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

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.

In Mathematics: The first mathematical studies of tessellations were conducted by Johannes Kepler in 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)

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!

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.

ANGLES AND BATS ANTS

LIZARDSSTING RAYS HEDGEHOGS DOGS

BIRDSFISH AND SHIPS DOLPHINSSTARS AND STRIPES

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

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

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

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

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

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

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.

Hmmm…. What could it be?

A Fish!!!

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

DOME OF THE ROCK in JERUSALEM

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

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.

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

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

1. Totally Tessellated 2. The Math Forum - Tessellation Tutorials By: Suzanne Alejandre