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Polar Coordinates by Jonathan Holland

Polar Coordinates by Jonathan Holland
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2018-02-02 06:31
VectorCoordinate GeometryGeometric Construction
This example demonstrates point representation, graph drawing, and conversion between polar and Cartesian coordinates. Core concepts include polar coordinates, vectors, lines, integral calculus, logarithmic functions, and plane figures. GeoGebra commands like Intersect, Vector, OrthogonalLine, Segment, Sequence, Midpoint, Circle, Ray, and Angle are used in construction. Suitable for high school and above mathematics learners to understand polar coordinate applications and geometric constructions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Vector(A, B) → v
  3. OrthogonalLine(B, xAxis) → f
  4. Intersect(f, xAxis) → C
  5. Segment(A, C) → x_B
  6. Segment(C, B) → y_B
  7. Sequence(Circle[A, i], i, 1, n) → L_1
  8. Sequence(Circle[A, i + 0.5], i, 0, n - 1) → L_2
  9. Sequence(Circle[A, i + 0.75], i, 0, n - 1) → L_3
  10. Sequence(Circle[A, i + 0.25], i, 0, n - 1) → L_4
  11. Midpoint(A, B) → D
  12. Circle(A, 1) → c
  13. Ray(A, B) → g
  14. Intersect(c, g) → E,
  15. Vector(A, E) → u
  16. Segment(A, B) → r
  17. Midpoint(A, B) → F
  18. Angle(l, r) → θ
  19. Sequence(Rotate[l, t, A], t, 0, π, π / 12) → L_5