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# Transformations in art and math.

In art, transformations may be created in many ways, but in mathematics, transformations are functions of geometry geometry [Gr.,=earth measuring], branch of mathematics concerned with the properties of and relationships between points, lines, planes, and figures and with generalizations of these concepts.  that involve congruent con·gru·ent
1. Corresponding; congruous.

2. Mathematics
a. Coinciding exactly when superimposed: congruent triangles.

b.
shapes--shapes that are exactly the same in size and shape. The repetition REPETITION, construction of wills. A repetition takes place when the same testator, by the same testamentary instrument, gives to the same legatee legacies of equal amount and of the same kind; in such case the latter is considered a repetition of the former, and the legatee is entitled  of congruent shapes, depending on their particular transformation, results in designs known as tessellations. A tessellation In surface modeling and solid modeling, the method used to represent 3D objects as a collection of triangles or other polygons. All surfaces, both curved and straight, are turned into triangles either at the time they are first created or in real time when they are rendered.  is the tiling of a plane without any gaps or overlaps by a pattern of one or more congruent shapes. Though M. C. Escher Maurits Cornelis Escher (June 17 1898 – March 27 1972), usually referred to as M. C. Escher, was a Dutch graphic artist. He is known for his often mathematically inspired woodcuts, lithographs and mezzotints.  is the artist most recognized for his work with tessellations, a number of contemporary artists are exploring these concepts, especially through art made on the computer.

For Teachers

www.mcescher.com The official website from the Escher Esch·er   , M(auritis) C(ornelius) 1898-1972.

Dutch artist whose lithographs and woodcuts depict imaginary metamorphoses, geometric distortions, and architectural impossibilities.
Foundation.

cybermuse.gallery.ca/cybermuse/ youth/escher/index_e.jsp From the National Gallery of Canada National Gallery of Canada

National art museum founded in Ottawa in 1880. Its holdings include extensive collections of Canadian art as well as important European works. Its nucleus was formed with the donation of diploma works by members of the Royal Canadian Academy.
.

www.escherinhetpaleis.nl/ Escher in the Palace.

www.nga.gov/collection/gallery/ ggescher/ggescher-main1.html From the National Gallery of Art.

www.tessellations.org See .org.

(networking) org - The top-level domain for organisations or individuals that don't fit any other top-level domain (national, com, edu, or gov). Though many have .org domains, it was never intended to be limited to non-profit organisations.

RFC 1591.
This website gives a good art-based introduction to tessellations.

www.princetonol.com/ groups/iad/lessons/middle/ tessell.htm and www.cln.org/ themes/tessellations.html Numerous tessellation links may also be found at these sites.

mathforum.org/sum95/suzanne/ whattess.html and www.42 explore.com/teslatn.htm Basic mathematical introductions to tessellations can be found here.

www.jimmcneill.com/demo.html Contemporary artist Jim McNeill McNeill may refer to:
• McNeill, West Virginia, a US community
• McNeill (surname), people with the surname McNeill
• Port McNeill, British Columbia

mathcentral.uregina.ca/RR/database/RR.09.96/archamb1.html A unit of ten sequential tessellation lessons for fifth grade.

illuminations.nctm.org/lessonplans/6-8/tiles/index.html and illuminations.nctm.org/lessonplans/prek-2/triangle-p2/index.html Other specific lessons for tessellations are found here.

For Students

Directions: Visit the websites detailed below and answer the questions or complete the activities on a separate piece of paper.

www.teachers.ash.org.au/mike math/movies/triangle2.html Watch the example and then use ejad.best.vwh.net/java/patterns/ patterns_j.shtml to make a tessellation with triangles.

matti.usu.edu/nlvm/nav/frames _asid_163_g_3_t_3.html Read the instructions to make a tessellation using squares.

www.coolmath.com/tesspag1. htm An overview of tessellations can be found at this site.

M.C. Escher is the artist most famous for his tessellation designs, though artists of our time also make them, often using the computer as an art-making tool. Enter cybermuse.gallery.ca/cybermuse/youth/escher/index_e.jsp, read the short introduction, and then click on Escher's Gallery to see his work, clicking on each of the four artworks This article is about the software drawing application. For art objects, see work of art.

ArtWorks is an advanced vector drawing package for RISC OS created by Computer Concepts (now Xara) in 1991. It has been developed by MW Software since 1996.
shown. Make a list of his works you believe to be tessellations.

www.tess-elation.co.uk/, www18.big.or.jp/~mnaka/home.index.html The default name for a home page in a Web server. The page is appropriately named, because the home page is an index to the entire Web site. When you type in a URL such as www.computerglossary.com, it is the same as entering www.computerglossary.com/index.html. INDEX. , www.cromp.com/tess/home.html, and members. cox.net/tessellation/index.html Click on the Mathematical Art of Robert Fathauer to see tessellations by contemporary artists. How are their works different from Escher's? Which do you like best? Why? Three types of tessellations are translations or slides, reflections or flips, and rotations.

www.escherinhetpaleis.nl/ Explore Escher's work interactively.

www.jimmcneill.com/demo.html Follow the step-by-step directions to make your own translation or slide tessellation.

www.iproject.com/escher/ teaching/maketessel.html Try the slightly different approach at this website. How is the second method different? Which do you prefer and why? See more of McNeill's work at www.art.unt. edu/ntieva/news/vol_9/issue3/ bowl.htm
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Title Annotation: Printer friendly Cite/link Email Feedback ArtEd Online Walkup, Nancy School Arts Nov 1, 2004 611 Tom finery. Margaret Bourke-White (1904-1971). Geometrical drawing Tessellations (Mathematics) Web sites Web sites (World Wide Web)