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Equiangular Spiral on Nautilus Shell

Equiangular Spiral on Nautilus Shell
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2014-08-05 22:01
TrigonometrySequenceCoordinate GeometryIntegralGeometric Construction
In collections Symmetry, Transformation and Tessellation
This example demonstrates the equiangular spiral formed on a nautilus shell. It involves core mathematical concepts like trigonometry, coordinate geometry, sequence generation, and integral operations. The construction highlights GeoGebra commands and objects such as Polygon, Angle, and Sequence. Suitable for high school and above, it helps understand the geometric construction and mathematical principles of the equiangular spiral.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, e, a, b
  2. Angle(B, A, C) → α
  3. Sequence(Rotate[Dilate[shape, r^(k), A], (k * α), A], k, 0, n) → list1

AI Drawing Prompt Reference

Draw an equiangular spiral on a nautilus shell starting from the center, construct an initial shape using a polygon tool, then generate a series of similar shapes by rotating and scaling them, with each shape rotated by the same angle and scaled by a geometric sequence, demonstrating the formation of the equiangular spiral.
The prompt above was compiled from the original drawing commands and is for reference only.