正六边形的动态演示
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这是一个动态可修改的正六边形问题示例,展示了正六边形的性质和相关几何变换。涉及的核心数学概念包括多边形、旋转和平移。通过使用GeoGebra命令如Polygon、Circle、Rotate等进行构造。适合初中及以上学生学习几何变换和多边形性质。
GeoGebra 命令及参数
Polygon(A, B, 6) → poly1, f, F, g, h, i, j, k, C, D, ECircle(F, A) → cLine(F, D) → lIntersect(c, l) → G, HLine(D, B) → mCircle(D, Distance[A, F]) → dIntersect(d, m) → I, JSegment(A, F) → nSegment(F, E) → pSegment(E, D) → qSegment(D, C) → rSegment(C, B) → sSegment(B, A) → tDistance(E, H) → aDistance(H, J) → bDilate(F, If[0 < u ≤ 1, 1 - u, 0], H) → F'Segment(F, F') → f_1Dilate(H, If[1 < u ≤ 2, 2 - u, 0], D) → H'Segment(H, H') → g_1Dilate(D, If[2 < u ≤ 3, 3 - u, 0], J) → D'Segment(D, D') → h_1Dilate(J, If[3 < u ≤ 4, 4 - u, 0], B) → J'Segment(J, J') → i_1Rotate(A, If[4 < u ≤ 5, ((u - 4) * π / 2), π / 2], F) → A'Rotate(F, If[4 < u ≤ 5, ((u - 4) * π / 2), π / 2], F) → F'_1Segment(A', F'_1) → n'Rotate(D, If[5 < u ≤ 6, ((-(u - 5)) * π / 2), ((-π)) / 2], D) → D'_1Rotate(C, If[5 < u ≤ 6, ((-(u - 5)) * π / 6), ((-π)) / 6], D) → C'Segment(D'_1, C') → r'Dilate(E, If[7 < u ≤ 8, 8 - u, 0], H) → E'Segment(E, E') → j_1Dilate(H, If[8 < u ≤ 9, 9 - u, 0], J) → H'_1Segment(HH, H'_1) → k_1