图案块对称性
几何画板及绘图内容加载中,请稍等……
①本范例演示如何基于给定图案创建对称图形;②涉及核心数学概念包括对称性、变异性、全等性、外接圆、立方体、坐标几何;③作图要点:使用 GeoGebra 命令如点、线段、多边形、旋转、角度、圆、交点、中点等;④适合初中及以上学生学习和探索几何对称性。
GeoGebra 命令及参数
Point(Circle[A, a]) → BSegment(A, B) → fPolygon(A, B, 6) → poly1, g, F, h, i, j, k, l, C, D, EPoint(Circle[G, a]) → HSegment(G, H) → mPolygon(G, H, 3) → poly2, n, p, q, IPoint(Circle[J, a]) → KSegment(J, K) → rPolygon(J, K, 3) → poly3, s, t, b, LPolygon(L, K, 3) → poly4, c, d, e, MPolygon(J, K, M, L) → poly5, j_1, k_1, m_1, l_1Point(Circle[S, a]) → TSegment(S, T) → a_1Polygon(S, T, 4) → poly10, b_1, c_1, d_1, e_1, U, VPoint(Circle[W, a]) → ZSegment(W, Z) → f_2Rotate(Z, 30°, W) → Z'Angle(Z, W, Z') → αCircle(Z, W) → c_2Circle(Z', W) → d_2Intersect(c_2, d_2, 2) → A_1Polygon(W, Z, A_1, Z') → poly11, w, z_1, a_2, z'Point(Circle[A_2, a]) → B_1Segment(A_2, B_1) → f_3Polygon(A_2, B_1, 6) → poly1_1, g_2, F_1, h_2, i_2, j_2, k_2, l_2, C_1, D_1, E_1Point(Circle[W_1, a]) → Z_1Segment(W_1, Z_1) → f_4Rotate(Z_1, 30°, W_1) → Z'_1Angle(Z_1, W_1, Z'_1) → α_1Circle(Z_1, W_1) → c_3Circle(Z'_1, W_1) → d_3Intersect(c_3, d_3, 2) → A_3Point(Circle[W_2, a]) → Z_2Segment(W_2, Z_2) → f_5Rotate(Z_2, 30°, W_2) → Z'_2Angle(Z_2, W_2, Z'_2) → α_2Circle(Z_2, W_2) → c_4Circle(Z'_2, W_2) → d_4Intersect(c_4, d_4, 2) → A_4Polygon(W_2, Z_2, A_4, Z'_2) → poly11_1, w_1, z_2, a_3, z'_1Point(Circle[G_1, (2 * a)]) → H_1Segment(G_1, H_1) → m_2Polygon(G_1, H_1, 3) → poly12, s_2, t_2, b_2, I_1Midpoint(G_1, I_1) → J_1Midpoint(H_1, I_1) → K_1Polygon(G_1, H_1, K_1, J_1) → poly13, g_3, h_3, k_3, j_3Point(Circle[G_2, (2 * a)]) → H_2Segment(G_2, H_2) → m_3Polygon(G_2, H_2, 3) → poly12_1, s_3, t_3, b_3, I_2Midpoint(G_2, I_2) → J_2Midpoint(H_2, I_2) → K_2Polygon(G_2, H_2, K_2, J_2) → poly13_1, g_4, h_4, k_4, j_4Point(Circle[G_3, a]) → H_3Segment(G_3, H_3) → m_4Polygon(G_3, H_3, 3) → poly2_1, n_1, p_1, q_1, I_3Point(Circle[J_3, a]) → K_3Segment(J_3, K_3) → r_1Polygon(J_3, K_3, 3) → poly3_1, s_1, t_1, b_4, L_1Polygon(L_1, K_3, 3) → poly4_1, c_5, d_5, e_2, M_1Polygon(J_3, K_3, M_1, L_1) → poly5_1, j_5, k_5, m_5, l_3Point(Circle[W_3, a]) → Z_3Segment(W_3, Z_3) → f_1Rotate(Z_3, 30°, W_3) → Z'_3Angle(Z_3, W_3, Z'_3) → α_3Circle(Z_3, W_3) → c_6Circle(Z'_3, W_3) → d_6Intersect(c_6, d_6, 2) → A_5Polygon(W_3, Z_3, A_5, Z'_3) → poly11_2, w_2, z_3, a_4, z'_2Point(Circle[G_4, (2 * a)]) → H_4Segment(G_4, H_4) → m_6Polygon(G_4, H_4, 3) → poly12_2, s_4, t_4, b_5, I_4Midpoint(G_4, I_4) → J_4Midpoint(H_4, I_4) → K_4Polygon(G_4, H_4, K_4, J_4) → poly13_2, g_1, h_1, k_6, j_6Point(Circle[J_5, a]) → K_5Segment(J_5, K_5) → r_2Polygon(J_5, K_5, 3) → poly3_2, s_5, t_5, b_6, L_2Polygon(L_2, K_5, 3) → poly4_2, c_7, d_7, e_3, M_2Polygon(J_5, K_5, M_2, L_2) → poly5_2, j_7, k_7, m_7, l_4
AI 绘图提示语参考
绘制一个由多个对称几何图形组成的图案。首先,以一个大圆上的点为起点,构造一个正六边形;接着,在六边形的一侧构造一个正三角形,并在其相邻位置再构造两个正三角形,其中一个与另一个共用一条边,形成菱形组合。然后,构造一个正方形,以及一个由两个相交圆和旋转点形成的菱形。重复这些基本形状,包括另一个正六边形、两个菱形和一个更大的正三角形,并在大三角形内部通过中点连接构造一个四边形。所有图形围绕中心对称分布,整体呈现对称美感。
以上提示语为根据原始绘图命令整理而来,仅供参考。