MathPlotAI Logo MathPlotAI

GeoGebra Geometry Construction: Circle and Polygon Integration

GeoGebra Geometry Construction: Circle and Polygon Integration
Loading the math board and drawing, please wait…
2018-10-23 18:22
CirclePolygonGeometric ConstructionSlider Animation
In collections Fraction Division (2018)
This example demonstrates comprehensive geometric construction in GeoGebra. Core mathematical concepts include basic circle properties, polygon construction, perpendicular lines, and point intersections. Construction points: Use Circle command for drawing circles, Polygon for creating polygons, OrthogonalLine for perpendicular lines, Intersect for finding intersections, Sequence for generating series, and LCM for calculating least common multiple. Suitable for middle to high school students as geometry construction practice, and for teachers demonstrating geometric construction methods.

GeoGebra Commands & Parameters

  1. Circle(B, r) → e
  2. Segment(A, B) → f
  3. OrthogonalLine(A, f) → h
  4. OrthogonalLine(B, f) → g
  5. Intersect(e, g, 1) → C
  6. OrthogonalLine(C, g) → i
  7. Intersect(h, i) → D
  8. Line(E, f) → j
  9. Circle(E, f) → k
  10. Intersect(k, j, 1) → F
  11. OrthogonalLine(E, j) → l
  12. OrthogonalLine(F, j) → p
  13. Circle(E, r) → q
  14. Circle(F, r) → s
  15. Intersect(q, l, 1) → H
  16. Intersect(s, p, 1) → G
  17. Polygon(B, A, D, C) → poly1, b_1, a_1, d_1, c_1
  18. Polygon(E, F, G, H) → poly2, e_1, f_1, h_1, g_1
  19. Textfield(a) → InputBox1_1
  20. Textfield(b) → InputBox2
  21. Textfield(c) → InputBox3
  22. Textfield(d) → InputBox4
  23. Circle(B, (2 * r)) → p_1
  24. Intersect(p_1, g, 1) → I
  25. OrthogonalLine(I, g) → n_1
  26. Intersect(h, n_1) → J
  27. Circle(E, (2 * r)) → s_1
  28. Intersect(s_1, l, 1) → K
  29. OrthogonalLine(K, l) → t_1
  30. Intersect(p, t_1) → L
  31. Segment(C, I) → f_2
  32. Segment(I, J) → g_2
  33. Segment(D, J) → h_2
  34. Textfield(n) → InputBox5
  35. Textfield(m) → InputBox6
  36. Polygon(C, D, J, I) → poly3, c_2, d_2, j_1, i_1
  37. Circle(B, (3 * r)) → t
  38. Intersect(t, g) → M, N
  39. OrthogonalLine(M, g) → k_1
  40. Intersect(h, k_1) → O
  41. Polygon(I, J, O, M) → poly4, i_2, j_2, o, m_1
  42. Circle(B, (4 * r)) → q_1
  43. Intersect(q_1, g) → P, Q
  44. OrthogonalLine(P, g) → l_1
  45. Intersect(h, l_1) → R
  46. Polygon(M, O, R, P) → poly5, m_2, o_1, r_1, p_2
  47. Polygon(H, G, L, K) → poly6, h_3, g_3, l_2, k_2
  48. Circle(E, (3 * r)) → e_2
  49. Intersect(e_2, l) → S, T
  50. OrthogonalLine(S, l) → n_2
  51. Intersect(p, n_2) → U
  52. Intersect(l_2, k_2) → V
  53. Polygon(V, L, U, S) → poly7, v, l_3, u, s_2
  54. Circle(E, (4 * r)) → q_2
  55. Intersect(q_2, l) → W, Z
  56. OrthogonalLine(W, l) → r_2
  57. Intersect(p, r_2) → A_1
  58. Polygon(S, U, A_1, W) → poly8, s_3, u_1, a_2, w
  59. Polygon(A, B, B + ((C - B) / b * ((n * b) + a)), A + ((D - A) / b * ((n * b) + a))) → poly9, a_3, b_2, t_2, f_3
  60. Polygon(E, F, F + ((G - F) / d * ((m * d) + c)), E + ((H - E) / d * ((m * d) + c))) → poly10, e_3, f_4, i_3, j_3
  61. Sequence(Segment[B + ((C - B) / LCM[b, d] * i), A + ((D - A) / LCM[b, d] * i)], i, 1, (n * LCM[b, d]) + LCM[b, d] - 1) → list3
  62. Polygon(A, B, B + (((C - B) / d * ((m * d) + c)) * ceil(ans)), A + (((D - A) / d * ((m * d) + c)) * ceil(ans))) → poly11, k_3, m_3, n_3, p_3
  63. Sequence(Segment[E + ((H - E) / LCM[b, d] * i), F + ((G - F) / LCM[b, d] * i)], i, 1, (m * LCM[b, d]) + LCM[b, d] - 1) → list4
  64. LCM(b, d) → o_2
  65. Sequence(Segment[B + ((C - B) / ((b * u_2)) * i), A + ((D - A) / ((b * u_2)) * i)], i, 1, (n * (b * u_2)) + (b * u_2) - 1) → list1
  66. Sequence(Segment[E + ((H - E) / ((d * v_2)) * i), F + ((G - F) / ((d * v_2)) * i)], i, 1, (m * (d * v_2)) + (d * v_2) - 1) → list2
  67. Sequence(Segment[A + ((D - A) / ((d * v_2)) * i), B + ((C - B) / ((d * v_2)) * i)], i, 1, ((((m * d) + c) * ceil(ans)) * v_2) - 1) → list5
  68. Sequence(Segment[A + (((D - A) / d * ((m * d) + c)) * i), B + (((C - B) / d * ((m * d) + c)) * i)], i, 1, ceil(ans) - 1) → list6

AI Drawing Prompt Reference

Draw a figure with multiple concentric circles and polygons. Start by drawing a circle e with point B as the center. Then, draw a segment f between points B and A, and draw perpendicular lines h and g through points A and B, respectively. Find point C at the intersection of circle e and line g, and draw a perpendicular line i through point C. The intersection of line i and h is point D. Next, draw a circle k with point E as the center and line f as the radius, and draw a line j through point E. Draw another circle q with point E as the center and line f as the radius. Find point F at the intersection of circle q and line j, and draw a perpendicular line p through point F. Find point H at the intersection of circle e and line p, and find point G at the intersection of circle k and line l. Draw a quadrilateral poly1 with points B, A, D, and C as vertices, and draw a quadrilateral poly2 with points E, F, G, and H as vertices. Continue this process to draw more concentric circles and polygons.
The prompt above was compiled from the original drawing commands and is for reference only.