有理数与无理数判别互动练习（含开放题）

GeoGebra 命令及参数

1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {9, 7, 2, 7, 9, 6, 10, 3, 6, 5}
2. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
3. Textfield(input) → inputBox
4. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, 0, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, 0, RasterMaxY / RasterStepXY]}) → RasterStrecken
5. Join({Sequence[Text[UnicodeToLetter[65 + k], Midpoint[Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY)), Corner[4] + (RasterPixMat * (((k + 1) * RasterStepXY), RasterMaxY))], false, true, 0, -1], k, 0, RasterMaxX / RasterStepXY - 1], Sequence[Text[("" * k), Midpoint[Corner[4] + (RasterPixMat * (RasterMaxX, ((k - 1) * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], false, true, 1, 0], k, 1, RasterMaxY / RasterStepXY]}) → RasterBeschriftung
6. Sequence(Sequence[Corner[4] + (RasterPixMat * ((k * RasterStepXY), (m * RasterStepXY))), k, 0, RasterMaxX / RasterStepXY], m, 0, RasterMaxY / RasterStepXY) → RasterPunkte, {{(-0.3899999999999999, 10.379999999999999), (0.61250626566416, 10.379999999999999), (1.61501253132832, 10.379999999999999), (2.6175187969924805, 10.379999999999999), (3.62002506265664, 10.379999999999999), (4.6225313283208, 10.379999999999999), (5.625037593984961, 10.379999999999999), (6.62754385964912, 10.379999999999999), (7.6300501253132795, 10.379999999999999), (8.63255639097744, 10.379999999999999), (9.6350626566416, 10.379999999999999), (10.637568922305759, 10.379999999999999), (11.64007518796992, 10.379999999999999), (12.64258145363408, 10.379999999999999), (13.645087719298239, 10.379999999999999), (14.6475939849624, 10.379999999999999), (15.650100250626558, 10.379999999999999)}, {(-0.3899999999999999, 9.37665551839465), (0.61250626566416, 9.37665551839465), (1.61501253132832, 9.37665551839465), (2.6175187969924805, 9.37665551839465), (3.62002506265664, 9.37665551839465), (4.6225313283208, 9.37665551839465), (5.625037593984961, 9.37665551839465), (6.62754385964912, 9.37665551839465), (7.6300501253132795, 9.37665551839465), (8.63255639097744, 9.37665551839465), (9.6350626566416, 9.37665551839465), (10.637568922305759, 9.37665551839465), (11.64007518796992, 9.37665551839465), (12.64258145363408, 9.37665551839465), (13.645087719298239, 9.37665551839465), (14.6475939849624, 9.37665551839465), (15.650100250626558, 9.37665551839465)}, {(-0.3899999999999999, 8.373311036789298), (0.61250626566416, 8.373311036789298), (1.61501253132832, 8.373311036789298), (2.6175187969924805, 8.373311036789298), (3.62002506265664, 8.373311036789298), (4.6225313283208, 8.373311036789298), (5.625037593984961, 8.373311036789298), (6.62754385964912, 8.373311036789298), (7.6300501253132795, 8.373311036789298), (8.63255639097744, 8.373311036789298), (9.6350626566416, 8.373311036789298), (10.637568922305759, 8.373311036789298), (11.64007518796992, 8.373311036789298), (12.64258145363408, 8.373311036789298), (13.645087719298239, 8.373311036789298), (14.6475939849624, 8.373311036789298), (15.650100250626558, 8.373311036789298)}, {(-0.3899999999999999, 7.3699665551839475), (0.61250626566416, 7.3699665551839475), (1.61501253132832, 7.3699665551839475), (2.6175187969924805, 7.3699665551839475), (3.62002506265664, 7.3699665551839475), (4.6225313283208, 7.3699665551839475), (5.625037593984961, 7.3699665551839475), (6.62754385964912, 7.3699665551839475), (7.6300501253132795, 7.3699665551839475), (8.63255639097744, 7.3699665551839475), (9.6350626566416, 7.3699665551839475), (10.637568922305759, 7.3699665551839475), (11.64007518796992, 7.3699665551839475), (12.64258145363408, 7.3699665551839475), (13.645087719298239, 7.3699665551839475), (14.6475939849624, 7.3699665551839475), (15.650100250626558, 7.3699665551839475)}, {(-0.3899999999999999, 6.366622073578597), (0.61250626566416, 6.366622073578597), (1.61501253132832, 6.366622073578597), (2.6175187969924805, 6.366622073578597), (3.62002506265664, 6.366622073578597), (4.6225313283208, 6.366622073578597), (5.625037593984961, 6.366622073578597), (6.62754385964912, 6.366622073578597), (7.6300501253132795, 6.366622073578597), (8.63255639097744, 6.366622073578597), (9.6350626566416, 6.366622073578597), (10.637568922305759, 6.366622073578597), (11.64007518796992, 6.366622073578597), (12.64258145363408, 6.366622073578597), (13.645087719298239, 6.366622073578597), (14.6475939849624, 6.366622073578597), (15.650100250626558, 6.366622073578597)}, {(-0.3899999999999999, 5.3632775919732465), (0.61250626566416, 5.3632775919732465), (1.61501253132832, 5.3632775919732465), (2.6175187969924805, 5.3632775919732465), (3.62002506265664, 5.3632775919732465), (4.6225313283208, 5.3632775919732465), (5.625037593984961, 5.3632775919732465), (6.62754385964912, 5.3632775919732465), (7.6300501253132795, 5.3632775919732465), (8.63255639097744, 5.3632775919732465), (9.6350626566416, 5.3632775919732465), (10.637568922305759, 5.3632775919732465), (11.64007518796992, 5.3632775919732465), (12.64258145363408, 5.3632775919732465), (13.645087719298239, 5.3632775919732465), (14.6475939849624, 5.3632775919732465), (15.650100250626558, 5.3632775919732465)}, {(-0.3899999999999999, 4.359933110367896), (0.61250626566416, 4.359933110367896), (1.61501253132832, 4.359933110367896), (2.6175187969924805, 4.359933110367896), (3.62002506265664, 4.359933110367896), (4.6225313283208, 4.359933110367896), (5.625037593984961, 4.359933110367896), (6.62754385964912, 4.359933110367896), (7.6300501253132795, 4.359933110367896), (8.63255639097744, 4.359933110367896), (9.6350626566416, 4.359933110367896), (10.637568922305759, 4.359933110367896), (11.64007518796992, 4.359933110367896), (12.64258145363408, 4.359933110367896), (13.645087719298239, 4.359933110367896), (14.6475939849624, 4.359933110367896), (15.650100250626558, 4.359933110367896)}, {(-0.3899999999999999, 3.3565886287625455), (0.61250626566416, 3.3565886287625455), (1.61501253132832, 3.3565886287625455), (2.6175187969924805, 3.3565886287625455), (3.62002506265664, 3.3565886287625455), (4.6225313283208, 3.3565886287625455), (5.625037593984961, 3.3565886287625455), (6.62754385964912, 3.3565886287625455), (7.6300501253132795, 3.3565886287625455), (8.63255639097744, 3.3565886287625455), (9.6350626566416, 3.3565886287625455), (10.637568922305759, 3.3565886287625455), (11.64007518796992, 3.3565886287625455), (12.64258145363408, 3.3565886287625455), (13.645087719298239, 3.3565886287625455), (14.6475939849624, 3.3565886287625455), (15.650100250626558, 3.3565886287625455)}, {(-0.3899999999999999, 2.353244147157195), (0.61250626566416, 2.353244147157195), (1.61501253132832, 2.353244147157195), (2.6175187969924805, 2.353244147157195), (3.62002506265664, 2.353244147157195), (4.6225313283208, 2.353244147157195), (5.625037593984961, 2.353244147157195), (6.62754385964912, 2.353244147157195), (7.6300501253132795, 2.353244147157195), (8.63255639097744, 2.353244147157195), (9.6350626566416, 2.353244147157195), (10.637568922305759, 2.353244147157195), (11.64007518796992, 2.353244147157195), (12.64258145363408, 2.353244147157195), (13.645087719298239, 2.353244147157195), (14.6475939849624, 2.353244147157195), (15.650100250626558, 2.353244147157195)}, {(-0.3899999999999999, 1.3498996655518454), (0.61250626566416, 1.3498996655518454), (1.61501253132832, 1.3498996655518454), (2.6175187969924805, 1.3498996655518454), (3.62002506265664, 1.3498996655518454), (4.6225313283208, 1.3498996655518454), (5.625037593984961, 1.3498996655518454), (6.62754385964912, 1.3498996655518454), (7.6300501253132795, 1.3498996655518454), (8.63255639097744, 1.3498996655518454), (9.6350626566416, 1.3498996655518454), (10.637568922305759, 1.3498996655518454), (11.64007518796992, 1.3498996655518454), (12.64258145363408, 1.3498996655518454), (13.645087719298239, 1.3498996655518454), (14.6475939849624, 1.3498996655518454), (15.650100250626558, 1.3498996655518454)}, {(-0.3899999999999999, 0.346555183946494), (0.61250626566416, 0.346555183946494), (1.61501253132832, 0.346555183946494), (2.6175187969924805, 0.346555183946494), (3.62002506265664, 0.346555183946494), (4.6225313283208, 0.346555183946494), (5.625037593984961, 0.346555183946494), (6.62754385964912, 0.346555183946494), (7.6300501253132795, 0.346555183946494), (8.63255639097744, 0.346555183946494), (9.6350626566416, 0.346555183946494), (10.637568922305759, 0.346555183946494), (11.64007518796992, 0.346555183946494), (12.64258145363408, 0.346555183946494), (13.645087719298239, 0.346555183946494), (14.6475939849624, 0.346555183946494), (15.650100250626558, 0.346555183946494)}, {(-0.3899999999999999, -0.6567892976588574), (0.61250626566416, -0.6567892976588574), (1.61501253132832, -0.6567892976588574), (2.6175187969924805, -0.6567892976588574), (3.62002506265664, -0.6567892976588574), (4.6225313283208, -0.6567892976588574), (5.625037593984961, -0.6567892976588574), (6.62754385964912, -0.6567892976588574), (7.6300501253132795, -0.6567892976588574), (8.63255639097744, -0.6567892976588574), (9.6350626566416, -0.6567892976588574), (10.637568922305759, -0.6567892976588574), (11.64007518796992, -0.6567892976588574), (12.64258145363408, -0.6567892976588574), (13.645087719298239, -0.6567892976588574), (14.6475939849624, -0.6567892976588574), (15.650100250626558, -0.6567892976588574)}, {(-0.3899999999999999, -1.660133779264207), (0.61250626566416, -1.660133779264207), (1.61501253132832, -1.660133779264207), (2.6175187969924805, -1.660133779264207), (3.62002506265664, -1.660133779264207), (4.6225313283208, -1.660133779264207), (5.625037593984961, -1.660133779264207), (6.62754385964912, -1.660133779264207), (7.6300501253132795, -1.660133779264207), (8.63255639097744, -1.660133779264207), (9.6350626566416, -1.660133779264207), (10.637568922305759, -1.660133779264207), (11.64007518796992, -1.660133779264207), (12.64258145363408, -1.660133779264207), (13.645087719298239, -1.660133779264207), (14.6475939849624, -1.660133779264207), (15.650100250626558, -1.660133779264207)}}
7. SelectedIndex(dropdown071) → index071
8. Textfield(input051) → InputBox051
9. Textfield(input052) → InputBox052
10. Textfield(input053) → InputBox053
11. Textfield(input054) → InputBox054
12. Textfield(input071) → InputBox071
13. Textfield(input072) → InputBox072
14. If(step ≟ 1, (0.5, 5.75), step ≥ 11, (0.5, 6.75), (0.5, 5.75)) → PosImgToni1
15. SelectedIndex(dropdown021) → index021
16. SelectedIndex(dropdown022) → index022
17. SelectedIndex(dropdown041) → index041
18. SelectedIndex(dropdown081) → index081
19. SelectedIndex(dropdown101) → index101
20. Invert(RasterPixMat) → invPixMat
21. PolyLine(PosSB, Corner[txt022, 4] + (-0.1, -0.5), Corner[txt022, 4] + (-0.1, 0.1), Corner[txt022, 3] + (0.1, 0.1), Corner[txt022, 2] + (0.1, -0.1), Corner[txt022, 1] + (-0.1, -0.1), Corner[txt022, 1] + (-0.1, 0.75), PosSB) → sb02
22. Ellipse(MP031 + ((-sqrt(ellA031^(2) - ellB031^(2))), 0), MP031 + (sqrt(ellA031^(2) - ellB031^(2)), 0), ellA031) → ell031
23. Text("\textsf{ℕ}", MP031, false, true, 0, 0) → Cap0311
24. Ellipse(MP032 + ((-sqrt(ellA031^(2) - ellB031^(2))), 0), MP032 + (sqrt(ellA031^(2) - ellB031^(2)), 0), ellA031) → ell032
25. Ellipse(MP033 + ((-sqrt(ellA031^(2) - ellB031^(2))), 0), MP033 + (sqrt(ellA031^(2) - ellB031^(2)), 0), ellA031) → ell033
26. Text("\textsf{Die ganzen Zahlen ℤ}", MP032 + (0, ellB031 + 0.25), false, true, 0, 1) → Cap0322
27. Text("\textsf{ℤ}", MP032, false, true, 0, 0) → Cap0321
28. Text("\textsf{DZ}", MP033, false, true, 0, 0) → Cap0331
29. Text("\textsf{1}", MP031 + (0.65, 0.7), false, true, 0, 0) → Cap0313
30. Text("\textsf{0}", MP031 + (1.1, -0.3), false, true, 0, 0) → Cap0314
31. Text("\textsf{4}", MP031 + (-0.75, -0.55), false, true, 0, 0) → Cap0315
32. Text("\textsf{38}", MP031 + (-1, 0.5), false, true, 0, 0) → Cap0316
33. Text("\textsf{17}", MP032 + (-1, 0.2), false, true, 0, 0) → Cap0323
34. Text("\textsf{\(-\)3}", MP032 + (0.15, 0.8), false, true, 0, 0) → Cap0324
35. Text("\textsf{0}", MP032 + (1.1, 0.2), false, true, 0, 0) → Cap0325
36. Text("\textsf{\(-\)100}", MP032 + (-0.25, -0.75), false, true, 0, 0) → Cap0326
37. Text("\textsf{0,\dot{3}}", MP033 + (-0.75, 0.65), false, true, 0, 0) → Cap0333
38. Text("\textsf{\(-\)1,8}", MP033 + (0.85, 0.5), false, true, 0, 0) → Cap0334
39. Text("\textsf{0,12345...}", MP033 + (-0.1, -0.75), false, true, 0, 0) → Cap0335
40. Circle(MP041, radius04) → circle041
41. Circle(MP042, radius04) → circle042
42. Circle(MP043, radius04) → circle043
43. Text((((("\textsf{\textcolor{" * If[step ∈ {5}, "#db6114", "#000000"]) * "}{") * If[step ∈ {5}, "\bold{", "{"]) * "ℕ}}}"), MP041 + (0, 0.05), false, true, 0, 0) → Cap041
44. Text((((("\textsf{\textcolor{" * If[step ∈ {5}, "#db6114", "#000000"]) * "}{") * If[step ∈ {5}, "\bold{", "{"]) * "ℤ}}}"), MP042 + (0, 0.05), false, true, 0, 0) → Cap042
45. Text((((("\textsf{\textcolor{" * If[step ∈ {6, 7, 8, 9, 10}, "#db6114", "#000000"]) * "}{") * If[step ∈ {6, 7, 8, 9, 10}, "{", "{"]) * "DZ}}}"), MP043 + (0, 0.05), false, true, 0, 0) → Cap043
46. Translate(imgLupe2, Vector[MP041, MP042]) → imgLupe3
47. Translate(imgLupe3, Vector[MP041, MP042]) → imgLupe4
48. PolyLine(PosSB, Corner[txt061, 4] + (0.25, 0.1), Corner[txt061, 3] + (0.1, 0.1), Corner[txt061, 2] + (0.1, -0.1), Corner[txt061, 1] + (-0.1, -0.1), Corner[txt061, 4] + (-0.1, -0.25), PosSB) → sb06
49. Text("\textsf{ \:Endliche\\Dezimalzahlen}", Pos061, false, true, 0, -1) → Cap061
50. Text("\textsf{ \:\:Unendliche,\\ \:\:periodische\\Dezimalzahlen}", Pos062, false, true, 0, -1) → Cap062
51. Text("\textsf{ \:\:\:\:Unendliche,\\\vphantom{g}nicht periodische\\\:\:\:Dezimalzahlen}", Pos063, false, true, 0, -1) → Cap063
52. Segment(Corner[txt062, 1], Pos061) → seg061
53. Segment(Midpoint[Corner[txt062, 1], Corner[txt062, 2]], Pos062) → seg062
54. Segment(Corner[txt062, 2], Pos063) → seg063
55. Sequence(PosTxt091 + (If[k ≟ 0, 0, k ≟ 1, 0.25, k < 11, 0.15 + ((k - 1) * 0.4), 0.05 + 3.55 + ((k - 10) * 0.77)], 0), k, 0, Length[TextList09] - 1) → PosList091
56. Join({{"#9C4381", "#DB6114", "#1565C0"}, {"#9C4381", "#DB6114", "#1565C0"}, {"#9C4381", "#DB6114", "#1565C0"}, {"#9C4381", "#DB6114", "#1565C0"}, {"#9C4381", "#DB6114", "#1565C0"}, {"#9C4381", "#DB6114", "#1565C0"}, {"#9C4381", "#DB6114", "#1565C0"}}) → Colors09
57. PolyLine(PosSB, Corner[txt111, 1] + (0.25, -0.1), Corner[txt111, 2] + (0.1, -0.1), Corner[txt111, 3] + (0.1, 0.1), Corner[txt111, 4] + (-0.1, 0.1), Corner[txt111, 1] + (-0.1, 0.25), PosSB) → sb11
58. Ellipse(MP111 + ((-sqrt(ellA111^(2) - ellB111^(2))), 0), MP111 + (sqrt(ellA111^(2) - ellB111^(2)), 0), ellA111) → ell111
59. Ellipse(MP112 + ((-sqrt(ellA112^(2) - ellB112^(2))), 0), MP112 + (sqrt(ellA112^(2) - ellB112^(2)), 0), ellA112) → ell112
60. Ellipse(MP113 + ((-sqrt(ellA113^(2) - ellB113^(2))), 0), MP113 + (sqrt(ellA113^(2) - ellB113^(2)), 0), ellA113) → ell113
61. Ellipse(MP114 + ((-sqrt(ellA114^(2) - ellB114^(2))), 0), MP114 + (sqrt(ellA114^(2) - ellB114^(2)), 0), ellA114) → ell114
62. Midpoint(Corner[Cap111, 1], Corner[Cap111, 3]) → Point111
63. Midpoint(Corner[Cap112, 1], Corner[Cap112, 3]) → Point112
64. Midpoint(Corner[Cap113, 1], Corner[Cap113, 3]) → Point113
65. Midpoint(Corner[Cap114, 1], Corner[Cap114, 3]) → Point114
66. Midpoint(Corner[Cap115, 1], Corner[Cap115, 3]) → Point115
67. Midpoint(Corner[Cap116, 1], Corner[Cap116, 3]) → Point116
68. SelectedIndex(dropdown051) → index051
69. SelectedIndex(dropdown072) → index072
70. SelectedIndex(dropdown082) → index082
71. SelectedIndex(dropdown102) → index102
72. If(step ≟ 2, correctdd021 ∧ correctdd022, step ≟ 7, correctdd071 ∧ correct071 ∧ correct072 ∧ correctdd072, step ≟ 8, correctdd081 ∧ correctdd082, step ≟ 9, anim09 ≟ 19, step ≟ 10, correctdd101, step ≟ 11, show111 ∧ show112 ∧ show113 ∧ show114 ∧ show115 ∧ show116, step ≟ 3, true, anim03 ≟ disTime030 + (3 * disTime031) + (11 * disTime032) + (3 * disTime033), step ≟ 4, correctdd041, step ≟ 5, correct051 ∧ correct052 ∧ correct053 ∧ correct054 ∧ correctdd051, step ≟ 6, anim06 ≟ 3) → clickableBtnNext
73. Segment(Point[seg061, 0], Point[seg061, 0] + (Min[anim06, 1] * (Point[seg061, 1] - Point[seg061, 0]))) → seg061Dynam
74. Segment(Point[seg062, 0], Point[seg062, 0] + (Min[Max[anim06 - 1, 0], 1] * (Point[seg062, 1] - Point[seg062, 0]))) → seg062Dynam
75. Segment(Point[seg063, 0], Point[seg063, 0] + (Min[Max[anim06 - 2, 0], 1] * (Point[seg063, 1] - Point[seg063, 0]))) → seg063Dynam
76. Segment(PosImgFingerStart, PosImgFingerEnd) → segFinger
77. Sequence(Text[((("\textsf{" * If[anim09 ≟ k ∧ step ≟ 9, (("\textcolor{" * Colors09(k)) * "}{\bold{"), "{{"]) * TextList09(k)) * "}}}"), PosList091(k), false, true, 0, 1], k, 1, Length[PosList091]) → CapList09
78. Text("\textsf{Die natürlichen Zahlen ℕ\phantom{g}}", MP031 + (0, ellB031 + 0.25), false, true, 0, 1) → Cap0312
79. Text("\textsf{Die Dezimalzahlen (DZ)\vphantom{g}}", MP033 + (0, ellB031 + 0.25), false, true, 0, 1) → Cap0332
80. PolyLine(PosSB, Corner[txt041, 4] + (-0.1, -0.5), Corner[txt041, 4] + (-0.1, 0.1), Corner[txt041, 3] + (0.1, 0.1), Corner[txt041, 2] + (0.1, -0.1), Corner[txt041, 1] + (-0.1, -0.1), Corner[txt041, 1] + (-0.1, 1.5), PosSB) → sb04
81. PolyLine(PosSB, Corner[txt121, 1] + (-0.1, 1.5), Corner[txt121, 1] + (-0.1, -0.1), Corner[txt121, 2] + (0.1, -0.1), Corner[txt121, 3] + (0.1, 0.1), Corner[txt121, 4] + (-0.1, 0.1), Corner[txt121, 4] + (-0.1, -0.75), PosSB) → sb12