated in the play.

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Pictures

• Acoustics
• www.generativeart.com/200/CIAO.HTM
• www.theconcertband.com/MusicPhysics_concert_hall
  s.htm
• www.sciencenews.org/articles/20010707/mathtrek.as
  p
• Mathematics in Plays
• http//www.ardentheatre.org/2004/proof_bios.html
• http//www.amazon.com/gp/product/0571199976/102-8
  592483-0328928?vglancen283155
• Set Design
• http//www.fortfact.org/images/Noises20Off/SetBa
  ck.jpg
• http//www.lakeshoreplayersdorval.org/images/set_
  construction_arsenicoldlace.jpghttp//library.osu
  .edu/sites/tri/abtri/jabberwock.jpg

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PAGE CITED

• Peterson, Ivars. Science News. 7 July 2001. 30
  Apr. 2006 lthttp//www.sciencenews.org/articles/200
  10707/mathtrek.aspgt.
• The Concert Band. Concert Halls. 16 Feb. 2006. 30
  Apr. 2006 lthttp//www.sciencenews.org/articles/200
  10707/mathtrek.aspgt.
• The Generative Art. The Generative Art
  Conference. 15 Jan. 2006. 30 Apr. 2006
  lthttp//www.sciencenews.org/articles/20010707/math
  trek.aspgt.
• Walter Kerr Theatre. The Culturevulture. 22 Sep.
  2001. 30 Apr. 2006 lthttp//www.culturevulture.net/
  Theater2/Proof.htmgt.
• Alexanderson, Gerald L. The Mathematical
  Association of America. 22 Oct. 2006. 30 Apr.
  2006 lthttp//www.maa.org/features/proof.htmlgt.
• Holden, Alys E., and Bronislaw J. Sammler.
  Structural Design for the Stage. Boston Focal
  P, 1999. 5-20.
• "Robert Hooke." Wikipedia. 2006. 25 Mar. 2006.