## Strip symmetry patterns of several snakes

The snake names listed below will connect you to various snakes found across North America. When selecting a link, you will be connected to a Word document with the snake's common name, a picture of the snake, an image of the snake's skin constructed with The Geometer's Sketchpad (GSP), and a breakdown of the pattern of the snake's skin. The breakdown will show the fundamental region of the pattern, and all the symmetries of the pattern. Also provided for the learner is a link to the GSP file where the strip symmetry, also known as frieze symmetry, was created. A final link will connect the learner to the GSP file where the fundamental region is shown. Once you have downloaded these files, the curious student may wish to alter either of them in some fashion to see what aspects of the figure change. A suggestion to aid one in their exploration is to choose "show all hidden" from the display menu in GSP in order to learn how we actually created these images. Click here to jump directly to the snake names and bypass the explanation of the symbols which we employ. If the reader prefers to learn more about snakes, clicking here will send one to the link which connects to a list of web sites which we used.

Try to figure out the fundamental region and the symmetries before scrolling to the bottom of each snake page to see the answer!

The same notation that is identified on Dr. McCrory's (our Geometry professor) website will also be used for this page, so see the notation guide below for clarification of the symbols used on each page to which we is link:

Let L denote the center line of the strip. (To fix ideas, we think of L as horizontal.)

I = Identity

T = Translation (with vector parallel to L)

R = Rotation (with center on L and angle 180 degrees, i.e. a half-turn)

V = reflection (with mirror line perpendicular to L, i.e. with Vertical mirror)

H = reflection (with mirror line L, i.e. with Horizontal mirror)

G = Glide reflection (with mirror line L and vector parallel to L)

Also, when viewing the second template of the snake's symmetry, note the following clarifications of symbols:

The fundamental region is the region lying within the thin black lines.

Horizontal dashed lines are horizontal mirrors.

Thin, vertical, blue lines are vertical mirrors.

Thick, horizontal, blue lines located at the top of the fundamental region are translation vectors.

Thick, horizontal, purple (or black on Macintosh versions of GSP) lines located on the horizontal mirror are glide vectors.

Points are rotation centers.

Ideally, these snakes would be uncoiled and lying in a nice straight line. But, since snakes seem to cooperate as they please, the following pictures will have to do. If you find images of snakes where they are stretched out, please send them to one of us at:

Kevin Adams: kevinadams55@hotmail.com

Jeremy Elrod: jelr4480@hotmail.com

Jake Klerlein: jklerlei@coe.uga.edu

### Western Longnose Snake

Note: an asterick following the Snake's name means the snake is venomous, so watch out for these!

Having now gained some experience looking at snakes and viewing the strip symmetries of their coloring, we provide a link to some images of which you may determine the symmetries on your own. We suggest that after viewing the snake the user attempt to create a fundamental region similar to those linked to above and then use the various transformations of the pattern in order to create the entire strip. Click here to access some more snake pictures.

Click this link in order to access a page with links to pages about snakes. Some are information that may be used to relate the activities to science classes. Other links are to sites with good pictures that may be used to find more pictures for your own investigations. Finally, if you are so interested in these reptiles and would like some of your own, some pages of breeders are included as well.

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