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Lesson Plans

Re: tesselation lesson plans (long post

[ Thread ][ Subject ][ Author ][ Date ]
Chris Merriam (
Fri, 08 Nov 1996 15:49:59 -0700

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cainwm wrote:
> I would be interested in any information I could get on
> lesson plans for tesselations. (Note: we do not have use
> of a computer for the project)

Try Dale Seymore Press tesselations are the core of the expanding
catalog they publish.
Chris Merriam
Christine Merriam, Art Educator
Kayenta Intermediate School
PO Box 337, Kayenta,AZ 86033 *****

also... here is a copy of a web page:)

Introductory References about Tessellations
(tilings) and Sources for Illustrations

Compiled by Doris Schattschneider, Moravian College,
My recommendation for the best introduction to making tessellations is
the book Introduction to Tessellations by
Britton and Seymour. The comprehensive collection of Escher's drawings
of tessellations is in Visions of
Symmetry by Schattschneider.

There are many articles on tessellations in The Mathematics Teacher and
Mathematics Teaching (the journal of
the British Association of Mathematics Teachers). Only a few of these
articles are listed below.

Dover Books has a very rich offering of books that have examples of
tessellations. Two recently published books
on polyominoes (one by George Martin, published by the MAA, the other by
Solomon Golomb, published by
Princeton University Press) contain tiling recreations; see also books
by Martin Gardner that contain reprints and
updates of his previous Scientific American columns, several of which
discussed tilings.

Břggild, J.K., "Breeding Tessellations." Mathematics Teaching 90
(1980): 31-36.
Boles, Martha and Newman, Rochelle, The Surface Plane, The Golden
Relationship: Art, Math & Nature,
Book 2.
Bradford, MA: Pythagorean Press, 1992.
Boswell, Thom, ed., The Kaleidoscope Book: A Spectrum of
Spectacular Scopes to Make.
New York: Sterling Publishing, 1992.
Bourgoin, J., Arabic Geometrical Pattern and Design.
New York: Dover, 1973. (Plates of original, 1879.)
Britton, Jill, and Dale Seymour, Introduction to Tessellations.
Palo Alto: Dale Seymour Publications, 1989.
Critchlow, Keith, Islamic Patterns. An Analytical and Cosmological
New York: Schocken Books, 1976.
Crowe, Donald W., Symmetry, Rigid Motions, and Patterns, HIMAP
module 4.
Arlington MA: COMAP, 1987.
Edwards, Lois and Kevin Lee, TesselMania! Math Connection.
Berkeley: Key Curriculum Press, 1994.
El-Said, Issam and Ayse Parman, Geometric Concepts in Islamic Art.
London: World of Islam Festival Publishing Company, 1976.
(Available from Dale Seymour Publications.)
Field, Robert, Geometric Patterns from Roman Mosaics and how to
draw them.
Stradbroke (England): Tarquin Publications, 1988.
Gardner, Martin, "Tiling with Polyominoes, Polyiamonds, and
Polyhexes." Time Travel and Other
Mathematical Bewilderments.
New York: W.H. Freeman, 1988.
Dr. Matrix's informational WWW page on Penrose tilings:
Giftwrap by Artists: M.C. Escher.
New York, Harry Abrams, 1987. (Look for others, too.)
Grünbaum, Branko and Geoffrey Shephard, Tilings and Patterns.
New York: W. H. Freeman, 1987.
Haak, S. "Transformation Geometry and the Artwork of M. C.
Escher." Mathematics Teacher 69 (1976):
Hargittai, I. and M. Hargittai, Symmetry, A Unifying Concept.
Bolinas, CA: Shelter Publications, 1994. Also available from Key
Curriculum Press.
Hoffer, Alan and George Bratton, Kaleidoscope Math.
Palo Alto, CA: Creative Publications, 1978.
Hofstadter, Douglas, "Parquet Deformations: Patterns of Tiles that
Shift Gradually in One Dimension."
Scientific American (July 1983) 14-20.
Jones, Owen, The Grammar of Ornament.
New York: Van Nostrand Reinhold, 1972. (Original 1856) Plates
only, New York: Dover, 1988.
Kappraff, Jay, Connections: The Geometric Bridge Between Art and
New York: McGraw-Hill, 1991.
Lockwood, E.H. and R.H. Macmillan, Geometric Symmetry.
Cambridge: Cambridge University Press, 1978.
The Mathematics Teacher 67, no. 4 (1974). (Special issue on
O'Daffer, Phares and Stanley Clemens, Geometry: An Investigative
Menlo Park, CA: Addison Wesley, 1976; second edition 1992.
Pearce, Peter, Structure in Nature is a Strategy for Design.
Cambridge, MA: M. I. T. Press, 1978.
Racinet, Auguste, L'ornement polychrome.
Paris: Firmin-Didot, 1869-1873. Plates only, Racinet's Historic
Ornament in Full Color (ser. 1) and
Full-Color Picture Sourcebook of Historic Ornament. New York:
Dover, 1988, 1989.
Ranucci, E. R., and J. L. Teeters, Creating Escher-Type Drawings.
Palo Alto, CA: Creative Publications, 1977.
Rigby, J. F., "Napolean, Escher, and Tessellations." Mathematics
Magazine 64 (1991): 242-246.
Schattschneider, Doris, "In Black and White: How to Create
Perfectly Colored Symmetric Patterns."
Symmetry: Unifying Human Understanding, ed. I. Hargittai, pp.
New York: Pergamon, 1986.
Schattschneider, Doris, "The Fascination of Tiling." Leonardo 25,
no 3/4 (1992): 341-348.
Reprinted in The Visual Mind: Art and Mathematics, ed. Michele
Emmer, pp. 157-164. Boston: MIT Press,
Schattschneider, Doris, "In Praise of Amateurs." The Mathematical
Gardner, ed. David A. Klarner, pp.
140-166. Boston: Prindle, Weber & Schmidt (now Wadsworth).
Schattschneider, Doris, "The Plane Symmetry Groups, Their
Recognition and Notation." American
Mathematical Monthly 85 (1978): 439-450.
Schattschneider, Doris, "Tiling the Plane with Congruent
Pentagons," Mathematics Magazine 51 (1978) :
Schattschneider, Doris, "Will it Tile? Try the Conway Criterion!"
Mathematics Magazine 53 (1980):
Schattschneider, Doris, Visions of Symmetry: Notebooks, Periodic
Drawings and Related Work of M. C.
New York: W.H. Freeman, 1990.
Schattschneider, Doris and Wallace Walker, M.C. Escher
Petaluma, CA: Pomegranate Publications, 1987.
Senechal, Marjorie, "Escher Designs on Surfaces." M. C. Escher:
Art and Science, ed. Coxeter, H.S. M.,
M. Emmer, R. Penrose, and M. L. Teuber.
Amsterdam: North Holland, 1986.
Senechal, Marjorie, Quasicrystals and Geometry.
Cambridge University Press, 1995.
Serra, Michael, Discovering Geometry, An Inductive Approach.
Berkeley: Key Curriculum Press, 1993.
Stevens, Peter S., Handbook of Regular Patterns: An Introduction
to Symmetry in Two Dimensions.
Cambridge, MA: MIT Press, 1980.
Wade, David, Pattern in Islamic Art.
Woodstock, NY: Overlook, 1976.
Washburn, Dorothy K. and Donald W. Crowe, Symmetries of Culture:
Theory and Practice of Plane Pattern
Seattle, WA: University of Washington Press, 1988.
Wiltshire, Alan, Symmetry Patterns: The art of making beautiful
patterns from special grids. Stradbroke
(England): Tarquin Publications, 1989.
Yaglom, I. M., Geometric Transformations I. Washington DC:
Mathematical Association of America, New
Mathematical Library no. 8.

Films and videotapes

The Alahambra Past and Present - A Geometer's Odyssey, Parts I and II
(Lorraine Foster), California State
University, Northridge, 1992. (VHS color videotape; approx 30 min each)
Dihedral Kaleidoscopes (H.S.M. Coxeter), College Geometry Project,
1966. Available from International Film
Bureau, Chicago. (16mm film & VHS color videotape, 13 min.)
Isometries (S. Schuster, W.O.J. Moser), College Geometry Project,
1967. Available from International Film
Bureau, Chicago. (16 mm color & VHS videotape, 26 min.)

Sets of tiles and tiling games

There are several commercially available sets of tiles and tiling games.
Actually building a tiling with cut-out tiles is
one of the best ways to come to understand its properties. Check the
catalogs of distributors of mathematics
supplemental teaching materials such as Dale Seymour, Creative
Publications, Cuisenaire, and Tarquin (British).
Also check the shops and catalogs of art museums and science museums.

Pattern Blocks and other activity tiles can be used to explore
tessellations with simple polygon tiles. Pentaplex
produces variations on the aperiodic sets of Penrose tiles; Kadon
Enterprises has several tiling puzzles; Tessera
(Damert Company) has 8 different bugs that fit together in many
different ways.

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