对数性质动态演示 by Tim Brzezinski
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①本范例动态演示对数的倒数性质,通过交互式图形展示对数函数的特性;②涉及核心数学概念包括对数函数、几何变换、向量运算;③作图要点运用了Textfield, Intersect, Dilate, Segment, Vector, Translate, Rotate, Distance等GeoGebra命令与对象;④适合高中数学教学,用于加深学生对对数性质及几何变换的理解。
GeoGebra 命令及参数
Textfield(a) → InputBox1Textfield(f_1) → InputBox2Textfield(f) → InputBox3Intersect(f, h, 1) → EDilate(F, If[0 < d ≤ 1, 1 - d, 0], A) → F'Dilate(A, If[1 < d ≤ 2, 2 - d, 0], B) → A'Segment(A, A') → jDilate(B, If[2 < d ≤ 3, 3 - d, 0], G) → B'Vector(B, B') → uTranslate(A, u) → A'_1Translate(A', u) → A''Segment(A'_1, A'') → j'Rotate(A'_1, If[3 < d ≤ 4, ((-(d - 3)) * π / 2), ((-π)) / 2], F) → HRotate(A'', If[3 < d ≤ 4, ((-(d - 3)) * π / 2), ((-π)) / 2], F) → A'''Segment(H, A''') → j''Rotate(A'_1, If[3 < d ≤ 4, ((d - 3) * π / 2), π / 2], F) → IRotate(A'', If[3 < d ≤ 4, ((d - 3) * π / 2), π / 2], F) → A'''_1Dilate(D, If[4 < d ≤ 5, 5 - d, 0], E) → D'Segment(D, D') → lDilate(A, If[1 < d ≤ 2, 2 - d, 0], C) → A'_2Segment(A, A'_2) → mDilate(A, If[2 < d ≤ 3, 3 - d, 0], R) → C'Vector(C, C') → vIntersect(f, p, 1) → NRotate(F, If[5 < d ≤ 6, ((d - 5) * π / 2), π / 2], F) → F'_1Rotate(F', If[5 < d ≤ 6, ((d - 5) * π / 2), π / 2], F) → F''Dilate(F, If[6 < d ≤ 7, 7 - d, 0], M) → F'_2Vector(F, F'_2) → wTranslate(F'_1, w) → PTranslate(F'', w) → F'''Distance(A, C) → distanceACVector(A, A'_2) → iVector(A, C') → b_1Translate(i, b_1) → i'Dilate(W, If[6 < d ≤ 7, 7 - d, 0], L) → W'Vector(W, W') → w_1Distance(W, L) → distanceWLDilate(T, If[2 < d ≤ 3, 3 - d, 0], U) → T'Vector(T, T') → eDistance(T, U) → distanceTURotate(C, If[3 < d ≤ 4, ((-(d - 3)) * π), (-π)], A) → C'_1Vector(A, C'_1) → qDilate(A, If[4 < d ≤ 5, 5 - d, 0], T) → A'_3Vector(A, A'_3) → u_1Translate(C'_1, u_1) → QVector(A'_3, Q) → v_1