Percentage Change Demonstration by Anthony OR 柯志明

Percentage Change Demonstration by Anthony OR 柯志明
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2019-05-28 08:54
This example demonstrates how to construct dynamic geometric visualizations of percentage change using GeoGebra. It involves core math concepts like percentage calculations, algebraic operations, and geometric transformations. Key GeoGebra commands used include If, Point, Polygon, Sequence, Textfield, Segment, and Vector. Suitable for high school mathematics education to understand the application of percentage change in geometry and algebra.

GeoGebra Commands & Parameters

  1. If(a, "d", ((If[p ∧ x(P) < 10, "−", If[p ∧ x(P) > 10, "+"]] * abs(d)) * "")) → dtext
  2. If(c', "n", (n * "")) → ntext
  3. Point(yAxis) → A
  4. Point(yAxis) → B
  5. If(x(P) ≤ 10, A + (10, 0), B + (10, 0)) → A0
  6. If(x(P) ≤ 10, P, (x(P), y(B))) → P0
  7. Polygon(P, Q, (0, y(Q)), (0, y(P))) → q1, p_1, q_1, g, h
  8. Polygon({P0, A0, A0 + (0, 1), P0 + (0, 1)}) → q2
  9. Polygon({B, B + (10, 0), B + (10, 1), B + (0, 1)}) → q3
  10. Polygon({B, B + (10, 0), B + (10, 1), B + (0, 1)}) → q4
  11. Sequence(Segment[B + (i, 0), B + (i, 1)], i, 1, 9, 1) → l1
  12. Sequence(Sequence[Segment[B + (j + i, 0), B + (j + i, 1)], j, 0, 9, 1], i, 0.1, 0.9, 0.1) → l2
  13. Sequence(Segment[A + (i, 0), A + (i, 1)], i, 1, 9, 1) → l3
  14. Sequence(Sequence[Segment[A + (j + i, 0), A + (j + i, 1)], j, 0, 9, 1], i, 0.1, 0.9, 0.1) → l4
  15. Textfield(n) → InputBox1
  16. Textfield(m) → InputBox2
  17. If(b, "m", (m * "")) → mtext
  18. Segment(If[b_1 ≟ 0, A, A0] + (0, 1.2), If[b_1 ≟ 0, A, A0] + (0, 1.5)) → i
  19. Segment(If[b_1 ≟ 0, P, P0] + (0, 1.2), If[b_1 ≟ 0, P, P0] + (0, 1.5)) → j
  20. Vector(Midpoint[i], Midpoint[j]) → u
  21. Vector(Midpoint[j], Midpoint[i]) → v
  22. Segment(A0 - (0, 0.2), A0 - (0, 0.5)) → k
  23. Segment(P0 - (0, 0.2), P0 - (0, 0.5)) → l
  24. Vector(Midpoint[k], Midpoint[l]) → w
  25. Vector(Midpoint[l], Midpoint[k]) → e
  26. Segment(B + (0, 1.2), B + (0, 1.5)) → f
  27. Segment(B + (10, 1.2), B + (10, 1.5)) → r
  28. Vector(Midpoint[f], Midpoint[r]) → s
  29. Vector(Midpoint[r], Midpoint[f]) → t
  30. Segment(B - (0, 0.2), B - (0, 0.5)) → f_1
  31. Segment(B + (10, -0.2), B + (10, -0.5)) → g_1
  32. Vector(Midpoint[f_1], Midpoint[g_1]) → u_1
  33. Vector(Midpoint[g_1], Midpoint[f_1]) → v_1
  34. If(a, "d", If[b, If[b_1 ≟ 0, "m", "c"], "n"]) → text12
  35. Sequence(Segment[A + (10 + i, 0), A + (10 + i, 1)], i, 0.1, x(P) - 10, 0.1) → l6
  36. Sequence(Segment[A + (10 + i, 0), A + (10 + i, 1)], i, 0, floor(x(P) - 10)) → l5
  37. Sequence(Segment[A0 + (i, 0), A0 + (i, 1)], i, 0, floor(x(P0) - 10)) → l7
  38. Sequence(Segment[A0 + (i, 0), A0 + (i, 1)], i, 0.1, x(P0) - 10, 0.1) → l8
  39. If(p, "Change", If[x(P) < 10, "Decrease", If[x(P) > 10, "Increase", ""]]) → change
  40. If(p, m - n, abs(n - m)) → c
  41. Segment(If[x(P) ≤ 10, A + (10, 0), P], If[x(P) ≤ 10, B + (10, 1), x(P)]) → h_1
  42. Segment(A, B + (0, 1)) → i_1
  43. Segment(A - (0, 0.2), A - (0, 0.5)) → j_1
  44. Segment(P - (0, 0.2), P - (0, 0.5)) → k_1
  45. Vector(Midpoint[k_1], Midpoint[j_1]) → w_1
  46. Vector(Midpoint[j_1], Midpoint[k_1]) → c_1
  47. Segment(A0 + (0, 1.2), A0 + (0, 1.5)) → k'
  48. Segment(P0 + (0, 1.2), P0 + (0, 1.5)) → l'
  49. Vector(Midpoint[k'], Midpoint[l']) → e_1
  50. Vector(Midpoint[l'], Midpoint[k']) → l_1

AI Drawing Prompt Reference

Create a dynamic geometric visualization showing percentage change, featuring an axis and two points. Display percentage change direction and values based on the points' positions, using colored rectangles to represent change areas, and label the percentage values and change direction. Construct the figure by first establishing the axis and points, then drawing rectangles and labels according to the points' positions, and finally connecting relevant points to form the complete graphic.
The prompt above was compiled from the original drawing commands and is for reference only.