It is obvious from the diagram that they tessellate but we also know mathematically by doing 60 x 6 = 360. In the middle of the above diagram, 6 triangles meet at one corner. The same works for the equilateral triangle. The square has a 90 degree angle and 4 squares meet in one corner, which means that you can check mathematically that they will tessellate. Where the corners meet, they will always add up to 360 degrees. For all the others, the interior angles are not exact divisors of 360 degrees, and therefore those figures cannot tile the plane. This works for the triangle, square, and hexagon. Regular polygons in a tessellation must fill the plane at each vertex, the interior angle must be an exact divisor of 360 degrees. Tessellation is used to look appealing to the eye, such as in art work or in peoples home, for example, tiles on walls or floors.īelow is a demonstration on how I tessellated squares and regular triangles. There are different types of tessellation: regular, semi-regular and then other tessellations of circular, curved and irregular shapes that mathematicians agree on how to name. Therefore, tessellation is when shapes are repeated over and over again covering a plane without any gaps or overlaps. Lastly, check out these cross-curricular art ideas if you’re looking to include art in other subjects.Tessellation is another word for tiling. We would also love to see it in the Masterpiece Society Facebook Group. When you finish, your tessellation art is ready to share or display.Īs always, we look forward to seeing your tessellation art! Be sure to use #masterpiecesociety or tag us on social media when you share your fun creations. You can also add any desired accents or designs to your tessellation art at this time. This is an optional step, but it pulls the project together nicely and adds definition to your design. (Prefer to skip the watercolors? Add color to your tessellations with crayons, colored pencils, or markers instead.)Īfter the paint dries, use a Sharpie to outline the original tracings. When you finish tracing, grab your watercolors and paint the tessellation however you wish. Repeat this process, rotating and repositioning as needed, until your paper is covered with your tessellation pattern. After the first tracing, line up the cutout next to the previous tracing and trace a new shape. Using a pencil, carefully trace the cutout onto a sheet of watercolor paper. If it doesn’t, you can always rethink your creation and try again! Move on to the next step to see if your new creation will tessellate. Tape the second cutting to the remaining flat surface. (You can do a different cutout on this step or recreate the first cutout.)Īfter removing both cuttings, tape the first cutting to one of the flat edges of the square. Set aside the cutout, rotate the square 90 degrees, and repeat the cutting process. Next, cut a unique design into one side of the square. Prefer to try a custom tessellation? You can create a unique pattern by cutting a square from a scrap piece of paper. Then cut it out before moving on to the next step. If you want to use a basic pattern, trace the chosen shape onto your scrap paper.
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