Go to Object-> Transform -> ("Rotate" or "Reflect"). Hint: As with Persons 1 and 2, you will also need to rotate lines and shapes with precision. Also, you do not need to add details- just concentrate on the overall shape of the tile. Instead of translating the "squiggly" lines, you will try rotation or glide reflection transformations. Additionally, it covers techniques, tips, and templates to facilitate the creation of mathematical art based on tessellations.
Irregular Tessellations from a Square, using Rotation or Glide Reflection (Person 4)- You will create an irregular tessellation starting with a square. Tessellations: Mathematics, Art and Recreation aims to present a comprehensive introduction to tessellations (tiling) at a level accessible to non-specialists. You should also be able to answer these questions: Do all pentominoes tessellate? Do all 7-pin polygons tessellate? Are there pentominoes or 7-pin polygons that require transformations other than translation in order to tessellate?
This makes it possible to add more details to geometry, though in this tutorial we'll focus on the tessellation process itself. In our case, we're going to subdivide triangles so we end up with smaller triangles that cover the same space.
#TESSELLATION TRIANGLE ART HOW TO#
(You do not need to create any "squiggly" lines, but you do need to know how to create two different tessellations- one pentomino tessellation, and one 7-pin polygon tessellation). Tessellation is the art of cutting things into smaller parts. Tessellations from Pentominoes and 7-Pin Polygons (Person 3)- While this seems like more work because you are researching two different types of tessellations, both of these are fairly easy to understand and create tessellations with. Last, you will have to precisely determine an exact midpoint for one of the sides of the triangle. Go to Object->Transform ->Rotate and choose the appropriate angle (you might need to use a little math, or just "undo" until you get it right). Hints: You will need to discover how to make an equilateral triangle in Illustrator (Google it)! You will also need to rotate lines with precision. Select colors that make a pleasing pattern.Irregular Tessellations from a Triangle (Persons 1 and 2)- Create a tessellation using an equilateral triangle as the base. Use 4 of these to make 2 squares with the two B triangles. Take three more B triangles, each in different colors, and cut them in half, from the long edge to the 90-degree corner, these are C triangles. The project is all about making these three part squares. Take two of these B triangles, each a different color, and place them with a short side touching along the long edge of the A triangle on the background paper. Take three more of the A triangles, each of a different color and cut them in half, from the center of the long side to the 90 degree corner, these are B triangles. Experiment with designing a planar tesselation using a recognizable image.
Place one A triangle on your large sheet of paper (the background paper). Explore formal and psychological themes in MC Eschers work. Set one triangle from each color aside for the moment. Divide the paper up into equal width rows (or columns) about 3-4 rows for a small sheet will work very well. We recommend starting with half of a regular 8.5' x 11' white sheet of paper. Start with the polygon with the fewest number of sides first, then rotate clockwise or counterclockwise and count the number of sides for the successive polygons to complete the order. Start with a piece of paper and a pencil. Make three more squares the same size from different colors of construction paper. The order of the semi-regular tessellation composed of equilateral triangles, squares, and regular hexagons shown above is 3-4-6-4. Using a ruler and pencil, draw and cut out a large square from colored construction paper. If you placed two identical right triangles together at their long side, they would form a square.
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