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Tessellations

Tessellations. Group #7:. Christi Kimball Stacy Clarke Lisa Booze Nancy Lilly Melissa Mueller. What is it?. Tessellation * : A pattern made up of one or more shapes, completely covering the surface without any gaps or overlaps.

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Tessellations

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  1. Tessellations Group #7: Christi Kimball Stacy Clarke Lisa Booze Nancy Lilly Melissa Mueller

  2. What is it? Tessellation*:A pattern made up of one or more shapes, completely covering the surface without any gaps or overlaps. *Also known as tilings, but the word “tilings” usually refers to patterns of polygons, which is a more restrictive category of repeating patterns.

  3. HISTORY In Mathematics: The first mathematical studies of tessellations were conducted by Johannes Kepler in 1619. At this point in time, they had made an inaccurate definition. Two hundred years passed before new scientific progress concerning tessellations was made. Others: Russian crystallographer, E.S. Fedorov (1891) Heinrich Heesch and Otto Kianzle (1963)

  4. HISTORY In Science: Tessellations have been linked with x-ray crystallography (a field of science concerned with the repeating arrangements of identical objects as found in nature). Many of these discoveries are similar to many of M.C. Escher. Several other scientific and engineering applications have been found for tessellations. Example: Tilings have benefited the conservation of sheet material and reduction of scrap metal, which means less waste!

  5. Maurits Cornelis Escher MASTER ARTIST AND CREATOR OF TESSELLATIONS Born in Leeuwarden, Netherlands (1898) attempted to become an architect Studied graphic art at the School for Architecture and Decorative Arts in Haarlem Intrigued by mosaics around the world created hundreds, perhaps thousands, of tessellations in the form of fish, birds, dogs, lizards, etc.

  6. GALLERY ANGLES AND BATS ANTS

  7. LIZARDS STING RAYS HEDGEHOGS DOGS

  8. BIRDS FISH AND SHIPS STARS AND STRIPES DOLPHINS

  9. Simple Tessellations WITH REGULAR POLYGONS 1. Regular: tessellations of only one type of regular polygons 2.Semiregular: tessellations that involve more than one type of regular polygon and that have the same polygon arrangements at every vertex *only 8

  10. Simple Tessellations WITH NON-REGULAR POLYGONS 1. Triangles: tessellations of any 3-sided polygons 2. Quadrilaterals: tessellations of any 4-sided polygon others: pentagons, hexagons

  11. How? Rigid Transformation: A motion that moves a figure from one location on a plane to a new location without changing the size or shape of the figure. Rotation Reflection Translation Glide Reflection

  12. To rotate an object means to turn it around. Every rotation has a center and an angle. ROTATION

  13. To translate an object means to move it without rotating or reflecting it. Every translation has a direction and a distance. TRANSLATION

  14. To produce its mirror image. Every reflection has a mirror line. A reflection of an “R” is a backwards “R”. REFLECTION

  15. A glide reflection combines a reflection with a translation along the direction of the mirror line. Glide reflections are the only type of symmetry that involves more than one step. GLIDE REFLECTION

  16. Hmmm…. What could it be?

  17. A Fish!!!

  18. Architecture Alhambra in Granada, Spain * The decorated walls indicate that the Moor artists of the 700-1500s knew all 17 types of patterns.

  19. DOME OF THE ROCK in JERUSALEM

  20. Around Towson

  21. The picture above is a tessellation located above the biology lecture hall.

  22. Left: This is a giftbag at the Hallmark off of Dulaney Valley Rd. Right: This is a box of stationary with a decoratively tessellation using triangles.

  23. This picture was taken at Towson-Run. It is the sidewalk surrounding the building.

  24. This is a canopy of a restaurant. It uses the traditional checkers pattern.

  25. SOURCES: 1. Totally Tessellated http://library.thinkingquest.org/1661/ 2. The Math Forum - Tessellation Tutorials By: Suzanne Alejandre http://forum.swarthmore.edu/sum95/Suzanne/tess.intor.html

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