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Spiral of Circles

Spiral of Circles
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2019-03-14 07:07
CircleVectorTrigonometryCoordinate Geometry
This example demonstrates the dynamic construction of a spiral of circles. It involves core mathematical concepts like circles, vectors, angles, sequences, and coordinate geometry. Key GeoGebra commands and objects used include Point, Circle, UnitVector, Angle, nextcirc, Center, Sequence, Textfield, and CurveCartesian. Suitable for high school mathematics education, exploring parametric equations, loci, and geometric transformations.

GeoGebra Commands & Parameters

  1. Point(Ray[A, A + (1, 0)]) → B
  2. Circle(A, B) → c
  3. UnitVector(Segment[B, A]) → u
  4. Circle(B + (u * (Radius[c] + d)), Radius[c] + d) → d_1
  5. Point(d_1) → C
  6. Angle(B, C_1, C) → a
  7. nextcirc(C_1, C, d, a) → e, F, G
  8. Circle(A, C_1, F) → f
  9. Center(f) → H
  10. Sequence(Circle[Rotate[A, (i * a), H], Radius[c] + (i * d)], i, 1, n) → l1
  11. Textfield(ang) → InputBox1
  12. CurveCartesian((p + (q * θ); θ), θ, 0, ((π * n) * ang / (180°))) → b