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Equiangular Spiral

Equiangular Spiral
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2014-11-12 10:07
Coordinate GeometryParametric EquationGeometric Construction
In collections About Exponents
This example demonstrates a nautilus shell and an equiangular (logarithmic) spiral. An equiangular spiral is a special curve where the angle between the curve and the radius is constant. The core mathematical concepts involved include coordinate geometry and parametric equations. Using GeoGebra commands such as Vector, Angle, Length, and CurveCartesian, the equiangular spiral can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Vector(F, A) → u
  2. Vector(F, B) → v
  3. Angle(u, v) → α
  4. Length(u) → b
  5. Length(v) → c
  6. Angle(u) → d
  7. CurveCartesian(g(t), h(t), t, 0, 6.283185307179586) → a
  8. Segment(F, A) → e
  9. Segment(F, B) → i

AI Drawing Prompt Reference

Draw a shape resembling a nautilus shell featuring an equiangular spiral where the angle between the curve and the radius remains constant. Include two straight lines: one connecting the starting point to the center and another extending from the center. The spiral should start at the center and expand outward, showcasing a beautiful mathematical curve.
The prompt above was compiled from the original drawing commands and is for reference only.