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Planar Graph Construction

Planar Graph Construction
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2017-11-20 15:03
CirclePolygonAngleGeometric Construction
This example demonstrates the construction of a planar graph, illustrating the intersection relationships between polygons and circles. Key mathematical concepts include plane geometry, polygon construction, circle-line intersection, angle measurement, etc. Construction highlights involve using commands like Circle, Intersect, Rotate, Polygon, Line, OrthogonalLine, Angle, Midpoint, Segment, Point, and Textfield. Suitable for high school mathematics education, explaining the basic properties and drawing methods of planar graphs.

GeoGebra Commands & Parameters

  1. Circle(OO, 1, xOyPlane) → c
  2. Intersect(yAxis, c, 2) → A
  3. Rotate(A, 60°) → B
  4. Rotate(A, 120°) → C
  5. Rotate(A, 180°) → D
  6. Rotate(A, 240°) → E
  7. Rotate(A, 300°) → F
  8. Polygon(A, B, C, D, E, F) → veelhoek1, a, b, c_1, d, e, f
  9. Polygon(B, A, 6, xOyPlane) → veelhoek2, g, J_1, h, i, j, k, l, G_1, H_1, I_1
  10. Polygon(D, C, 6, xOyPlane) → veelhoek3, m, N, n, p, q, r, s, K_1, L_1, M
  11. Polygon(F, E, 6, xOyPlane) → veelhoek4, t, R, f_1, g_1, h_1, i_1, j_1, O, P, Q
  12. Circle(c_1, K_1) → d_1
  13. Circle(a, J_1) → e_1
  14. Intersect(e_1, d_1) → J, T, ,
  15. Line(D, C) → k_1
  16. OrthogonalLine(K_1, k_1, xOyPlane) → l_1
  17. Intersect(k_1, l_1) → KK
  18. Angle(K_1, KK, J) → α
  19. Rotate(veelhoek3, (-α), c_1) → veelhoek3'
  20. Line(OO, OOO) → as
  21. Rotate(veelhoek3', 120°, as) → veelhoek3''
  22. Rotate(veelhoek3', (-(120°)), as) → veelhoek3''_1
  23. Rotate(J, (-(120°)), as) → L
  24. Rotate(J, 120°, as) → G
  25. Midpoint(L, J) → U
  26. OrthogonalLine(U, veelhoek3''_1) → mm
  27. Rotate(J, (-(60°)), mm) → I
  28. Rotate(I, 120°, as) → H
  29. Rotate(I, (-(120°)), as) → K
  30. Polygon(D, E, G) → driehoek1, s'_1, d_2, e_2
  31. Rotate(driehoek1, 120°, as) → driehoek1'
  32. Rotate(driehoek1, (-(120°)), as) → driehoek1'_1
  33. Polygon(W, Z, 6, xOyPlane) → veelhoek5, m_1, D_1, n_1, p_1, q_1, r_1, s_1, A_1, B_1, C_1
  34. Segment(C_1, M_1) → t_1
  35. Segment(M_1, D_1) → a_1
  36. Segment(M_1, N_1) → b_1
  37. Segment(N_1, O_1) → f_2
  38. Segment(O_1, E_1) → g_2
  39. Segment(E_1, W) → h_2
  40. Segment(E_1, Z) → i_2
  41. Segment(O_1, P_1) → j_2
  42. Segment(P_1, F_1) → k_2
  43. Segment(F_1, A_1) → l_2
  44. Segment(N_1, P_1) → m_2
  45. Segment(F_1, B_1) → n_2
  46. Point(ribben) → PP
  47. Point(vlakken3) → PPP
  48. Textfield(leeg1) → Invulvak1
  49. Textfield(leeg2) → Invulvak2

AI Drawing Prompt Reference

Draw a planar graph showing the intersection relationships between polygons and circles. Start by creating a circle and marking its intersections with the coordinate axes. Extend line segments from these points and rotate them to form a hexagon. Then, build multiple connected smaller polygons around the hexagon and add intersection points where the circles meet the polygons. Finally, rotate and connect these points to create a complex geometric structure, labeling key angles and segments.
The prompt above was compiled from the original drawing commands and is for reference only.