Tessellations-Demonstration.pptx
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This document provides an overview of tessellation through animated demonstrations and examples. Tessellation is defined as using shapes to cover a flat surface without gaps or overlaps. Only some shapes like triangles, hexagons, and rectangles can tessellate. Regular tessellations use one shape with equal vertex angles, while irregular tessellations mix shapes. Tessellation is used in areas like tiling, packaging, and M.C. Escher artwork which transform shapes through translations, rotations, and reflections.
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Project Description for Tessellation Project in High School Geometry. For use after Rigid Transformations.
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This document provides information about a student project on tessellations. It includes an introduction to tessellations and the artist M.C. Escher. It then discusses different types of tessellations created through translations, glide reflections, and rotations. Examples are shown of each type. Suggestions are given for how students should approach creating their own tessellation template, such as reading the packet first and trying multiple designs. The due date for the project is provided.
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1. Tessellation is the repetition of geometric shapes to cover a plane without gaps or overlaps. It originated from the Roman practice of using small stone cubes (tesserae) in mosaic designs (tessellata).
2. There are four main types of tessellation - translation, reflection, rotation, and glide reflection - which can be used alone or combined to create complex patterns.
3. Artist M.C. Escher was famous for his works featuring tessellation patterns that play with perspective and the morphing of geometric shapes into organic forms. His works demonstrated how geometric forms can blend with their environment.
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Tessellation Project High School Geometry
Project Description for Tessellation Project in High School Geometry. For use after Rigid Transformations.
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This document provides information about a student project on tessellations. It includes an introduction to tessellations and the artist M.C. Escher. It then discusses different types of tessellations created through translations, glide reflections, and rotations. Examples are shown of each type. Suggestions are given for how students should approach creating their own tessellation template, such as reading the packet first and trying multiple designs. The due date for the project is provided.
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Tessellations-Demonstration.pptx
- 1. Tessellation – Demonstration This resource provides animated demonstrations of the mathematical method. Check animations and delete slides not needed for your class.
- 2. Denise wants to tile her bathroom. Which shape tiles could she use? To stop water leaking, the tiles must join together with no gaps.
- 3. Rectangles Tessellation Only some shapes can fill a plane (flat surface) without any gaps. For example… Triangles Hexagons
- 4. Many shapes don’t tessellate. There will always be gaps. How could we fill the gaps?
- 5. Tessellation Roman mosaic (2000 years old) ‘Using shapes to cover a flat surface, with no gaps and no overlaps’ tessella: small cubes used to make mosaics. Hexagonal shower tiles Modern Moroccan mosaic tessellate: to create a tessellation
- 6. Regular tessellations One type of shape & vertices (corners) with equal angles. Only 3 shapes can do this. Irregular tessellations Any mix of shape or shapes.
- 7. As well as on a plane (flat surface), we can also tessellate in 3D space! When we package goods (like food & drinks), why do we want the shapes to tessellate? Rhombic dodecahedrons
- 8. At each vertex, what is the total of the angles? Why is this important? 120° × 3 60° × 6 90° × 4 Where tiles meet, the interior angles must total 360° so there are no gaps.
- 9. Which shapes do you think will tesselate? Do we need do change the orientation of the shape to make it tessellate? reflect, or rotate?
- 10. We can tesselate shapes using 3 transformations. Translate move the shape Rotate spin the shape Reflect mirror the shape
- 11. Maurits Cornelis Escher 1898 –1972 M. C. Escher was a Dutch graphic artist who used maths in lots of his artwork. He was interested in transforming shapes. ‘Day and Night’ 1938
- 12. How can you describe this tessellation? translation
- 13. How can you describe this tessellation? reflection
- 14. How can you describe this tessellation? rotation
- 15. How can you describe this tessellation? reflection
- 16. How can you describe this tessellation? translation
- 17. How can you describe this tessellation? reflection
- 18. How can you describe this tessellation? rotation
- 19. How can you describe this tessellation? 2 different shapes, translated
- 20. Questions? Comments? Suggestions? …or have you found a mistake!? Any feedback would be appreciated . Please feel free to email: tom@goteachmaths.co.uk