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Plotting Points and Tracing Graphs

Plotting Points and Tracing Graphs
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2014-09-06 04:59
VectorCoordinate GeometryCalculusDerivativeGeometric Construction
In collections Modeling Volume as a function of height
This example demonstrates how to plot a function by tracing the slopes of its tangents. It involves core mathematical concepts such as derivatives, vectors, geometric transformations, and coordinate geometry. Key GeoGebra commands and objects used in the construction include Circle, Vector, Translate, Intersect, Rotate, Polygon, Segment, OrthogonalLine, Point, Tangent, and Slope. It is suitable for high school and above students studying calculus, function graphing, and geometric constructions.

GeoGebra Commands & Parameters

  1. Circle(Origin, len - (2 * h)) → c
  2. Vector((width - (2 * h), 0)) → u
  3. Translate(A, u) → A'
  4. Intersect(c, xAxis) → B, C
  5. Rotate(C, α) → C'
  6. Vector(C') → v
  7. Translate(A, v) → A'_1
  8. Translate(A', v) → A''
  9. Polygon(A, A'_1, A'', A') → poly1, a, a'_1, a'', a'
  10. Vector((0, h)) → w
  11. Translate(A, w) → A'_2
  12. Translate(A', w) → A''_1
  13. Translate(A'_1, w) → D
  14. Translate(A'', w) → A'''
  15. Segment(A'_2, A) → b
  16. Segment(A''_1, A') → d
  17. Segment(D, A'_1) → e
  18. Segment(A''', A'') → f
  19. Polygon(A'_2, A''_1, A', A) → poly2, a'_2, a''_1, a'_3, a_1
  20. Polygon(D, A''', A'', A'_1) → poly3, d_1, a''', a''_2, a'_4
  21. Polygon(A''_1, A''', A'', A') → poly4, a''_3, a'''_1, a''_4, a'_5
  22. Polygon(D, A'_2, A, A'_1) → poly5, d_2, a'_6, a_2, a'_7
  23. Segment(W_1, A_2) → c_7
  24. Segment(A_2, Z_1) → d_7
  25. Segment(Z_1, V_1) → e_7
  26. Segment(V_1, W_1) → f_7
  27. Segment(Paper, U_1) → g_7
  28. Segment(U_1, S_1) → h_7
  29. Segment(S_1, T_1) → i_7
  30. Segment(T_1, Paper) → j_7
  31. OrthogonalLine(Z_1, g_7) → m_7
  32. OrthogonalLine(Z_1, h_7) → n_7
  33. OrthogonalLine(A_2, h_7) → a_8
  34. OrthogonalLine(W_1, i_7) → b_8
  35. Intersect(j_7, a_8) → B_2
  36. Intersect(i_7, b_8) → C_2
  37. Intersect(m_7, i_7) → D_2
  38. Intersect(h_7, a_8) → E_2
  39. Intersect(n_7, h_7) → F_2
  40. Intersect(m_7, g_7) → G_2
  41. Intersect(g_7, b_8) → H_2
  42. Intersect(n_7, j_7) → I_2
  43. Polygon(B_2, W_1, 4) → poly26, c_8, d_8, e_8, f_8, J_2, K_2
  44. Polygon(Paper, H_2, 4) → poly27, g_8, h_8, i_8, j_8, L_2, M_2
  45. Polygon(G_2, U_1, 4) → poly28, k_8, l_8, m_8, n_8, N_2, O_2
  46. Polygon(A_2, E_2, 4) → poly29, p_8, q_8, r_8, s_8, P_2, Q_2
  47. Polygon(V_1, Z_1, A_2, W_1) → poly31, v_1, z_1, a_9, w_1
  48. Polygon(B_2, W_1, V_1, I_2) → poly9, b_2, w_2, v_2, i_2
  49. Polygon(W_1, A_2, D_2, C_2) → poly10, w_3, a_3, d_3, c_2
  50. Point(w_3) → N
  51. Polygon(N, Z_1, F_2, E_2) → poly11, n_1, z_2, f_2, e_2
  52. Point(n_1) → O
  53. Point(w_2) → P
  54. Polygon(H_2, G_2, O, P) → poly12, h_3, g_3, o, p_1
  55. OrthogonalLine(E, xAxis) → i
  56. Tangent(E, g) → j
  57. Slope(j) → m
  58. Circle(E, 3) → k
  59. Intersect(k, i) → F, G
  60. Intersect(i, xAxis) → H
  61. Segment(H, ET) → q

AI Drawing Prompt Reference

Draw a function graph by tracing the slopes of its tangents. Start by creating a circle, then make a vector and translate points, intersect with the x-axis to get two points, rotate one point, create a vector, and translate points to get new points, connecting them to form polygons. Next, create new vectors and points, translate and connect to form more polygons. Finally, create regular polygons and orthogonal lines, connecting intersection points to form complex geometric shapes.
The prompt above was compiled from the original drawing commands and is for reference only.