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Star Design

Star Design
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2017-05-11 23:49
PolygonAngleTrigonometrySequenceGeometric Construction
This GeoGebra example investigates the construction of diverse star polygons and patterns through geometric transformations, angle manipulation, and sequence generation. Core mathematical concepts include trigonometry, angle symmetry, polygon properties, and numerical sequences. Construction highlights utilize GeoGebra commands such as Rotate, Intersect, Polygon, Angle, and Sequence, along with objects like A, B, ang, B′, N, α, InputBox1, and A′. The dynamic interplay of these elements reveals underlying geometric rules and is suitable for high school geometry and trigonometry courses, as well as mathematical art enrichment projects.

GeoGebra Commands & Parameters

  1. Rotate(B, ang, A) → B'
  2. Textfield(ang) → InputBox1
  3. Rotate(A, α, B) → A'
  4. Intersect(AngularBisector[B', A, B], AngularBisector[A, B, A']) → C
  5. Polygon(Join[Sequence[Rotate[{B', A, B}, ((i * 360) * ° / N), C], i, 1, N]]) → poly1
  6. Angle(A, B, A') → β
  7. Rotate(poly1, 180°, Midpoint[A, B']) → poly1'
  8. Rotate(poly1', 180°, Rotate[Midpoint[B, A'], 180°, Midpoint[A, B']]) → poly1''
  9. Sequence(Rotate[poly1', ((i * 360) * ° / N), C], i, 1, N) → list1
  10. Sequence(Rotate[poly1'', ((i * 360) * ° / N), C], i, 1, N) → list2