Teaching the History of Mathematics Using Art and Architecture

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Teaching the History of Mathematics Using Art and
Architecture

• Maria Zack
• Point Loma Nazarene University
• June 2, 2005

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The Course Special Topics in Mathematics

• Annual class that rotates among the faculty
• Content based on faculty research interest
• Organized as a seminar with the students making
  some presentations
• Meets for two hours every week

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Student Involvement

• Reading of selected texts
• Projects
• Presentations
• Hands-on experiences
• Field trips

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Motivation for the Course

• Research in the connections between the
  mathematics and church architecture of
  Christopher Wren
• Interested in integration
• Discussions about General Education at PLNU

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Mathematics Involved in the Course

• Not highly technical
• Practical knowledge how things work
• Connections to other disciplines

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Symmetry

• Used classical texts
• Vetruvius
• Alberti
• Palladio
• Specific examples of both the real and the ideal
• Used ancient worship spaces
• Connection to careful reading of texts for
  meaning and definitions plus geometry

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Ideal vs. Real
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Construction Techniques

• The physics behind domes and arches
• The physics behind cantilevers
• The role of flying buttresses
• Student presentations
• Connection to Physics (GE requirement for our
  majors)

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The Meaning in Church Architecture

• The role of narthex, nave, aisle and altar in
  conveying theological meaning (Geometry of Love)
• Field trips to Roman Catholic and Greek Orthodox
  churches
• Creeds and Stations of the Cross
• Connection to Christian Tradition (GE)

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Traditional Church Floor Plan
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The Work of Christopher Wren

• Parish churches as examples of parameterized
  problems
• Student solutions to problems
• St. Pauls Cathedral
• Requirements of a church
• Engineering behind the dome
• Connection to thought processes in mathematics
  courses

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Problem
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Solution
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St. Stephen Walbrook
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Vanishing Point in Art

• An architectural example
• Alberti and others on technique
• The Day the Universe Changed
• Connection to World Civilization (GE) and the
  careful reading of texts needed for mathematics

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Architectural Example
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The Development of Perspective

• Crash course in tracing the development of
  realistic perspective in painting
• Use of specific well know art works and a few
  interesting distortions
• Connection to Art History (GE)

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The Flagellation of Christ (1459) Piero della
Francesca
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Perspective Using Tiling

• In class use of Albertis technique to draw a
  paved floor
• Use alternative techniques as well
• Connection to Art History (GE) as well as reading
  complex texts

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Lessons Learned

• Cross discipline integration is hard but it is
  good for students to see us stretch
• Students like the opportunity to connect GE with
  their major
• Students are excited to see mathematics crop up
  in unfamiliar places
• Next time let the students struggle for a longer
  period with the original texts