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Teaching the History of

Mathematics Using Art andArchitecture

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 researchinterest

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 churcharchitecture ofChristopher Wren

Interested in integration

Discussions about General Education atPLNU

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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 andthe 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 requirementfor our majors)

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The Meaning in Church

Architecture The role of narthex, nave, aisle and altar

in conveying theological meaning

(G

eometry 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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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 neededfor 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 ofAlbertis 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 itis good for students to see us stretch

Students like the opportunity to connectGE with their major

Students are excited to seemathematics crop up in unfamiliar

places Next time: let the students struggle for a

longer period with the original texts