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Logarithmic Construction

Logarithmic Construction
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2020-05-05 21:42
FunctionGeometric ConstructionGraphing
This example demonstrates the graphical construction of logarithmic functions. Key math concepts include logarithmic functions, straight lines, circles, and tangents. The construction utilizes GeoGebra commands and objects such as Intersect, Line, Circle, Tangent, and OrthogonalLine as outlined in the summary. It is suitable for high school and above students to understand the geometric properties and construction techniques of logarithmic functions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Line(A, P0) → f
  3. Circle(A, 1) → c
  4. Tangent(P0, c) → g,
  5. Intersect(g, xAxis) → G01
  6. OrthogonalLine(G01, xAxis) → j
  7. Intersect(j, f) → P1
  8. Circle(A, P1) → d
  9. Line(P1, g) → h
  10. Intersect(h, xAxis) → G03
  11. OrthogonalLine(G03, xAxis) → i
  12. Intersect(i, f) → P2
  13. Circle(A, P2) → e
  14. Intersect(c, xAxis) → G0_1, G00
  15. Intersect(e, xAxis) → G4, G04
  16. Line(P2, h) → k
  17. Intersect(k, xAxis) → G05
  18. OrthogonalLine(G05, xAxis) → l
  19. Intersect(l, f) → P3
  20. Intersect(d, xAxis) → G2, G02
  21. OrthogonalLine(G02, xAxis) → m
  22. OrthogonalLine(G04, xAxis) → n
  23. Circle(A, P3) → p
  24. Intersect(p, xAxis) → G6, G06
  25. OrthogonalLine(G06, xAxis) → q
  26. Line(P3, k) → s
  27. Intersect(s, xAxis) → G07
  28. OrthogonalLine(G07, xAxis) → t
  29. Intersect(t, f) → P4
  30. Circle(A, P4) → u
  31. Intersect(u, xAxis) → G8, G08
  32. OrthogonalLine(G08, xAxis) → a
  33. Line(P4, s) → b
  34. Intersect(b, xAxis) → G09
  35. OrthogonalLine(G09, xAxis) → cc
  36. Intersect(cc, f) → P5
  37. Circle(A, P5) → v
  38. Intersect(v, xAxis) → G10_1, G10
  39. OrthogonalLine(G10, xAxis) → f_1
  40. OrthogonalLine(G00, xAxis) → g_1
  41. OrthogonalLine(A1, yAxis) → h_1
  42. OrthogonalLine(A2, yAxis) → i_1
  43. OrthogonalLine(A3, yAxis) → j_1
  44. OrthogonalLine(A4, yAxis) → k_1
  45. OrthogonalLine(A5, yAxis) → l_1
  46. OrthogonalLine(A6, yAxis) → m_1
  47. OrthogonalLine(A7, yAxis) → n_1
  48. OrthogonalLine(A8, yAxis) → p_1
  49. OrthogonalLine(A9, yAxis) → q_1
  50. OrthogonalLine(A10, yAxis) → r_1
  51. Intersect(h_1, j) → C
  52. Intersect(i_1, m) → D
  53. Intersect(j_1, i) → E
  54. Intersect(k_1, n) → F
  55. Intersect(l_1, l) → G
  56. Intersect(m_1, q) → H
  57. Intersect(n_1, t) → I
  58. Intersect(p_1, a) → J
  59. Intersect(q_1, cc) → K
  60. Intersect(r_1, f_1) → L

AI Drawing Prompt Reference

Draw a logarithmic function graph, including its intersections with the coordinate axes, tangents, and related circles. Start by drawing the intersection point A of the x-axis and y-axis, then draw a line f through point A. Next, draw a unit circle c centered at A and find a point P0 on it. Draw a tangent g to circle c at point P0, which intersects the x-axis at G01. Then, draw a vertical line j through G01, which intersects line f at P1. Continue this process to draw a series of circles and lines tangent to the x-axis until the entire graph is completed.
The prompt above was compiled from the original drawing commands and is for reference only.