What shapes can tile the plane In other words shape can you put next to itself and NOT have any gaps Circles Octagons Hexagons Triangles Regular Tessellations When the shape used to tile the plane are the same regular polygons the tessellation is called regular These are the only reg ID: 652142
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Slide1
Tesselations
Where Art and Geometry Meet!Slide2
What shapes can tile the plane?In other words, shape can you put next to itself and NOT have any gaps?
Circles?
Octagons?
Hexagons?
Triangles?Slide3
Regular TessellationsWhen the shape used to tile the plane are the same regular polygons the tessellation is called regular. These are the only regular tessellations.
Triangles
Hexagons
SquaresSlide4
American Quilters have been using simple shapes to tile the plane for hundreds of years.
Sometimes they repeat the same shape and use color to create a pattern.Slide5
Even the simplest of shapes, the triangle, can be used to create complex and beautiful patterns.Slide6
This quilt uses repeated right triangles. Notice that the big triangles are made up of the little ones. The pattern is called “Birds in Flight”. If you look at the white triangles, you see flocks of white birds flying south!Slide7
Just changing the orientation can change the way a tessellation is perceived. Here the “Birds in Flight” pattern is aligned vertically.Slide8
What do you see?,hexagons or triangles?What is the shape that is repeated to make this quilt? Slide9
The artist reversed the light and dark triangles to create different directions.Slide10
Rectangles and squares can also be used to create interesting designs.Slide11
Pattern: Log CabinSlide12
Pattern: Resolution SquareSlide13
Pattern: Courthouse Steps Border: Birds in the AirSlide14
Rectangles can even be used to “paint” a picture!Catch A Falling Star on A Hot August Night by Joen WolfromSlide15
Semi-Regular TessellationsIf you vary the shapes you can still tile the plane. If the same group of regular polygons meet at every vertex, the tessellation is call Semi-Regular. There are only eight semi-regular tessellations. Can you name all eight semi-regular tessellations? Remember that the angles at each intersection must add up to 360. Use this chart to aid you in naming at least four of them.
Regular Polygon
Measure of Interior Angle
Triangle
60
⁰
Square90
⁰Hexagon
120⁰
Octagon135⁰Dodecagon
150⁰Slide16
You name semi-regular tessellations by polygons (number of sides) going clockwise. Try to name the eight pictured tessellations.
3.4.6.4
4.8.8
3.12.12
3.3.3.3.6
3.3.3.4.4
3.3.4.3.4
3.6.3.6
4.6.12Slide17
Beautiful, interesting patterns emerge when the different polygons are repeated across the plane. Even
trompe
l’oeil
!Slide18
Classic 3-DSlide19
EXTREME 3-D!Do you see holes or hills?Slide20Slide21
Trompe L’Oeil From the Past
Medieval Italian Mosaics Slide22
Storm at SeaSlide23Slide24Slide25Slide26
The Fantabulous Worlds of Escher!Slide27Slide28Slide29Slide30Slide31
Escher created this lithograph to demonstrate how his tessellations evolve. 2 through 4 are rhombi. In 5 he starts his metamorphosis. By 7 the birds are formed. In 8, 9, and 10 he adds detail. Magically, in 11 and 12 the birds become fish!Slide32Slide33Slide34Slide35
Works CitedSlide 6: Image from http://jenniferchiaverini.com. “Birds in the Air” by Jennifer Chiaverini. Slide 7: Image from http://jenniferchiaverini.com. “The Runaway Quilt” by Jennifer Chiaverini. Slide 8: Image from http://jenniferchiaverini.com. “Road to Triumph Ranch” Machine pieced by Heather
Neidenbach
, machine quilted by Sue
Vollbrecht
, 2006.
Slide 12
: Image from http://jenniferchiaverini.com. “The Giving Quilt” Gretchen Hartley .
Slide 13: Image from
http://jenniferchiaverini.com. “Joanna’s Freedom” Pieced by Geraldine Neidenbach and Heather
Neidenbach. Quilted by Sue Vollbrecht.
Slide 11: Image from http://jenniferchiaverini.com. “Gerda’s Log Cabin” by Jennifer Chiaverini.
Slide 9
: Image from http://jenniferchiaverini.com. “Eleanor’s Ocean Waves” Machine pieced by Geraldine Neidenbach and Heather
Neidenbach, machine quilted by Sue Vollbrecht, 2003
Slide 14: Image from
http://joenwolfrom.com “Catch a Falling Star on a Hot August Night” by Joen Wolfrom. Slide36
Slide 16: Images from http://www.mathsisfun.com/geometry/tessellation.html Works Cited, cont.Slide 21: Images from
http://www.csun.edu/~lmp99402/Math_Art/Tesselations/tesselations.html