8+Math+in+the+Arts

Art Contacts:

field trip to ICA to see artist Josiah McElheny's work on time, space, and human history - ends 10/22 - go early! ask for 3 min video from the website for future use!

mosiac or tesselations hands on activity for the students to work through MFA field trip - grace & betty go first and scout out galleries - can they custom make gallery tours that will focus on math & art? Architecture walking tour? maybe connect with Boston Architecture College [|DeCordova]Sculpture Park and Museum MC Escher video (Betty) Lincoln Parent -Margaret DeBruin article: http://blog.theautry.org/2011/04/27/crochet-as-an-act-of-mathematics-to-save-the-environment/


 * 12 Day Unit Plan**


 * Introduction ~ 6 days**


 * Day 1: Math in Art - general overview**

[|Magic squares] have a history dating so far back they disappear into the boundary between history and myth. From ancient Chinese literature we have the following story : //At one time, there was a huge flood. The people tried to offer sacrifices to the god of one of the flooding rivers, the Lo river, to calm his anger. As they were doing this, a turtle emerged from the water with a curious pattern on its shell, with patterns of circular dots arranged in a three-by-three grid on the shell, such that the sum of the numbers in each row, column and diagonal was the same: 15. The people were able to use this magic square to control the river and reduce the flood//


 * Stone Engraving: Albrecht Durer: Melancolia from 1514
 * Filippo Brunelleschi: first use of a vanishing point: p. 84 - 87 (Zero: Biography of a Dangerous Idea)

Make a powerpoint with lots of examples of how math is connected to art: Golden Ratio, perspective/vanishing points, origami, architecture, music, artists - escher, hokusai, davinci, symmetry & balance, ancient tilings

Alhambra tilings in Spain - Ascent of Man video clip

Arthur Ganson - MIT Museum visit -coordinate with the MIT Museum to highlight Arthur Ganson's work and other relations to math in the arts.
 * Day 2: MIT Museum**

//Homework:// watch [|Arthur Ganson TED talk], write about one of the pieces that inspired or moved you and why?

Start with National Geographic article on origami - discusses how origami is used today. http://ngm.nationalgeographic.com/big-idea/03/origami -have a discussion about what other uses origami might have in the world. . .how many kids do origami? [|Online game] - matching the fold to the origami shape Play the tangram game at the national geographic page. Watch Between the Folds ~ 25 min. Robert Lang Ted talk //Homework:// Watch origami videos and bring in your best creation. - go to youtube and search Japanzor or Oritube Watch part of Erik Dermaine's talk from Math Museum - geometry of origami.
 * Day 3: Origami Day**

Start with excerpts of article: Doris Schattschneider. Best Writing on Mathematics 2011.
 * Day 3: MC Escher Day**

Show tessellation applet of simple hexagon, triangle, square: http://www.shodor.org/interactivate/activities/Tessellate/ why does that work? bridge into activity: Which polygons will tessellate, how do you know, etc? - reference of shape combinations that tessellate: http://mathworld.wolfram.com/Tessellation.html give kids different shapes and have them try to create their own pattern. ..

Escher: Looking at pieces and categorize them according to infinity, tesselations, hyperbolic geometry, find examples from Betty's book.

Looking at some examples of how he distorted some of his drawing.

//Homework:// Finish their geometric tessellation with color, etc.

what does pi sound like video on youtube @http://www.youtube.com/watch?v=wK7tq7L0N8E
 * Day 4: Music**

Fractals music: - Daniel Wolfe Music : http://www.DanielWolfeMusic.com/ Also, Betty's fractal music article

General math and music connection article: watch clips from The Music Instinct: Science & Song from Netflix Instant Play or youtube Read essay by Vijay Iyer Strength in Numbers: On Math & Musical Rhythm in Best Math WRitings book as a class. audio of NPR interview on Fresh Air with Vijay Iyer

Listen to musical references: original Mystic Brew by Ronnie Foster and cover by Vijay Iyer trio Opening chords of Michael Jackson's Billie Jean. Bela Bartok, An Analysis of his Music - go through some of the book's examples, listen to parts of his music, etc.

Music clips: - find more information about these clips and relation to golden ratio http://ouchmath.wordpress.com/2011/01/10/bartoksatiedebussy-and-chopin-used-the-golden-section/

Check out the music and golden ration section: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibInArt.html#daVinci

Fib. Golden ratio: rhythmic durations and pitch ratios in works from Bartok and Debussy to John Coltrane and Steve Coleman.

Architecture & Golden Ratio Golden Ratio: architecture - pyramids of Giza and Parthenon, constructions by le corbusier and mies van der rohe http://www.geom.uiuc.edu/~demo5337/s97b/art.htm - website
 * Day 6:**

Site full of golden ratio information: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibInArt.html#daVinci

Decide on Topic Research Topic - article reading, information Plan / Create Final Product - could be something artistic or slide show or composition, instruments. . . endless possibilities here Some kind of experience - either a trip to a museum or park or place, or meeting and interview someone in the related field
 * Final Project ~ 6 days**

Link to Math Art Exhibits at Bridges Conference 2012

Mobile Structures Dance? Sculpture Landscape Design Holograms

Da Vinci Albrecht Durer Juan Gri Mondrian Dali
 * __Golden Ratio Paintings:__**

__**Artist:**__ Charles Perry. //Computer Generation of Ribbed Sculptures//. James Hamlin & Carlo Sequin., "ribbed sculptures" sculptures: Solstice, Harmony, Early Mace, Figure-8 Knot, DNA Arch __**Ambigrams**__ http://www.ambigram.com/ambigram-definition Scott Kim

__**Origami**__ Between the Folds video Origami Design Secrets: Mathematical Methods for an Ancient Art Modular Polyhedra Origami

Also has cool Fibonacci sequence facts AB musical patterns: (lesson for younger kids, but the idea is there. . . .) http://artsedge.kennedy-center.org/educators/lessons/grade-k-2/Creating_AB_Patterns.aspx
 * __Math and Music: [|Amazing Fibonacci]__**How the Hidden Life of Numbers Make Memorable Music

__**PAINTINGS**__ Lessons on Math and Art from Philadelphia Museum of Art The golden rectangle is a geometric concept found in many aspects of the natural world as well as in architecture, art, and popular culture. This lesson is designed to be part of a geometry curriculum discussing the mathematical and aesthetic qualities of basic shapes, and of their use in society and nature.
 * Golden Ratio:** Math & Aesthetic Response, [|lesson] creating golden rectangle, examining the following paintings:
 * // [|Choir Screen from the Chapel of the Château of Pagny, France] //, ARTstor search: "PMA_.1930-1-84a–d
 * // [|Sugar Cane] // by Diego Rivera, ARTstor search: "1943-46-2"
 * // [|At the Moulin Rouge: The Dance] // by Henri de Toulouse-Lautrec, ARTstor search: "PMA_.1986-26-32"
 * // [|Breaking Home Ties] // by Thomas Hovenden, ARTstor search: "PMA_.1942-60-1

Is there a formula for people?
 * Math & Proportion and Measurement for People** [|lesson plan] with modifications for high school lesson:
 * // [|The Moorish Chief] // by Eduard Charlemont
 * // [|Figure of a Woman] // Mexican object, artist unknown
 * // [|At the Moulin Rouge: The Dance] // by Henri de Toulouse-Lautrec
 * // [|Avalokiteshvara] // Khmer Empire, artist unkown
 * // [|Zapata] // by Jose Diego Maria Rivera

Of the many connections between mathematics and art, none is stronger than the shared concept of symmetry. Mathematicians find symmetry pleasing in geometry, physicists find it pleasing in the study of motion, poets appreciate it in the play of words, and artists employ it in the creation of beauty.
 * Symmetry and Balance in Art and Math** [|lesson plan] :

> //Thou shalt remain, in midst of other woe// > //Than ours, a friend to man, to whom thou say’st,// > //‘Beauty is truth, truth beauty,—that is all// > //Ye know on earth, and all ye need to know.’// > —John Keats, from //Ode on a Grecian Urn//

Symmetry and Balance in Art and Math
This lesson, designed to accompany the teaching of geometry, examines mirror (line) symmetry and its effects on the viewer.

[|Observing] [|Imagining] [|Abstracting] Simple geometry art project after a Dutch artist
 * Thinking Tools for Innovators**: 3 part lesson