动画278:多边形与变换
几何画板及绘图内容加载中,请稍等……
①本范例通过动画演示多边形的旋转、缩放及轨迹变化;②涉及核心数学概念包括多边形构造、角度变换、向量运算、二次函数与分形几何;③作图要点运用了Polygon, Rotate, Dilate, Vector, Translate等GeoGebra命令;④适合高中及以上数学学习,用于理解几何变换与函数图像关系。
GeoGebra 命令及参数
Polygon(A, B, 5) → poly1, f, g, h, i, j, C, D, ERotate(B, 144°, C) → B'Ray(C, B') → sLine(B, C) → kCircle(C, a) → cIntersect(c, s) → N,Intersect(c, k) → F, GCircleArc(C, F, N) → eLine(C, D) → lIntersect(c, l) → H, ICircleArc(C, F, I) → dPoint(e) → JPolygon(C, J, 5) → poly2, m, n, p, q, r, K, L, MAngle(B, C, B') → αSegment(D, A) → tSegment(D, B) → bLineBisector(D, C) → f_1LineBisector(B, C) → g_1LineBisector(M, L) → h_1LineBisector(L, K) → i_1Segment(M, J) → j_1Segment(E, K) → k_1Segment(A, L) → l_1Intersect(k_1, l_1) → QCircle(D, (0.2 * j_1)) → c_1Segment(D, E) → m_1Intersect(c_1, t, 1) → RIntersect(i, m_1) → SIntersect(c_1, m_1) → T,CircleSector(D, T, R) → d_1Dilate(E, If[0 < o ≤ 1, 1 - o, 0], K) → E'Segment(E, E') → n_1Dilate(A, If[1 < o ≤ 2, 2 - o, 0], Q) → A'Segment(A, A') → p_1Dilate(Q, If[2 < o ≤ 3, 3 - o, 0], L) → Q'Segment(Q, Q') → q_1Dilate(D, If[3 < o ≤ 4, 4 - o, 0], A) → D'Dilate(D, If[3 < o ≤ 4, 4 - o, 0], B) → D'_1Segment(D, D') → r_1Segment(D, D'_1) → s_1Rotate(d_1, If[5 < o ≤ 6, (((o - 5) * 36) * π / 180), (36 * π / 180)], D) → e_1Rotate(e_1, If[7 < o ≤ 8, (((o - 7) * 36) * π / 180), (36 * π / 180)], D) → t_1Line(Q, s_1) → a_1Dilate(D, If[9 < o ≤ 10, 10 - o, 0], Q) → D'_2Vector(D, D'_2) → uTranslate(t_1, u) → c_2Segment(D, E) → b_1Segment(E, A) → f_2Segment(A, B) → g_2Segment(B, C) → h_2Segment(C, D) → i_2Segment(C, M) → j_2Segment(M, L) → k_2Segment(L, K) → l_2Segment(K, J) → m_2Segment(J, C) → n_2Point(a_1) → OAngle(O, Q, K) → βRotate(c_2, If[10 < o ≤ 11, ((o - 10) * β), β], Q) → d_2