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Equiangular Spiral by GeoGebra Institute of Hong Kong

Equiangular Spiral by GeoGebra Institute of Hong Kong
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2014-08-05 21:46
AngleTrigonometrySequenceLimitGeometric Construction
In collections Symmetry, Transformation and Tessellation
This example demonstrates the geometric construction and properties of an equiangular spiral. Key math concepts include angles, ratios, scalene triangles, natural numbers, and limits. The construction uses GeoGebra commands like Polygon, Angle, and Sequence to build the spiral step-by-step. Suitable for high school and above, helping learners understand the generation process and applications of equiangular spirals in mathematics.

GeoGebra Commands & Parameters

  1. Polygon(D, E, F, G, H, I, J, K) → poly2, d, e, f, g, h, i, j, k
  2. Polygon(A, B, C) → poly1, c, a, b
  3. Angle(B, A, C) → α
  4. Sequence(Rotate[Dilate[shape, r^(k), A], (k * α), A], k, 0, n) → list1

AI Drawing Prompt Reference

Draw an equiangular spiral by progressively constructing and rotating multiple triangles, showing the step-by-step generation process. Each triangle has equal angles and increasing sizes, demonstrating the continuous expansion and limiting behavior of the spiral.
The prompt above was compiled from the original drawing commands and is for reference only.