The Mathematics of Tessellation University of （大学的数学镶嵌）.pdf

The Mathematics of Tessellation © 2000 Andrew Harris The Mathematics of Tessellation 1 © 2000 Andrew Harris Contents Defining Tessellation 3 Tessellation within the Primary School Curriculum 3 Useful Vocabulary for Tessellation 3 Prior Knowledge Required for Understanding the Mathematics of Tessellation 4 Useful Resources for Teaching Tessellation 5 Progression in Learning about Tessellation 5 1. Tessellation by Repeated Use of One Regular Shape6 2. Tessellation by Repeated Use of Two or More Regular Shapes 9 3. Tessellation of Triangles and Quadrilaterals 11 Preparatory Knowledge for Understanding the Tessellation of Triangles and Quadrilaterals 11 (a) Tessellating with Triangles 12 (b) Tessellating with Quadrilaterals14 4. Tessellation of Irregular Shapes obtained by Mutation of Tessellating Shapes18 The designs of M.C. Escher 19 5. Tessellations involving other irregular shapes 21 Use of ICT in Teaching Tessellation 23 Resources Hexagonal Tiling Mats 25 Square Tiling Mats - 1 26 Square Tiling Mats - 2 27 Square Tiling Mats - 3 28 Useful References: Tessellation 29 The Mathematics of Tessellation 2 © 2000 Andrew Harris Defining Tessellation A tessellation can be defined as the covering of a surface with a repeating unit consisting of one or more shapes in such a way that: • there are no spaces between, and no overlapping of, the shapes thus employed