利用45-45-90三角形反射生成的镶嵌
几何画板及绘图内容加载中,请稍等……
通过拖动45-45-90三角形内部的点,可以生成不同的镶嵌图案。本范例展示了反射变换在几何作图中的应用,涉及的核心数学概念包括反射变换和几何作图。使用了Polygon, Segment, PointIn, Mirror等GeoGebra命令,适合初中及以上学生学习几何变换和镶嵌图案。
GeoGebra 命令及参数
Polygon(A, B, 4) → poly1, a_2, b_2, c_2, d, C, DSegment(A, C) → ePolygon(A, B, C) → poly2, c, a, bPointIn(poly2) → EMirror(E, a) → E'Mirror(E, b) → E'_1Mirror(E, c) → E'_2Segment(E, E'_1) → fSegment(E, E') → gSegment(E, E'_2) → hMirror(E'_1, a) → FMirror(E'_1, c) → GMirror(E', b) → E''Mirror(E', c) → E''_1Mirror(E'_2, b) → HSegment(E'_1, E'') → iSegment(E'_1, H) → jSegment(E'_2, G) → kSegment(E''_1, E') → lSegment(E'_2, E''_1) → mSegment(E', F) → pMirror(E'', a) → E'''Mirror(E'', c) → E'''_1Mirror(F, b) → F'Mirror(F, c) → F'_1Mirror(E''_1, b) → IMirror(G, b) → G'Mirror(H, a) → H'Mirror(H, c) → H'_1Segment(E'', F') → qSegment(E'', I) → rSegment(I, H) → sSegment(H, G') → tSegment(G, H'_1) → a_1Segment(G, E'''_1) → b_1Segment(E''_1, F'_1) → c_1Segment(F, H') → d_1Segment(F, E''') → e_1Mirror(F', a) → F''Mirror(F', c) → F''_1Mirror(I, a) → I'Mirror(I, c) → I'_1Mirror(G', a) → G''Mirror(G', c) → G''_1Mirror(H'_1, a) → JMirror(E'''_1, a) → KMirror(E'''_1, b) → LMirror(F'_1, b) → MMirror(H', b) → H''Segment(F', H'') → f_1Segment(I, M) → g_1Segment(G', L) → h_1Segment(G''_1, G') → i_1Segment(G''_1, H'_1) → j_1Segment(H'_1, I'_1) → k_1Segment(I'_1, E'''_1) → l_1Segment(E'''_1, F''_1) → m_1Segment(K, F'_1) → n_1Segment(F'_1, J) → p_1Segment(H', G'') → q_1Segment(H', I') → r_1Segment(I', E''') → s_1Segment(E''', F'') → t_1Segment(F'', F') → d_2Mirror(H'', a) → H'''Mirror(H'', c) → H'''_1Mirror(M, a) → M'Mirror(M, c) → M'_1Mirror(L, a) → L'Mirror(L, c) → L'_1Mirror(F''_1, a) → NMirror(F''_1, b) → OMirror(K, b) → K'Mirror(J, b) → J'Mirror(G'', b) → G'''Mirror(G'', c) → G'''_1Mirror(I', c) → I''Segment(H'', G''') → e_2Segment(M, J') → f_2Segment(M, K') → g_2Segment(L, O) → h_2Segment(L, L'_1) → i_2Segment(I'_1, M'_1) → j_2Segment(F''_1, H'''_1) → k_2Segment(F''_1, N) → l_2Segment(N, K) → m_2Segment(K, I'') → n_2Segment(I'', J) → p_2Segment(J, G'''_1) → q_2Segment(G'''_1, G'') → r_2Segment(I', M') → s_2Segment(F'', H''') → t_2Segment(H''', H'') → a_3Segment(G'', L') → b_3Mirror(G''', a) → PMirror(G''', c) → QMirror(J', a) → J''Mirror(J', c) → J''_1Mirror(K', a) → K''Mirror(K', c) → K''_1Mirror(O, a) → O'Mirror(O, c) → O'_1Mirror(L'_1, a) → RMirror(M'_1, a) → SMirror(H'''_1, a) → TMirror(H'''_1, b) → UMirror(I'', b) → I'''Mirror(G'''_1, b) → VMirror(L', b) → L''Segment(L'', G''') → c_3Segment(G''', V) → d_3Segment(V, J') → e_3Segment(J', I''') → f_3Segment(I''', K') → g_3Segment(O, U) → h_3Segment(L'_1, O'_1) → i_3Segment(K''_1, M'_1) → j_3Segment(J''_1, M'_1) → k_3Segment(Q, H'''_1) → l_3Segment(H'''_1, T) → m_3Segment(T, N) → n_3Segment(S, I'') → p_3Segment(R, G'''_1) → q_3Segment(R, L') → r_3Segment(L', O') → s_3Segment(K'', M') → t_3Segment(M', J'') → a_4Segment(P, H''') → b_4Segment(G''_1, L'_1) → c_4
AI 绘图提示语参考
先画一个正方形,连接其一条对角线,将正方形分成两个等腰直角三角形。取其中一个三角形,在其内部任意放置一个点。以该三角形的三条边为对称轴,分别反射这个点,得到三个镜像点。用线段连接原始点与三个镜像点,形成一个小三角形。接着,以相邻三角形的边为对称轴,继续反射这些点,并连接相应的镜像点,逐步向外扩展,形成由多个等腰直角三角形拼接而成的密铺图案。整个图形由对称反射生成,点在不同三角形间重复出现,构成复杂的网格状镶嵌结构。
以上提示语为根据原始绘图命令整理而来,仅供参考。