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Tessellations

Tessellations. Making Connections between the World of Math, Art, and FACS!. What are tessellations?.

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Tessellations

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  1. Tessellations Young 2012 Making Connections between the World of Math, Art, and FACS!

  2. What are tessellations? • Basically, a tessellation is a way to tile a floor (that goes on forever) with shapes so that there is no overlapping and no gaps. Remember the last puzzle you put together? Well,that was a tessellation! The shapes were just really weird. • We usually add a few more rules to make things interesting! http://www.coolmath4kids.com/tesspag1.html#

  3. REGULAR TESSELLATIONS: • RULE #1:   The tessellation must tile a floor (that goes on forever) with no overlapping or gaps. • RULE #2:  The tiles must be regular polygons - and all the same. • RULE #3:   Each vertex must look the same. • What can we tessellate using these rules? Where all the corners meet! What’s a vertex? http://www.coolmath4kids.com/tesspag1.html#

  4. Triangles? • Yep! • Notice what happens at each vertex! • The interior angle of each equilateral triangle is 60 degrees.....60 + 60 + 60 + 60 + 60 + 60 = 360 degrees http://www.coolmath4kids.com/tesspag1.html#

  5. Squares? • Yep! • What happens at each vertex? • 90 + 90 + 90 + 90 = 360 degrees again! • So, we need to use regular polygons that add up to 360 degrees. http://www.coolmath4kids.com/tesspag1.html#

  6. Will pentagons work? • The interior angle of a pentagon is 108 degrees. . . • 108 + 108 + 108 = 324 degrees . . . Nope! http://www.coolmath4kids.com/tesspag1.html#

  7. Hexagons? • 120 + 120 + 120 = 360 degrees Yep! http://www.coolmath4kids.com/tesspag1.html#

  8. Heptagons? • No way!! Now we are getting overlaps! • Octagons? Nope!They'll overlap too. • In fact, all polygons with more than six sides will overlap! So, the only regular polygons that tessellate are triangles, squares and hexagons! http://www.coolmath4kids.com/tesspag1.html#

  9. SEMI-REGULAR TESSELLATIONS: • These tessellations are made by using two or more different regular polygons. The rules are still the same. Every vertex must have the exact same configuration http://www.coolmath4kids.com/tesspag1.html#

  10. Complex Designs • Here are some tessellations using squares and triangles: http://www.coolmath4kids.com/tesspag1.html#

  11. Quilting Tessellations Young 2012

  12. Design Time • Design a tessellation to fit a 14 x 14 or 16 x 16 pillow form • Designs will be composed of triangles, squares or rectangles • Look at color scheme: monochromatic, complementary, warm, cool, analogous, etc. • http://www.tigercolor.com/color-lab/color-theory/color-theory-intro.htm#Color_Wheel • http://colorschemedesigner.com/ • Decide on a color scheme. Present plan/design to Mrs. Young. • Make a pattern for your geometric shapes adding ¼ “ seam allowances around the perimeter of each shape. • Be sure your final size is 14 x 14 or 16 x 16. • No shapes should be under 1 ½” or over 4” Young 2012

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