Process
You will work in groups of three to accomplish the task set before you. Each member will become an expert in one of the three following areas: symmetry, patterns, and geometric shapes, and then share their knowledge with the group.
You will use a variety of websites to research your topic, then you will critique pieces of art based on your area of expertise, and finally, you will combine all of your knowledge to create a new piece of art for Central Park.
Phase 1: Research your area of expertise
Review the websites beneath your role. What are important components, characteristics, or attributes of your topic?What information does each site give you about your area of geometry? How might this contribute to creating a final piece of art?
Symmetry
As you review these sites, consider the following questions:
What is symmetry? What about asymmetry? What types of designs show symmetry? How can it be created? Can you find some examples of symmetry on these websites?
About Symmetry and Pattern
http://mathforum.org/geometry/rugs/symmetry/whatis.html
Line Symmetry
http://www.linkslearning.org/Kids/1_Math/2_Illustrated_Lessons/4_Line_Symmetry/index.html
Space and Shape in Geometry
http://www.learner.org/teacherslab/math/geometry/shape/quilts/quilts_background.html
Quilts and Symmetry
http://www.learner.org/teacherslab/math/geometry/shape/quilts/index.html
Patterns
As you review these sites, consider the following questions:
What is a pattern? How are patterns created? Are there times when no patterns are present? How do color and shape play roles in creating patterns?
About Symmetry and Pattern
http://mathforum.org/geometry/rugs/symmetry/whatis.html
Tesselations
http://www.42explore.com/teslatn.htm
Inside Patterns
http://mathforum.org/geometry/rugs/symmetry/fp.html
Patterns in Mathematics
http://www.learner.org/teacherslab/math/patterns/index.html
Geometric Shapes
As you review these sites, consider the following questions:
What defines a geometric shape? What is not a geometric shape? What are some specific types of geometric shapes? Where do you find geometric shapes on these websites?
Geometric Shapes and Figures
http://www.42explore.com/geomet.htm
Definitions of various geometric shapes
http://www.mathleague.com/help/geometry/polygons.htm
Triangles
http://www.math.com/school/subject3/lessons/S3U2L2GL.html
Quilt Geometry
http://log24.com/log04/0809.htm
Phase 2: Review artwork based on your role
Keep in mind what you have learned about your area of geometry. Review the sites below as a group, and then critique each piece of art based on your own geometric perspective. Use the worksheet provided by your teacher to analyze and critique the pieces of art.
Escher/Tessellations
Regenerating salamanders: http://www.nature.com/nrm/covers/0802_cover.html
Work 72: http://users.tkk.fi/~tlampen/images/SymmetryE72Lg.jpg
Butterflies: http://users.tkk.fi/~tlampen/images/SymmetryE70Lg.jpg
Circle Limit: http://home.comcast.net/~eschermc/Circle_Limit_III.jpg
Oriental Rugs
Choose 2 from this site: http://mathforum.org/geometry/rugs/gallery/
Architechture
http://library.thinkquest.org/~16661/gallery/3.html
http://andrew.mcguckin.us/art/arches_640.jpg
Cubist Art
Pablo Picasso
http://wmmhs.org/users/art/marrero/painting_class/master_emulation/cubism.htm
Juan Gris
Violin and Guitar: http://www.artchive.com/artchive/G/gris/vio_gtr.jpg.html
Portrait of Picasso: http://www.artchive.com/artchive/G/gris/picasso.jpg.html
Indian Blankets
Red Mesa Rug: http://www.indianweaving.com/graphics/redmesa.jpg
Koshare Rug: http://www.indianweaving.com/graphics/koshareb.jpg
Historic Navajo Rugs (view 2 or 3): http://www.navajorug.com/historicrugs.htm
Phase 3: Create an original work of art
Talk with your group members about what you've learned as an expert in your area of geometry. Share your critiques of the artwork, and discuss similarities and differences in how you each analyzed these pieces of art.
Now work together to create a design of a new and original piece of art. You may want to play around with this website to look at some possible shape combinations.
Practice with Pattern Blocks
http://ejad.best.vwh.net/java/patterns/patterns_j.shtml
Combine your talents and knowledge gained so far to create a work of art that encompasses symmetry, patterns, and geometric shapes. Remember Mayor Bloomberg's desperate plea for original and creative art to hang over those crummy Gates!!!
Phase 4: Present your creations to the class
Now that you have combined all you knowledge, expertise, and creativity, it's time to share your artwork with the class! As a group, write up a short explanation (1-2 pages) describing how your final product includes symmetry, geometric shapes, and patterns. For your oral presentation, be prepared to share how you created your piece, why you chose to create it the way you did, and where and how each geometric component is used. Now it is time to present your piece to the class. Everyone will have a unique piece of artwork, so it is important that you include your rationale in your presentation.
Things to consider before your presentation:
Make sure that you discuss why you chose the geometric shapes, colors, and patterns that you used. How does your model reflect the wishes of Mayor Bloomberg? How does your model show symmetry? How did your group of experts collaborate to make the final product?
