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Tessellations “To me it remains an open question whether [this work] pertains to the realm of mathematics, or that of ar

Tessellations “To me it remains an open question whether [this work] pertains to the realm of mathematics, or that of art.” ~M.C. Escher. A guide for 4 th and 5 th graders By Heidi Norkoli. What is a tessellation?.

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Tessellations “To me it remains an open question whether [this work] pertains to the realm of mathematics, or that of ar

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  1. Tessellations“To me it remains an open question whether [this work] pertains to the realm of mathematics, or that of art.”~M.C. Escher A guide for 4th and 5th graders By Heidi Norkoli

  2. What is a tessellation? • A tessellation is a figure or combination of figures in a plane of regular repetition of the figure or figures that covers the plane so that there are no gaps and no overlapping of figures. • There are several kinds of tessellations, including: regular and semi-regular.

  3. Regular Tessellations • These kinds of tessellations are created using regular polygons. • The only three regular polygons that can tessellate are: • Equilateral triangles • Squares • Regular hexagons

  4. Semi-regular Tessellations • These are tessellations that have two or more regular polygons that are arranged so that the same polygons appear in the same order around each vertex point.

  5. Tessellation Rules • The tessellation must be able to tile a floor, with no overlapping or gaps. • All tiles must be the same. • Each vertex must look the same

  6. Why do we need to learn about tessellations? • Tessellations are helpful when you are learning geometry, because it helps you learn about symmetry. • It’s fun! • It combines math with art, which is important to learn how things are interconnected. • So you can spot tessellations in “the real world” and know how to identify them.

  7. The 4 symmetries in tessellations • In all tessellations, there are 4 basic patterns of symmetry that are used. • The symmetries are movement, without distortion of the size or shape of the original shape. • The kinds of symmetries are: translations (or slides), reflections, glide reflections, and rotations

  8. Translation • The figure at the right is an example of a translation. • This is also known as a slide.

  9. Reflection • This is an example of a reflection. • A good way to remember this is to think of it as a reflection in a mirror.

  10. Glide Reflection • In this symmetry, the shape is just flipped upside-down. • This one is probably the hardest to remember because the name doesn’t give it away like the others do.

  11. Rotation • The shape here is not only flipped upside-down, but also it is reflected, like you are looking at it upside down in a mirror.

  12. Who created tessellations? • The man who first drew and developed tessellations was a man named Maurits Cornelis Escher, from Leeuwarden, Netherlands. The picture on the right is his self-portrait.

  13. Famous Tessellations • This is one of Escher’s most famous tessellations. It is simply called “Reptiles”

  14. Another Famous One… • Another one of Escher’s famous tessellations is this one, called “Elephants”

  15. Octagons • This tessellation isn’t a famous one, but it would be easy to replicate.

  16. So, as you can see, tessellations are fun to learn about and easier to replicate than perhaps, you originally thought, so now it’s you turn to create your own.

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