Geometry Through Art (GART) CTY Course Syllabus STUDENT EXPECTATIONS:

Geometry Through Art (GART)
CTY Course Syllabus
STUDENT EXPECTATIONS:
Students will learn about geometric figures, properties, and constructions, and use this
knowledge to analyze works of art ranging from ancient Greek statues to the modern art
of Salvador Dalí.
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Starting with the foundations of Euclidean geometry, including lines, angles,
triangles, and other polygons, students will examine tessellations and twodimensional symmetry.
Using what they learn about points, lines, and planes, students will investigate
the development of perspective in Renaissance art.
Next they will investigate three dimensions, analyzing the geometry of polyhedra
and considering their place in ancient art.
Then they will venture into the fourth dimension by analyzing Flatland by Edwin
A. Abbott and considering its connection to cubist art.
Finally, students explore non-Euclidean geometry and its links to twentiethcentury art, including the drawings of M. C. Escher.
DAY TO DAY SCHEDULE
DAY
SESSION
1
(Monday)
Morning
1
(Monday)
TOPIC COVERED/WORK DONE
1. Introductions – Two Truths and a Lie
2. Honor Code, Class Rules
3. Pre-Assessment
Afternoon 1.
2.
3.
4.
Basic Definitions – What’s a widget?2 Investigation (point, line, plane)
Types of Angles - Defining angles investigation
Types of Polygons – defining polygons investigation
Similar Polygons - p. 582 Similar polygons investigation with patty
paper2
DAY
SESSION
TOPIC COVERED/WORK DONE
1
(Monday)
Evening
1. Computer lab - Introduction to Geometer’s Sketchpad and
investigation
a. Types of Quadrilaterals – rectangle, square, rhombus,
parallelogram, trapezoid, kite; convex and concave
b. Sum of angles in a quadrilateral, constructing parallelograms,
trapezoid and kite properties
2
(Tuesday)
Morning
1. Area - Stained glass area activity to discover the formulas for
polygons and circles
2. The Pythagorean Theorem - student activity to prove Pythagorean
theorem, discussion of artist Mel Bochner’s interpretation of proof of
theorem
2
(Tuesday)
Afternoon Identify polygons in cubist art:
1. Use Picasso’s Daniel-Henry Kahnweiler; The Guitar, by Jaun Gri; La
Dame aux bêtes (Woman with Animals) by Albert Gleizes; Paul Klee;
other cubist artwork.
2. Creating cubist artwork activity – cubist interpretation of Colton
Chapel fountain and statue of Lafayette
2
(Tuesday)
Evening
Area and cubist artwork, continued
1. Finish stained glass area activity
2. Cubist artwork
3
(Wednesday)
Morning
1. Monohedral and Regular tessellations
2. Archimedian tilings/ semiregular tessellations
*Exercises using cardboard cut-outs of regular polygons and patty
paper.
3
Afternoon 1. Irregular Tessellations - Patty paper activities
(Wednesday)
2. Transformations: rotations, reflections, translations - Patty paper
activities
3. M.C. Escher tessellations - Discover Escher tessellations using
transformations
3
(Wednesday)
Evening
1. Conway Criterion - Computer Lab - Geometer’s Sketchpad activity
2. Transformations and Tessellations review: Problems2 in groups – p.
416 – 418 #1 – 27
DAY
SESSION
4
(Thursday)
Morning
4
(Thursday)
TOPIC COVERED/WORK DONE
1. Tessellation Project - Students create their own M. C. Escher-like
tessellations
2. Rosette Groups: Point Symmetry - Book1 Exercises 1-10, 19, 20, 21
Afternoon 1. Frieze Patterns: Line Symmetry
a. Book1 Exercises 1, 2, 8, 9, 10
b. Human Frieze pattern activity outside
4
(Thursday)
Evening
1. Finish Frieze Pattern exercises
2. Finish Tessellation projects
5
(Friday)
Morning
1. Recognizing Frieze patterns in art and architecture - Students will
analyze and interpret architecture and Native American Border
Patterns that incorporate Frieze patterns and will classify them
2. Frieze Pattern activity - Students create their own Frieze patterns
3. Measuring Angles - Learning to measure angles with a protractor
(afternoon project requires it)
5
(Friday)
Afternoon 1. Penrose Tilings: periodic vs. non-periodic tilings
a. Penrose Tiling Project2 – create their own penrose tilings
6
(Sunday)
Evening
1. Finish Penrose tiling project
2. Introduce Fermat’s last Theorem - worksheet
3. From 8-9pm watch Nova on proof of Fermat’s last theorem with
other math courses
7
(Monday)
Morning
1. Pyramids, Prisms, Cylinders, Cones
a. Students will use nets to create polyhedra, cylinders, and
cones
b. Book problems2 p. 525 – 526 #10 – 22, 27 – 35
2. Antiprisms - Mini-Investigation2 comparing prisms to antiprisms p.
526 #36
3. Volume Formulae - Book problems2 pgs. 534-5 # 4-6, 8, 9, 11, 15, 18
and pgs. 540-1 #1-3, 7, 11, 15
7
(Monday)
7
(Monday)
Afternoon 1. The Platonic Solids - Exploration2 on pg. 544-6
Evening
1. Tetrahedral Kite (16 cells)
a. Illuminations has a lesson plan for this:
http://illuminations.nctm.org/LessonDetail.aspx?id=L639.
b. Other webpage:
http://britton.disted.camosun.bc.ca/tetrakite/tetra.html
DAY
SESSION
TOPIC COVERED/WORK DONE
8
(Tuesday)
Morning
1. Wallpaper Patterns: Plane Symmetry
a. Computer lab – web scavenger hunt to learn about wallpaper
patterns: http://www.scienceu.com/geometry/
b. Java Kali Program to make Rosette groups, Frieze patterns,
and Wallpaper patterns:
http://www.scienceu.com/geometry/handson/kali/kali.html
2. Archimedean Solids
a. Web scavenger hunt to learn about Archimedean solids
8
(Tuesday)
Afternoon 1. Polyhedra and Art - Analyzing art from Renaissance, post
Renaissance, 20th century: http://www.georgehart.com/virtualpolyhedra/art.html
8
(Tuesday)
Evening
1. Euler’s Formula - Marshmallow and toothpick polyhedra activity
9
(Wednesday)
Morning
1. Recursive sequences (taught by TA) - Introduce recursive sequences
2. Fibonnaci numbers and the golden ratio (taught by TA)
9
Afternoon 1. The golden ratio in art/nature (taught by TA) - exercises
(Wednesday)
9
(Wednesday)
Evening
1. Finish the golden ratio in art/nature (taught by TA)
2. Golden rectangle art project
10
(Thursday)
Morning
1. Constructions - Duplicating line segments and angles, finding
perpendicular bisectors of line segments and bisecting angles, etc.
Book exercises2
2. Perspective - History of perspective in art and finding vanishing
points, horizon lines, etc.
10
(Thursday)
10
(Thursday)
Afternoon 1. Perspective exploration2 – how to draw in perspective
Evening
1. Perspective and surrealism art project - Students will create their
own surrealist drawing using perspective
DAY
SESSION
11
(Friday)
Morning
11
(Friday)
TOPIC COVERED/WORK DONE
1. The Fourth Dimension and cubist art
a. Watch and discuss movie Flatland to illustrate how we may
not be able to conceptualize a 4th (or larger) dimension but it
could exist (worksheet)
b. History of cubist art and relation to 4th dimension
http://ion.uwinnipeg.ca/~vincent/4500.6001/Cosmology/dimensionality.htm
Afternoon 1. Finish perspective and golden rectangle projects
12
(Sunday)
Evening
1. Watch movie “War Games” with other math classes
13
(Monday)
Morning
Non-Euclidean Geometry: Elliptic/spherical and hyperbolic geometries –
2 dimensional case
1. Discuss Euclid’s axioms and speculate what it would mean if there
was no 5th postulate
2. Play-doh activity to introduce hyperbolic geometry
3. Tennis ball and rubber band activity to introduce spherical geometry
4. Book Exercises1 – p. 329 – 332 #1 - 22
13
(Monday)
Afternoon 1. More hyperbolic geometry
a. Computer lab – program NonEuclid
http://www.maths.gla.ac.uk/~wws/NonEuclid/NonEuclid.
html
b. NonEuclid activities:
http://www.maths.gla.ac.uk/~wws/NonEuclid/exercise.ht
ml
13
(Monday)
Evening
1. Finish hyperbolic geometry – Book exercises1 p. 333 #23 – 27
14
(Tuesday)
Morning
1. Final project: students will select and research an art topic, research
that topic, show how it is related to geometry, and create their own
piece of artwork in that style
a. in the library to select a topic and conduct research
b. work on project in the classroom
14
(Tuesday)
Afternoon 1. Students will continue work on their projects
DAY
SESSION
TOPIC COVERED/WORK DONE
14
(Tuesday)
Evening
1. Instant Insanity Activity with DMAT
15
(Wednesday)
Morning
1. Geometric Iterations – activity and problem set
2. Introduction to fractals – types of fractals, self-similarity, and the
relationship between the Sierpinski triangle and Pascal’s triangle
15
Afternoon 1. Review for post-test
(Wednesday)
15
(Wednesday)
Evening
1. Stage 5 Sierpinski Triangle using construction paper (6-7 feet tall on
wall of classroom – whole class project)
16
(Thursday)
Morning
1. Post-test
2. One hour to finish final projects
16
(Thursday)
Afternoon 1. Project presentations
16
(Thursday)
Evening
1. Project presentations
17
(Friday)
Morning
1. Project Day – finish any incomplete projects
2. Watch Numb3rs Season 4 Ep. 9 “Graphic” on fractal dimension
Books:
1
Symmetry, Shape, and Space: An Introduction to Mathematics Through Geometry by
Kinsey and Moore
2
Discovering Geometry: An Investigative Approach by Bothe, Serra, Rasmussen, and
Hicks