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折扣计算与几何演示

折扣计算与几何演示
几何画板及绘图内容加载中，请稍等……
2019-05-29 10:36
解析几何微积分几何作图
所属专题 Percentages and Applications RD-Percentages and Applications
①本范例通过动态交互演示折扣计算与几何图形结合的现象；②涉及核心数学概念包括代数、算术、百分比、体积、定积分、抛物线、期望值、金字塔；③构造要点使用了If、点、多边形、数列、文本框、线段、向量等GeoGebra命令与对象；④适合高中及以上数学学习者和教师用于教学演示与概念理解。

GeoGebra 命令及参数

  1. If(a, "d", ((If[p ∧ x(P) < 10, "-"] * abs(d)) * "")) → dtext
  2. If(c', "m", (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, "s", (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, "s", "x"], "m"]) → 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, m - n, abs(n - m)) → c
  40. Segment(If[x(P) ≤ 10, A + (10, 0), P], If[x(P) ≤ 10, B + (10, 1), x(P)]) → h_1
  41. Segment(A, B + (0, 1)) → i_1
  42. Segment(A - (0, 0.2), A - (0, 0.5)) → j_1
  43. Segment(P - (0, 0.2), P - (0, 0.5)) → k_1
  44. Vector(Midpoint[k_1], Midpoint[j_1]) → w_1
  45. Vector(Midpoint[j_1], Midpoint[k_1]) → c_1
  46. Segment(A0 + (0, 1.2), A0 + (0, 1.5)) → k'
  47. Segment(P0 + (0, 1.2), P0 + (0, 1.5)) → l'
  48. Vector(Midpoint[k'], Midpoint[l']) → e_1
  49. Vector(Midpoint[l'], Midpoint[k']) → l_1
  50. If(p, "Change", If[x(P) < 10, "Discount", If[x(P) > 10, "Profit", ""]]) → change