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2D Vectors and Circle Construction

2D Vectors and Circle Construction
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2019-10-08 04:23
CircleVectorGeometric Construction
This example demonstrates the geometric construction using 2D vectors and circles, involving core math concepts like vectors, circles, symmetry, and similar triangles. Construction highlights include using commands like Vector, OrthogonalVector, Line, OrthogonalLine, Intersect, Midpoint, Mirror, LineBisector, Polygon, CurveCartesian, Segment. Suitable for high school and above learning geometric constructions and vectors.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. OrthogonalVector(u) → v
  3. Line(A, B) → m
  4. Line(E, m) → f
  5. OrthogonalLine(B, f) → g
  6. Intersect(g, f) → C
  7. Midpoint(E, B) → D
  8. Line(F, m) → h
  9. OrthogonalLine(G, m) → i
  10. Mirror(h, D) → h'
  11. Mirror(i, D) → i'
  12. Intersect(i, h) → H
  13. Intersect(i, h') → I
  14. Line(D, h') → j
  15. Line(Q, j) → k
  16. Mirror(k, j) → k'
  17. LineBisector(K, L) → l
  18. LineBisector(O, N) → n
  19. Intersect(l, k') → R
  20. Intersect(n, k) → S
  21. Polygon(H, J, U, V) → q1, h_1, j_1, u_1, v_1
  22. Polygon(E, C, B, A) → q2, e, c, b, a
  23. Polygon(K, R, L) → t1, l_1, k_1, r
  24. Polygon(N, O, S) → t2, s, n_1, o_1
  25. Vector(H, J) → w
  26. Intersect(j, h_1) → C_1
  27. Intersect(q1, q2) → D_1
  28. Line(E_1, u_1) → p
  29. Mirror(B_1, C_1) → F_1
  30. Mirror(A_1, C_1) → G_1
  31. Mirror(Z, C_1) → Z'
  32. Mirror(W, C_1) → W'
  33. Intersect(p, h) → H_1
  34. Intersect(p, j) → K_1
  35. Mirror(J_1, K_1) → L_1
  36. Mirror(I_1, K_1) → M_1
  37. Polygon(Z, I_1, W) → t3, w_1, z_1, i_1
  38. Polygon(B_1, J_1, A_1) → t4, a_1, b_1, q
  39. Polygon(G_1, L_1, F_1) → t5, f_1, g_1, t
  40. Polygon(W', M_1, Z') → t6, z', w', m_1
  41. Intersect(j, u_1) → P_1
  42. Mirror(O_1, P_1) → Q_1
  43. Mirror(N_1, P_1) → R_1
  44. CurveCartesian(((1 - t)^(4) * M) + (((4 * (1 - t)^(3)) * t) * S_1) + (((6 * (1 - t)^(2)) * t^(2)) * T_1) + (((4 * (1 - t)) * t^(3)) * U_1) + (t^(4) * T), t, 0, 1) → d
  45. CurveCartesian(((1 - t)^(4) * T) + (((4 * (1 - t)^(3)) * t) * U_1) + (((6 * (1 - t)^(2)) * t^(2)) * V_1) + (((4 * (1 - t)) * t^(3)) * W_1) + (t^(4) * P), t, 0, 1) → c_1
  46. CurveCartesian(((1 - t)^(4) * R_1) + (((4 * (1 - t)^(3)) * t) * Z_1) + (((6 * (1 - t)^(2)) * t^(2)) * A_2) + (((4 * (1 - t)) * t^(3)) * B_2) + (t^(4) * Q_1), t, 0, 1) → d_1
  47. CurveCartesian(((1 - t)^(4) * O_1) + (((4 * (1 - t)^(3)) * t) * C_2) + (((6 * (1 - t)^(2)) * t^(2)) * D_2) + (((4 * (1 - t)) * t^(3)) * E_2) + (t^(4) * N_1), t, 0, 1) → e_1
  48. Polygon(U, M, T, P, V) → poly1, u_2, m_2, t_1, p_1, v_2
  49. Segment(L, M) → q_1
  50. Segment(O, P) → r_1

AI Drawing Prompt Reference

Draw a geometric construction involving 2D vectors and circles, highlighting core concepts like vectors, circles, symmetry, and similar triangles. Start by creating two vectors and their orthogonal counterparts, then draw lines and circles based on these vectors. Use intersections, midpoints, reflections, and angle bisectors to construct multiple polygons and curves, resulting in a complex figure that showcases symmetry and geometric properties.
The prompt above was compiled from the original drawing commands and is for reference only.