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利息计算与几何变换

利息计算与几何变换
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2019-04-11 03:30
函数解析几何微积分
①本范例演示了利息计算与几何变换的结合，通过动态演示等腰三角形的面积变化；②涉及核心数学概念包括利息计算、函数、坐标几何、几何变换、等腰三角形和面积计算；③构造中使用了Polygon（多边形）、Integral（积分）、Segment（线段）、Point（点）等GeoGebra命令和对象；④适合高中数学教学，用于理解函数与几何的关联及动态变化过程。

GeoGebra 命令及参数

  1. NumToMoney(E2) → G2
  2. NumToMoney(C3) → F3
  3. Polygon({(left, top), (left, bottom), (right, bottom), (right, top)}) → viewbox
  4. LaTeX((((("\text{\textbf{Question: }" * MainInstruc) * "\\\textbf{Instructions: } ") * SpecInstruc) * "}")) → allInstruc
  5. TableText({{"\text{\(1.5%\)}", "\text{\(3%\)}", "\text{\(4.5%\)}", "\text{\(6%\)}"}}) → txtIntRate
  6. Segment((0, 0), (25, 0)) → mySlider
  7. Point(mySlider) → sliderPt
  8. Integral(f, 0, x(sliderPt)) → compoundArea
  9. Integral(g, 0, x(sliderPt)) → simpleArea
  10. Polygon({(0, 0), (0, principal), (x(sliderPt), principal), (x(sliderPt), 0)}) → principalArea
  11. VerticalText("\text{Accumulated value in \$}") → yLabel
  12. Polygon({coverAnchor1, coverAnchor2, coverAnchor3, coverAnchor4}) → cover
  13. TableText({{"\cellcolor{#1565c0}{\phantom{hi}}", "\text{Compound Interest}"}, {"\cellcolor{#9c27b0}{\phantom{hi}}", "Simple Interest"}, {"\cellcolor{#1b5e20}{\phantom{hi}}", "No Interest"}}) → legend
  14. NumToMoney(C2) → F2
  15. NumToMoney(C4) → F4
  16. NumToMoney(C5) → F5
  17. NumToMoney(C6) → F6
  18. NumToMoney(C7) → F7
  19. NumToMoney(C8) → F8
  20. NumToMoney(C9) → F9
  21. NumToMoney(C10) → F10
  22. NumToMoney(C11) → F11
  23. NumToMoney(C12) → F12
  24. NumToMoney(C13) → F13
  25. NumToMoney(C14) → F14
  26. NumToMoney(C15) → F15
  27. NumToMoney(C16) → F16
  28. NumToMoney(C17) → F17
  29. NumToMoney(C18) → F18
  30. NumToMoney(C19) → F19
  31. NumToMoney(C20) → F20
  32. NumToMoney(C21) → F21
  33. NumToMoney(C22) → F22
  34. NumToMoney(C23) → F23
  35. NumToMoney(C24) → F24
  36. NumToMoney(C25) → F25
  37. NumToMoney(C26) → F26
  38. NumToMoney(C27) → F27
  39. NumToMoney(E3) → G3
  40. NumToMoney(E4) → G4
  41. NumToMoney(E5) → G5
  42. NumToMoney(E6) → G6
  43. NumToMoney(E7) → G7
  44. NumToMoney(E8) → G8
  45. NumToMoney(E9) → G9
  46. NumToMoney(E10) → G10
  47. NumToMoney(E11) → G11
  48. NumToMoney(E12) → G12
  49. NumToMoney(E13) → G13
  50. NumToMoney(E14) → G14
  51. NumToMoney(E15) → G15
  52. NumToMoney(E16) → G16
  53. NumToMoney(E17) → G17
  54. NumToMoney(E18) → G18
  55. NumToMoney(E19) → G19
  56. NumToMoney(E20) → G20
  57. NumToMoney(E21) → G21
  58. NumToMoney(E22) → G22
  59. NumToMoney(E23) → G23
  60. NumToMoney(E24) → G24
  61. NumToMoney(E25) → G25
  62. NumToMoney(E26) → G26
  63. NumToMoney(E27) → G27
  64. TableText({col1, col2}, "v|_10011111") → tblAccumulated
  65. NumToMoney(principal + ((A3 * principal) * currRate)) → I3
  66. NumToMoney(principal + ((A4 * principal) * currRate)) → I4
  67. NumToMoney(principal + ((A5 * principal) * currRate)) → I5
  68. NumToMoney(principal + ((A6 * principal) * currRate)) → I6
  69. NumToMoney(principal + ((A7 * principal) * currRate)) → I7
  70. NumToMoney(principal + ((A8 * principal) * currRate)) → I8
  71. NumToMoney(principal + ((A9 * principal) * currRate)) → I9
  72. NumToMoney(principal + ((A10 * principal) * currRate)) → I10
  73. NumToMoney(principal + ((A11 * principal) * currRate)) → I11
  74. NumToMoney(principal + ((A12 * principal) * currRate)) → I12
  75. NumToMoney(principal + ((A13 * principal) * currRate)) → I13
  76. NumToMoney(principal + ((A14 * principal) * currRate)) → I14
  77. NumToMoney(principal + ((A15 * principal) * currRate)) → I15
  78. NumToMoney(principal + ((A16 * principal) * currRate)) → I16
  79. NumToMoney(principal + ((A17 * principal) * currRate)) → I17
  80. NumToMoney(principal + ((A18 * principal) * currRate)) → I18
  81. NumToMoney(principal + ((A19 * principal) * currRate)) → I19
  82. NumToMoney(principal + ((A20 * principal) * currRate)) → I20
  83. NumToMoney(principal + ((A21 * principal) * currRate)) → I21
  84. NumToMoney(principal + ((A22 * principal) * currRate)) → I22
  85. NumToMoney(principal + ((A23 * principal) * currRate)) → I23
  86. NumToMoney(principal + ((A24 * principal) * currRate)) → I24
  87. NumToMoney(principal + ((A25 * principal) * currRate)) → I25
  88. NumToMoney(principal + ((A26 * principal) * currRate)) → I26
  89. NumToMoney(principal + ((A27 * principal) * currRate)) → I27
  90. Sequence(D3, i, 1, If[pageNum ≟ 1, 12, 13]) → simpleInterestCalc
  91. TableText({A1:A14, D1:D14, Join[{{E1}, G2:G14}], Join[{{H2, ""}, simpleInterestCalc}], Join[{{E1, G2}, I3:I14}]}, "vc|_") → dataPg1
  92. TableText({Join[{{A1}, A15:A27}], Join[{{D1}, D15:D27}], Join[{{E1}, G15:G27}], Join[{{H2}, simpleInterestCalc}], Join[{{E1}, I15:I29}]}, "vc|_") → dataPg2

AI 绘图提示语参考

画一个展示利息计算和几何变换的图形，包含一个动态变化面积的不等边三角形，显示复利和简单利息的计算结果，用不同颜色区分，并标注金额和利率，从底边长度滑块开始，计算并展示不同利率下的面积变化，最终形成包含多个图形和文本的完整模型。
以上提示语为根据原始绘图命令整理而来，仅供参考。