Tiling and Tessellations: Shapes That Cover the Plane
What is a Tessellation?
A tessellation (also called tiling) is a pattern made by fitting shapes together perfectly to cover a flat surface with no gaps and no overlaps. It's like a puzzle where all the pieces fit together perfectly!
✓ This IS a Tessellation
Perfect fit! No gaps or overlaps.
✗ This is NOT a Tessellation
Circles leave gaps - they don't tessellate!
The Magic Number: 360°
For shapes to tessellate, there's a special mathematical rule: at every point where shapes meet (called a vertex), the angles must add up to exactly 360°.
Think of it like this: 360° is a complete circle around a point. If the angles add up to less than 360°, there will be gaps. If they add up to more than 360°, the shapes will overlap. It has to be exactly 360°!