MathPlotAI Logo MathPlotAI

Three-Phase Circle: Representing Three-Phase Electricity Phases via Circular Mot

Three-Phase Circle: Representing Three-Phase Electricity Phases via Circular Mot
Loading the math board and drawing, please wait…
2016-05-12 05:23
CircleAngleTrigonometryParametric EquationSlider Animation
① This example demonstrates how the motion of points on a circle can represent the three phases (A, B, C) of three-phase alternating current, translating abstract phase differences into visible circular rotation and projections. ② Core mathematical concepts include trigonometric functions (sine waves), parametric equations, angle rotation, phase difference, and coordinate projections of points on a circle, along with geometric constructions involving intersections, perpendicular lines, and rays. ③ Construction highlights: Using GeoGebra commands such as Intersect, Point, Circle, Segment, Rotate, Angle, OrthogonalLine, Ray, and Line, the construction creates a circle, rotating points, perpendicular lines, and multiple auxiliary objects (e.g., V_1, V_2, V_3 and their projections), with sliders or animations controlling the rotation angle to generate three sine curve projections with 120° phase separation. ④ Suitable for high school physics or mathematics students learning trigonometric functions, vectors, and wave phenomena, as well as for university-level circuit theory instruction on three-phase electricity, providing an intuitive grasp of phase differences and rotating vector representation.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, B) → c
  4. Point(c) → V_1
  5. Segment(A, V_1) → v_1
  6. Rotate(V_1, 120°, A) → V_2
  7. Angle(V_1, A, V_2) → α
  8. Segment(A, V_2) → v_2
  9. Rotate(V_1, (-(120°)), A) → V_3
  10. Angle(V_3, A, V_1) → β
  11. Segment(A, V_3) → v_3
  12. Segment(V_1, V_2) → h
  13. Segment(V_2, V_3) → i
  14. Segment(V_3, V_1) → j
  15. Point(xAxis) → D
  16. OrthogonalLine(D, xAxis) → f
  17. OrthogonalLine(V_1, f) → g
  18. OrthogonalLine(V_2, f) → k
  19. OrthogonalLine(V_3, f) → l
  20. Intersect(f, k) → V_2y
  21. Intersect(f, l) → V_3y
  22. Intersect(f, g) → V_1y
  23. Segment(V_2, V_2y) → m
  24. Segment(V_1, V_1y) → n
  25. Segment(V_3, V_3y) → p
  26. Rotate(V_1, 150°, A) → C'_2
  27. Angle(V_1, A, C'_2) → γ
  28. Rotate(V_1, (-(90°)), A) → C'_3
  29. Angle(C'_3, A, V_1) → δ
  30. Rotate(V_1, 30°, A) → C'_4
  31. Angle(V_1, A, C'_4) → ε
  32. Ray(A, C'_2) → q
  33. Line(V_2, v_1) → r
  34. Intersect(r, q) → V12
  35. Segment(A, V12) → s
  36. Segment(V12, C'_2) → t
  37. OrthogonalLine(V12, f) → a
  38. Intersect(f, a) → V12y
  39. Segment(V12, V12y) → b
  40. Angle(B, A, V_1) → ζ
  41. Point({3 + ζ / 4, sin(ζ)}) → V1t
  42. Segment(V_1y, V1t) → d
  43. Angle(B, A, V_2) → η
  44. Angle(B, A, V_3) → θ
  45. Point({3 + ζ / 4, sin(η)}) → V2t
  46. Point({3 + ζ / 4, sin(θ)}) → V3t
  47. Segment(V_2y, V2t) → e
  48. Segment(V_3y, V3t) → f_1
  49. Angle(B, A, V12) → ι
  50. Point({3 + ζ / 4, (sqrt(3) * sin(ι))}) → V12t
  51. Segment(V12y, V12t) → g_1
  52. Segment(V1t, D) → j_1
  53. Segment(V2t, V12y) → k_1