Geometrical Golden Ratio Fibonacci Field Compass

45 mins Ages 10-14 Anywhere

A challenging, hands-on discovery and STEM project designed for curious young minds aged 10 to 14.

Materials Needed

  • • Dense heavy cardstock or illustration board (1 sheet)
  • • Brass paper fasteners (split brads) (4 units)
  • • Metric millimeter ruler and hole punch (1 set)
  • • Natural specimens (pinecone, large shell, or leaf) (2 units)

Pro Tips

  • → Assemble three linked cardboard strips with pivot holes spaced at the golden ratio (1.0 to 1.618).
  • → No matter how wide or narrow you open the calipers, the ratio between the large gap and the small gap remains 1.618.
  • → Use the calipers to measure nature finds: pinecone spirals, leaf vein widths, and facial proportions.

Safety First

Punch holes accurately; use care with pointed craft tools.

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Step-by-Step Instructions

1

Step 1

Cut three 2 cm wide strips of stiff cardboard to lengths of 30 cm, 20 cm, and 15 cm.

2

Step 2

Measure and punch pivot holes along the strips at specific golden-ratio distances (ratio of 1.0 to 1.618).

3

Step 3

Connect the strips using brass paper split brads to assemble an expandable golden ratio caliper.

4

Step 4

Test the calipers on a pinecone spiral, a photograph of the Parthenon, and the joints of your fingers to verify the 1.618 ratio.

What they are learning

The Golden Ratio (Phi ≈ 1.618) Fibonacci sequences in nature and human design Geometric pantograph linkage mechanics