Name: Date: Hour: A tessellation is a repeated polygon and/or combinations of polygons on a two dimensional plane. Each tessellated tile fits perfectly next to its adjacent twin. A true tessellation could repeat infinitely in all directions. The word is derived from the Latin word tessella. A tessella is the individual stone in Roman mosaic. M.C. Escher was a prominent artist who used tessellations in his works. There are several books available showing the use of geometry in his sketches, lithographs, and woodcuts. We will use some of the same techniques used by Escher. The basis of these tessellations for this project will be the regular polygons. The sides of these polygons will be changed, and the changes will be translated, rotated, or reflected to another side. The resulting shape will tessellate. 1
I (the student) will: 1. Understand the concept of and the process of making tessellations. 2. Create tessellations using translation, rotation, and/or reflection. 3. Understand the works of M. C. Escher. 4. Use elements and principles of design: color, balance, repetition and pattern. 5. Use the skills I have learned to produce UNIQUE tessellations of my own. For this Tessellation Project you will create a tessellation masterpiece done by hand. Your tessellation will be created based on specific criteria. You MUST follow the guidelines given in order to receive full credit. The tessellation will be constructed on 1 poster board. Your grade will be based on the following: **Tessellation Creation** Pattern tessellates the plane Template with modifications turned in Appearance and Neatness Creativity/Originality/Difficulty Be patient and a positive attitude is required to make this project successful. The appearance of your tessellation should be neat! Your tessellation (pattern) should cover the ENTIRE poster board (no gaps or unintentional white spaces). You are to turn in the template figure you used to create your tessellation. Coloring should be in between the lines, and NO wrinkled or torn projects! Your project will also be based on Creativity and Difficulty. The more difficult and complex the tessellation is, then the higher the grade. You may not simply take a polygon and slide, rotate, or reflect it over and over again to create your tessellation. You must use a figure you created! Go to this link to see DEMO: http://www.jimmcneill.com/demo.html The following steps are necessary in order to make this project complete. 1. Try out several designs, by doodling on paper until you find something you like. When you have decided on a design, create your template on a 3 x 5 index card. 2
2. Begin by creating a template on your 3 x 5 index card (you can cut the card to make a triangle, square, parallelogram, hexagon, etc). Once you have a polygon, follow the examples provided (see attached examples for techniques). Secure cut out pieces to the side you chose with tape. Be careful not to overlap the piece or make a gap. It should fit perfectly at the seam. Continue the process to all sides and this is your tessellating tile. 3. Once the template has been created, place your template at any of the four corners of your poster board and trace your first figure. 4. Once your figure has been traced slide it or reflect it and trace your next figure (whether you reflect or slide it depends on the technique you used) 5. Continue step 3 until the entire page is covered. All your figures on the paper should fit together so that it looks like a puzzle. Figures at the edge will only be partial images 6. Once you have the page covered in your tessellation, begin to add color in the figure. The figured should be animated with interior details added. (see attached examples of designs). 7. All drawings must be original work, not mere renditions of existing work. 8. Be creative and have fun with the project! Give your piece of art a name! Translation of One Side of Square A translation is a movement is a specific direction, without turning or reflecting. 3
Translation of Two Sides of Square This same process can be applied to a square when two adjacent sides are changed. Translation of Sides of Parallelogram This process may be applied to a parallelogram when two adjacent sides are changed. 4
Translation of Three Sides This same process can be applied to a hexagon when three adjacent sides are changed. Rotation of One Side of Square One side of a square can be changed and this change can be rotated 90 to an adjacent side. This same change can be rotated 180 and 270 so that it appears on all sides. 5
Rotation of One Side of Rhombus One side of a 60 rhombus can be changed and this change can be rotated 120 and 60 to the remaining sides. Rotation of One Side of Hexagon One side of a hexagon can be changed and this change can be rotated to the remaining sides. 6
Rotation of All Sides of Hexagon All sides of a hexagon can be changed and these changes can be rotated to adjacent sides. Rotation of Half Sides of Triangle The half-sides of a triangle can be rotated to the remaining half-side. Start with a triangle and change half of one side, rotate that change to the other half of that side, and rotate the entire side to all other sides. 7
Rotation of All Half Sides of Triangle All of the half-sides of a triangle can be rotated to each remaining half-side. Start with a triangle and change half of each side, and rotate that change to the other half of that side. Form the tessellation by tracing this shape at least 18 times and shade or color alternating shapes. Rotation of Half Sides of Quadrilateral The half-sides of a quadrilateral can be rotated to the remaining half-side. Start with a quadrilateral and change half of each side, and rotate each change to the other half of that side. 8
Rotation and Reflection of the Sides of a Triangle It is possible to form a tessellation by changing a half side of a triangle, and then rotating and reflecting the change to the other half side, followed by rotating and reflecting a second side to the third side. For this project you will need the following EVERYDAY: Pencil, Eraser, and Straightedge One 3x5 Index Card Scissors and Tape 1 Poster Board Colored Pencils/Markers/Glitter Glue This tessellation project will be entered into the grade book as a TEST GRADE. It should be visually appealing and original. Have fun with it! 9
Friday, May 10, 2013 Monday, May 13, 2013 Tuesday, May 14, 2013 Wednesday, May 15, 2013 Thursday, May 16, 2013 Read entire Tessellation Project Packet Research tessellations created by students online to get an idea of what template you would like to create to tile on poster board. Remember: Finding a design online and copying it is plagiarism. Doodle on a piece of paper to get final design. Begin drawing and cutting out template on 3 x 5 index card. Bring poster board to school. Begin tiling your template on poster board. Continue until most/entire poster board is covered. Finish tiling your template on poster board. It should be completely covered. Start adding color in the figure. The design of the figure should have interior details added. Continue adding color in the figure. The figured should be animated as well with interior details added. Finish adding color in the figure. The figured should be animated as well with interior details added. Hand in completed tessellation and template. The entire project is due by May 16, 2013. Remember that you have a deadline! All late projects will be deducted 5 points for each day that it is late, no project will be accepted after Monday May 20 th. 10
EXAMPLE 1: Draw a squiggle line on the left side of the rectangle. Squiggle line will be translated to the right side of rectangle. Draw long squiggle line at the bottom of the rectangle. Long squiggly line will be translated to the top of the rectangle. 11
It s imagination time! What does it look like? A fish? A bird? A dinosaur? A pig? A Rhino? RHINO!!!! Maybe it looks like a cat? 12
Tweak the shape to make the shape look more like a cat. Remember, any line you change you must change on both sides! 13
Fill your entire poster board with you template. 14
DECORATE IT! Use colored pencils to color in and animate your shapes. Use a marker to make the borders dark. Erase the pencil markings. You re finished! CONGRATULATIONS! :D EXAMPLE 2: 15
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To Tessellate or Not to Tessellate? Rubric to Assess Quality, Creativity, Originality, and Difficulty Make sure that you create your own tessellation and that it is an original piece of work! Hand created work of art in the form of a Tessellation using a traced template. Tessellation is Fully Colored and Designed Degree of Difficulty Appearance Effort Use of Time Beginner 10 Point Drawing has many gaps (not a tessellation). Poor creativity. No template. No use of color. No design. Escher type tessellations involving translations from a square, rectangle, or parallelogram. Not centered. Too many pencil marks showing. Colored terrible. Edges are a terribly bent/torn. Too many smudges. Poster board is extremely wrinkled. Below what was required to do! Student was rarely engaged in project during school time. Novice 20 Points Drawing has some (not a tessellation). Minimal creativity. Badly created template. Minimal use of color. Design unnoticeable. Escher type tessellations involving translation from a hexagon. Way off centered. Many pencil marks showing. Colored outside of lines. Edges are a mostly bent/torn. Many smudges. Poster board is too wrinkled. Bare minimum was completed. Student was sometimes engaged in project during school time. Intermediate 30 Points Drawing has some spaces. Some creativity and detail. Nicely created template. Some use of color. Design is not instantly recognizable. Escher type tessellations involving rotation. Slightly off centered. Some pencil marks showing. Colored mostly in the lines. Edges are a little bent/torn. Some smudges. Poser board is a bit wrinkled. All requirements were meet and done very well. Student was often engaged in project during school time. Expert 40 Points Drawing has no gaps! Very obvious creativity and detail! Template is perfect! Elaborate use of color. Design is detailed and identifiable! Escher type tessellations involving glide reflection. Centered. Crisp shapes. Attractive Coloring. Edges are not bent/torn. Smudge- free. Poster board is not wrinkled. Went beyond the call of duty!!! Student was engaged in project during all appropriate school time. Score 18
Scale: 200-240 = Expert 150-190 = Intermediate 100-140 = Novice 50-90 = Beginner 0 = Did not do! Grade: Expert = Awesome! Intermediate = Better than most! Novice = Could have done more Beginner = Didn t try very hard, Does lack effort Failed to complete, Forfeit grade I could have had! Final Score: Final Grade: Penalties: 10 points Template not handed in 5 points No name for tessellation masterpiece! 5% - Each day for being late 19