MathPlotAI Logo MathPlotAI

Cylindrical Coordinates: Dynamic Interactive Illustrator

Cylindrical Coordinates: Dynamic Interactive Illustrator
Loading the math board and drawing, please wait…
2017-12-30 02:54
Coordinate GeometrySolid GeometryTransformationParametric EquationSlider Animation
In collections GeoGebra 3D & AR: PreCalc & Calculus Resources Plotting Points Multivariable Calculus
① This example provides a dynamic and modifiable visual illustration of how a point's position is determined in cylindrical coordinates (r, θ, z), showing the relationship between radial distance, azimuthal angle, and height in 3D space. ② Core mathematical concepts include cylindrical coordinate systems, conversion between cylindrical and Cartesian coordinates, and the geometric construction of cylinders, sectors, arcs, and planes. ③ Construction highlights: using GeoGebra commands such as Dilate, Rotate, Segment, CircleSector, CircleArc, and Plane to build the 3D scene, with interactive Textfields and sliders (parameters a, b, c) for real-time adjustment; objects include points A, B and their projections A', B', along with auxiliary lines and filled regions. ④ Suitable for high school to undergraduate mathematics education, particularly in analytic geometry, introductory multivariable calculus, or 3D visualization courses, helping learners develop spatial intuition for coordinate transformations.

GeoGebra Commands & Parameters

  1. Dilate(A, If[0 < e ≤ 1, 1 - e, 0], B) → A'
  2. Segment(A, A') → f
  3. Rotate(B, If[1 < e ≤ 2, ((e - 1) * b), b], A) → B'
  4. Segment(A, B') → g
  5. CircleSector(A, B, B') → h
  6. Rotate(A, If[1 < e ≤ 2, ((e - 1) * π / 2), π / 2], A, Line[(0, 0, 0), (0, 1, 0)]) → A'_2
  7. CircleArc(A, (0, 0, a), (0, 0, (-a)), Plane[A, B', (0, 0, (-a))]) → p
  8. Plane((0, 0, 0), (1, 0, 0), (0, 1, 0)) → i
  9. Textfield(a) → InputBox1
  10. Textfield(b) → InputBox2
  11. Textfield(c) → InputBox3
  12. Dilate(B', If[2 < e ≤ 3, 3 - e, 0], C) → B''
  13. Segment(B', B'') → k