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Title: Math/Recreations/Tessellations - Tessellations with Java Examples and source code.
Tiling_Plain_and_Fancy Tiling from the mathematical and historical viewpoint by Steve Edwards. Provides a number of examples of various types of tiles that tile the plane and includes periodic tiling plus Penrose's aperiod

Tilings_and_Geometric_Ornament Applying principles of computer graphics to the creation of geometric ornament, as a continuation of the tradition of ornamental design using modern tools and algorithms.

Totally_Tessellated An introduction to tessellations explaining the basic underlying mathematics, and with many examples from real life.

17_Wall_Paper_Symmetry_Groups_to_Create_a_Regular_Division_of_the_Plane Graphics.

Wallpaper_Groups Images and descriptions of the 17 plane symmetry groups.

William\'s_Geometric_Construction_Page Activities to create patterns using simple resources, such as making equilateral triangle from a circle. Suitable for upper primary and lower secondary ages.


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Tessellations with Java

Tessellations with Java

By Roseann Krane, Monte Vista HS, Danville, CA, andstudents: Jefferson Ng, Mike Carns, and Amber Bullington, and Sherida Hare, Bellport HS, Brookhaven, NY, editor "Understanding symmetry is essential to the understanding of Escher artand understanding symmetry involves a familiarity with the movements thatmathematicians call transformations." (Jill and Walter Britton)Click to view the "Step byStep Tessellations" for a detailed explanation on tessellations. Click to print the "Step byStep Tessellations" for a detailed explanation on tessellations. Vocabulary: Tessellation - A tessellation is a pattern of one or more shapes,completely covering a two-dimensional plane. Picture a puzzle withpieces that have the same shape and size that fit together perfectly as ina square. (A circle would not be a shape for a tessellation becausecircles cannot fit together in a puzzle.) A tessellation is a patternthat is repeated. If we take squares and layer them on the floor, wecan cover the entire floor with them, without any space leftover.Plane - Imagine a plane to be a tabletop with no thickness thatcontinues infinitely in all directions. Translation - If we move a figure to a new location by sliding it afixed distance in a fixed direction, the motion is called a translation. Rotation - If we move a figure to a new location by turning it abouta fixed axis, the motion is referred to as a rotation or a turn. Center ofRotation - The point or axis about which a figure is rotated is called thecenter of rotation. The angle through which the figure turns is calledthe angle of rotation.Reflection - If we move a figure to a new location by flipping itabout a fixed line the motion is called a reflection or flip. Thefixed line about which the figure is flipped is called the line ofreflection. (It is called a reflectionbecause if a mirror were placed along a line the transformed figure wouldcoincide with the mirror image of the figure in its original location.)Glide Reflection - This final transformation combines the motions ofreflection andtranslation to move a figure to its new location. By flipping it about a fixed line.By sliding it at a fixed distance in a direction parallel to that line.The motion is called a glide reflection.Click on the following for a detailed explanation on:Step by Step Tessellations.How to use Java to create TessellationsSeeing the Tessellation Example of diamonds done with JavaSeeing the Java Tessellation source code.Student Exercises Modify the paint function to create a tessellation oftriangles. Modify the paint function to create a tessellation ofhexagons. Modify the paint function to create a tessellation ofoctagons and squares.Links about tessellations:World of EscherHan's ComputerArtSwarthmore Tessellation Tutorials Glide Reflections Tutorial Movies onTessellations Swarthmore Discussions ThreadStudent Workwith TesselmaniaStudent Workwith Paint ProgramsLesson PlanYou can contact me at : roseann@krane.netWeb site
 

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