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Folding, imagining, and constructing amath and art class

Special Session on Mathematics and the ArtsJoint Math Meetings 2015

Dina Buric and Teresa Downard

Department of MathematicsWestern Washington University

January 11, 2015

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A Collaborative Math Art Project

Instructions:

Fold / Draw / Construct a similar rectangle.

√3

Portrait of Luca Pacioli - Jacopo de’ BarbariThe disintegration of The persistence of memory - Salvador Dalí

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Course Development

We were motivated to create the course due to the myriad ofaccessible topics connecting math and art.

We started talking to people about interesting problemsand asking for advice.We collected information on issues like assessments,pre-requisites, and course structure.We sought out opportunities for community outreach &field testing.

Swans - M.C. Escher

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Course Development

We were motivated to create the course due to the myriad ofaccessible topics connecting math and art.

We started talking to people about interesting problemsand asking for advice.

We collected information on issues like assessments,pre-requisites, and course structure.We sought out opportunities for community outreach &field testing.

Swans - M.C. Escher

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Course Development

We were motivated to create the course due to the myriad ofaccessible topics connecting math and art.

We started talking to people about interesting problemsand asking for advice.We collected information on issues like assessments,pre-requisites, and course structure.

We sought out opportunities for community outreach &field testing.

Swans - M.C. Escher

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Course Development

We were motivated to create the course due to the myriad ofaccessible topics connecting math and art.

We started talking to people about interesting problemsand asking for advice.We collected information on issues like assessments,pre-requisites, and course structure.We sought out opportunities for community outreach &field testing.

Swans - M.C. Escher

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Example Topics: Number and Pattern

Spirolaterals

Pick a finite sequence, draw a line with length of your firstnumber, then your second number, and repeat, turning 90degrees after each number.

Example: 1,2,3

After trying a couple sequences, what questions come to mind?

Source: Frank Odds Spirolaterals - Mathematics Teacher Feb 1973

7 × graph paper with coloured pencil - Tina Jonsbu

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Example Topics: Groups and Symmetry

One way to describe the rotational symmetry of this star is withmodular addition. If we label the points of the star withnumbers from 1 to 12, like a clock, we can add them :

7 + 3 ≡ 10 and 10 + 4 ≡ 2

Closure If you add any two numbers, is the result in the set?Associativity Is this type of addition associative?Identity Which number behaves like zero?Inverses Does each element have an inverse?

Resource: David W. Farmer Groups and Symmetry: A Guide to Discovering Mathematics

E8 - J. Gregory Moxness

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Example Topics: Perspective

Where should you stand to view Interior of Antwerp Cathedralso that the painting really pops out of the page?

Source: Marc Frantz and Annalisa Crannell Viewpoints

The Biosphère, U.S. Pavilion Expo 67 - Buckminster Fuller

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Example Topics: Graph Theory and Origami

How do you create a PHiZZ unit dodecahedron using only threecolors where no two colors touch? What about for a truncatedicosahedron?

Source: Tom Hull Project Origami

Five Intersecting Tetrahedra - Thomas C. Hull

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Example Topics: Curves and String Art

What type of curve do the lines form? What is the equation?

Source: “String Art is Calculus" YouTube video

Chords Bridge, Jerusalem - Santiago Calatrava

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Wouldn’t it be beautiful to learn geometry in this way?

-Antoni Gaudí

Bascilica de La Sagrada Famìlia - Antoni Gaudì

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Course Structure

MATH 160 Mathematics and Art

Our goal for this class is to give students experience with realmathematics: the inquiry, exploration, innovation, the struggle,

and the sense of victory.

Each class day, students will be given an introduction to a topicor problem and spend the rest of the time engaged in hands-on

activities and problem solving....

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Course Structure: Calendar

Melancholia I - Albrecht Dürer

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Course Structure: Journal

Students chronical their problem solving process by writing anddrawing in a Math Journal.

Disney Concert Hall - Frank Gehry

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Course Structure: Projects

Students choose a course topic to investigate in greater depth.

Project Ideas ExpectationsDrawing and PaintingBuilt FormsDance and MusicFiber ArtsComputer GraphicsBe Creative and use yourown interests!

Research topic withbooks, articles, andinternetCommunicate what waslearnedCreate something new

GradingPROPOSAL BIBLIOGRAPHY PAPER/PRESENTATION

QUALITY OF CRAFT & MATHEMATICAL CONTENT

Platonic Solids - Johannes Kepler

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Community Outreach & Field Testing

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Rectangles and Thankyous

We love to see all the different ideaspeople come up with!

A big THANK YOU to theMathematics Department at Western,the organizers of the special session,and all the people who havecontributed to the area ofMathematics and Art!

Source: Jay Hambidge The Elements of Dynamic Symmetry

Square Roots to Sixteen (Theodorus of Cyrene) - Crockett Johnson

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Rectangles and Thankyous

We love to see all the different ideaspeople come up with!

A big THANK YOU to theMathematics Department at Western,the organizers of the special session,and all the people who havecontributed to the area ofMathematics and Art!

Source: Jay Hambidge The Elements of Dynamic Symmetry

Square Roots to Sixteen (Theodorus of Cyrene) - Crockett Johnson