Page 1 — Introduction

  • IPRESENTATION BY: GROUP1
  • GOOD AFTERNOON

Page 2 — Polygons & Tessellation: Definitions & Examples

  • Topic: Polygons & Tessellation; Definitions & Examples

Page 3 — Polygons: Definition

  • In mathematics, a polygon is a two-dimensional geometric shape formed by three or more straight line segments that connect to form a closed figure.
  • These line segments are called sides or edges.
  • The points where they meet are called vertices.
  • Polygons are defined by their number of sides, with examples including triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), and hexagons (6 sides).
  • (Note: The slide title is presented as "Definitions of Polygons".)

Page 4 — Polygons That Tessellate

  • Can Tessellate the Plane (no gaps or overlaps):
    • Equilateral Triangle
    • Square
    • Regular Hexagon
    • All Triangles
    • All Quadrilaterals

Page 5 — Polygons That cannot Tessellate

  • Cannot Tessellate Alone:
    • Regular Pentagon
    • Regular Octagon

Page 6 — Definitions of Tessellation

  • Tessellations are tiling patterns formed of shapes with no gaps in between.
  • Regular tessellations are formed of regular polygons.
  • We can see a regular polygon will tessellate by looking at the interior angles.
  • Keywords: Tiling patterns; No gap; Formed of regular polygons.
  • Additional mathematical context (conceptual, not explicitly stated in the slide):
    • Interior angle of a regular n-gon: θ=180 (n−2)n\theta = \frac{180\,(n-2)}{n} degrees.
    • Around a vertex with k polygons meeting: k θ=360∘.k\,\theta = 360^\circ.
    • For common tessellations:
    • Triangle (n=3): θ=180 (3−2)3=60∘\theta = \frac{180\,(3-2)}{3} = 60^\circ, so k = 6 around a point.
    • Square (n=4): θ=180 (4−2)4=90∘\theta = \frac{180\,(4-2)}{4} = 90^\circ, so k = 4 around a point.
    • Hexagon (n=6): θ=180 (6−2)6=120∘\theta = \frac{180\,(6-2)}{6} = 120^\circ, so k = 3 around a point.
    • Conclusion: Regular tessellations with a single polygon type are possible using triangles, squares, and hexagons.

Page 7 — Shapes examples that can tessellate

  • Square
  • Triangle
  • Hexagon

Page 8 — Shapes examples that cannot tessellate

  • Pentagon
  • Circle
  • Octagon

Page 9 — Real life examples that tessellate

  • Honeycomb
  • Floor tiles
  • Chessboard

Page 10 — Real life examples that cannot tessellate

  • Oranges
  • Eggs
  • Raindrops

Page 11 — That's all

  • THATS ALL THANK YOU!