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Year 6 Maths Art Aboriginal & Torres Strait Islander Knowledge

Aboriginal Art & Geometry

Explore the mathematical patterns within Aboriginal and Torres Strait Islander art, including symmetry, tessellation, geometric shapes and cultural symbolism.

Acknowledgement: Aboriginal and Torres Strait Islander peoples are the Traditional Custodians of the lands on which we learn. Aboriginal and Torres Strait Islander art carries deep cultural meaning and is often connected to Dreaming stories, Country and law. Art styles belong to specific communities. We pay our respects to Elders past, present and emerging.

Art and Mathematics Together

Aboriginal and Torres Strait Islander art is among the oldest art traditions in the world, with rock art dating back at least 65,000 years. But it is not just art; it is also mathematics in visual form.

These artworks contain precise geometric patterns, complex symmetry, tessellation (repeating patterns without gaps) and carefully calculated proportions. The artists who create these works are applying sophisticated mathematical concepts, even if they don't describe them using Western mathematical language.

In this lesson, we will explore the geometry hidden within different styles of Aboriginal and Torres Strait Islander art.

Dot Painting: Patterns and Symmetry

Dot painting is perhaps the best-known style of Aboriginal art worldwide. It originated in the Western Desert region and became widely practised from the 1970s onwards. Dot paintings often represent aerial views of Country, showing waterholes, paths, campsites and Dreaming stories.

The mathematical patterns in dot painting are remarkable:

Geometric Patterns in Dot Art

Concentric circles (waterhole/campsite)

Rotational symmetry (4 lines of symmetry)

Parallel lines (paths/tracks)

● Concentric circles (circles inside circles sharing the same centre) often represent waterholes or campsites
● Line symmetry is used extensively, with patterns reflecting equally on both sides of a central line
● Rotational symmetry appears in circular designs where the pattern repeats as you rotate around the centre
● Tessellation: dots are placed in regular patterns that tile the surface without gaps or overlaps

Cross-Hatching (Rarrk): Parallel Lines and Precision

Rarrk (cross-hatching) is an art style from Arnhem Land in the Northern Territory. It involves painting fine, closely spaced parallel lines in different directions to create complex patterns. Each pattern belongs to a specific clan and carries deep cultural meaning.

Cross-Hatching Patterns

Vertical parallel lines

Cross-hatching (two directions)

Diagonal parallel lines

Maths Connection: Rarrk art demonstrates understanding of parallel lines (lines that run in the same direction and never meet), angle of intersection (the angle where two sets of lines cross), and equal spacing (maintaining consistent distance between lines). The precision required is extraordinary, with some artists painting lines less than 1mm apart.

Symbols: Meaning and Geometry

Aboriginal art uses a set of symbols that carry specific meanings. These symbols are also geometric shapes with measurable properties.

Torres Strait Islander Art: Patterns of the Sea

Torres Strait Islander art often features marine themes: turtles, fish, dugong, waves and stars. The art is distinctly different from mainland Aboriginal art and includes linocut printmaking, sculpture and body art.

Linocut Prints

Torres Strait Islander printmaking often uses repeating patterns and tessellation. Fish and turtle motifs are arranged so they fit together without gaps, similar to the tessellation patterns studied in mathematics.

Symmetry in Marine Designs

Many marine creatures are naturally symmetrical. Torres Strait Islander artists use this bilateral symmetry (line symmetry) in their designs, where one half of a turtle or fish is the mirror image of the other.

Types of Symmetry in Indigenous Art

Line Symmetry (Reflection Symmetry)

A shape has line symmetry when one half is the mirror image of the other half. Many Aboriginal and Torres Strait Islander designs use one or more lines of symmetry.

The red line is the line of symmetry. The pattern on the left mirrors the pattern on the right.

Rotational Symmetry

A shape has rotational symmetry when it looks the same after being rotated (turned) by a certain angle. Concentric circles in dot painting have infinite rotational symmetry.

For example, a design with order 4 rotational symmetry looks the same when rotated 90 degrees (a quarter turn), 180 degrees (half turn), 270 degrees (three-quarter turn) and 360 degrees (full turn).

Tessellation

A tessellation is when shapes fit together to cover a surface completely with no gaps and no overlaps. This appears in both dot painting backgrounds and Torres Strait Islander printmaking.

Squares tessellate perfectly with no gaps. More complex shapes can also tessellate.

Key Vocabulary

Line Symmetry

When one half of a shape is the mirror image of the other half across a line.

Rotational Symmetry

When a shape looks the same after being rotated by a certain angle.

Tessellation

When shapes fit together to cover a surface with no gaps and no overlaps.

Rarrk

Cross-hatching art from Arnhem Land using fine parallel lines painted in different directions.

Worked Examples

1

How many lines of symmetry does a concentric circle design have?

Step 1: A circle looks the same no matter where you draw a line through its centre.

Step 2: Concentric circles share the same centre, so every line through the centre is a line of symmetry.

Answer: A concentric circle design has infinite lines of symmetry (any line through the centre works).

2

A diamond (rhombus) symbol appears in a painting. What is its order of rotational symmetry?

Step 1: Rotate the diamond. At 180 degrees (half turn), it looks the same.

Step 2: At 360 degrees (full turn), it looks the same again.

Step 3: It looks the same 2 times during a full rotation.

Answer: A diamond has rotational symmetry of order 2.

3

What angle do the lines cross at in cross-hatching if they go vertically and horizontally?

Step 1: Vertical lines go straight up and down. Horizontal lines go straight across.

Step 2: When these lines cross, they form right angles.

Answer: The lines cross at 90 degrees (right angles). In rarrk art, the angle varies and is deliberately chosen for visual and cultural effect.

Knowledge Check

Select the correct answer for each question. Click "Check Answer" to see if you are right.

Question 1

In Aboriginal dot painting, concentric circles often represent a:

Question 2

What is tessellation?

Question 3

What mathematical property is most prominent in cross-hatching (rarrk) art?

Question 4

A design has line symmetry. This means:

Question 5

Torres Strait Islander art often features marine creatures like turtles. A turtle design with bilateral symmetry has:

Key Concepts Summary

Year 5: Indigenous Astronomy Year 7: Land Management