Tessellation: Maths in Art
Explore how shapes can tile together perfectly with no gaps or overlaps, creating beautiful patterns.
What is Tessellation?
A tessellation is a pattern of shapes that fit together perfectly with no gaps and no overlaps. Think of tiles on a bathroom floor or bricks in a wall!
The word "tessellation" comes from the Latin word tessella, which means a small square tile used in mosaics. But tessellations can use many different shapes, not just squares!
The Maths Behind It
For shapes to tessellate, the angles where they meet at every point must add up to exactly 360 degrees (a full turn). This is a key geometry concept!
Which Regular Shapes Tessellate?
Only three regular (all sides and angles equal) shapes can tessellate on their own:
Equilateral Triangles
Interior angle: 60 degrees
6 triangles meet at each point: 6 x 60 = 360
TESSELLATESSquares
Interior angle: 90 degrees
4 squares meet at each point: 4 x 90 = 360
TESSELLATESRegular Hexagons
Interior angle: 120 degrees
3 hexagons meet at each point: 3 x 120 = 360
TESSELLATESRegular Pentagons Do NOT Tessellate
A regular pentagon has interior angles of 108 degrees.
3 pentagons = 3 x 108 = 324 (not enough, leaves a gap). 4 pentagons = 4 x 108 = 432 (too much, they overlap). No whole number of pentagons makes 360!
Tessellation in Art: M.C. Escher
The Dutch artist M.C. Escher (1898-1972) was famous for creating incredible tessellation art. He transformed simple geometric shapes into animals, birds, fish, and lizards that interlocked perfectly!
How Escher Did It
- 1 Start with a shape that tessellates (like a square)
- 2 Cut a piece from one side
- 3 Attach that piece to the opposite side
- 4 The new shape still tessellates! Add details to make it look like something.
Step-by-Step Example
Repeating Patterns in Aboriginal Art
Aboriginal Australian art is one of the oldest art traditions in the world. It features repeating patterns that connect to mathematical ideas like tessellation.
Dot Painting Patterns
Dot paintings use symmetry and repeating circular patterns. These patterns often represent important places, stories, and journeys.
Maths Connections
- ● Symmetry — Many Aboriginal designs have rotational and reflective symmetry
- ● Repetition — Patterns repeat at regular intervals, like tessellations
- ● Counting and spacing — Dots must be evenly spaced, using measurement skills
- ● Geometry — Circles, lines, and curves create geometric designs
Create Your Own Tessellation
Follow these steps to make your own tessellation from a square:
Cut out a square from card (about 5cm x 5cm)
Cut a shape from the top edge of your square
Tape it to the bottom edge in exactly the same position
Trace around your new shape to create a tessellation pattern!
Knowledge Check
Test your understanding of tessellations!
Question 1
Which of these regular shapes does NOT tessellate on its own?
Question 2
How many squares meet at each point in a square tessellation?
Question 3
What must the angles at each meeting point add up to in a tessellation?
Question 4
Which artist was famous for creating tessellation artwork with interlocking animals?
Key Concepts Summary
- ●A tessellation is a pattern of shapes with no gaps or overlaps.
- ●Only three regular shapes tessellate: triangles, squares, and hexagons.
- ●Angles at each meeting point must add up to 360 degrees.
- ●M.C. Escher created famous tessellation art by modifying basic shapes.
- ●Tessellation connects geometry and art — maths makes beautiful patterns!