4- FLIP over the RIGHT PIECE (from top to bottom), then slide to the left side. 2- Draw a line from the BOTTOM RIGHT corner to the TOP RIGHT corner. Let’s practice… REFLECTION 1- Draw a line from the BOTTOM RIGHT corner to the BOTTOM LEFT corner. 10- Hold down the BOTTOM LEFT corner and rotate counter-clockwise. 9- Hold down the LOWER RIGHT corner and rotate counter-clockwise. 8- Hold down the TOP RIGHT corner and rotate counter-clockwise. ![]() ![]() 6- Align the original corners of the new ‘transformed’ shape with the grid corners in the upper left box of the grid paper. 5- Rotate the LEFT piece clockwise holding down the BOTTOM LEFT corner ending up at the bottom. 4- Rotate the TOP piece counter-clockwise holding down the TOP RIGHT corner ending up on the right side. 2- Draw a line from the TOP LEFT corner to the BOTTOM LEFT corner. ROTATION 1- Draw a line from the TOP RIGHT corner to the TOP LEFT corner. ![]() 5- Slide the LEFT piece to the right and tape down. 4- Slide the TOP piece to the bottom and tape down. Let’s practice… TRANSLATION 1- Draw a line from the TOP RIGHT corner to the TOP LEFT corner. Types of Tessellations 1- Translation- moving every point of the figure the same distance in the same direction 2- Rotation- rotating the figure from a single point 3- Reflection- reflecting every point of the figure over an axis, as if looking in a mirror Three Fishes, 1994 Marathon, 2004, commissioned for the Chicago marathon Over time, Tessellations' product line has grown to include mathematics manipulatives, classroom posters, and books as well. Escher 1936 Strong Men 1938 Fish 1938 Dogs 1937 LionsĪrtist Robert Fathaueramerican, born 1960- In 1993, he founded a business, Tessellations, to produce puzzles based on his designs. Escherdutch 1898-1972 M.C.Escher said, "Mathematicians go to the garden gate but they never venture through to appreciate the delights within." 1958 Circle Limit III Sky & Water, woodcutĮarly work of M.C. Tessellations have been seen throughout art history, from ancient architecture to modern art.Īrtist M.C. Uses for tessellations…Talk with your “elbow partner” and identify some uses for tessellations.Be ready to tell me what your partner said. which can fill a page without overlapping to form a pattern (or mosaic). What’s a tessellation? A tessellation uses congruent figures to cover a plane in a symmetrical way without overlapping or leaving gaps. In art, we use Transformation techniques to create compositions called Tessellations.The term refers to four specific ways to manipulate shapes. In math, this is called Transformation.Tessellations Art and Math… How are they related?Īrt and Math…How are they related? One way art and math are related is through the manipulation of shapes. There are a lot of other things to take in to account when laser cutting but that should give you an idea of where to start.- E N D - Presentation Transcript The kerf is especially something you want to keep in mind when creating your shapes and choosing materials if you are planning on piecing these shapes back together after they have been cut. It can also result in incorrect cut thickness (knows as kerf). ![]() This can easily end up costing you a lot of money if you're doing this in volume and can also (depending on the material) damage the material. So if you have overlapping paths - like in the tessellation you posted - the machine will make the cut for each path. Don't overlap pathsĪnother thing to keep in mind when laser cutting is that the laser cutter will cut any paths you give it. From looking at the image you posted, you should probably completely redraw the shapes as vector paths. Adobe Illustrator is probably the most popular but there are free alternatives such as Inkscape.įor laser cutting you will want your paths to be very precise. Laser cutting requires vector paths so you will need to use a vector graphics program. The important part of the question is the fact that it is going to be used for laser cutting.
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