GeoGebra 几何变换与积分演示
几何画板及绘图内容加载中,请稍等……
所属专题
Tessellations
①本范例通过 GeoGebra 动态演示函数图像、向量变换及积分计算;②涉及核心概念:余弦函数、解析几何、定积分、算术与几何平均数;③作图要点:使用 Segment, OrthogonalLine, Point, Intersect, Vector, Translate, Polygon, Circle, Semicircle 等命令构建几何图形与函数模型;④适合高中及以上数学学习,用于理解函数变换、积分应用及几何作图方法。
GeoGebra 命令及参数
Segment(A, B) → fOrthogonalLine(A, f) → gOrthogonalLine(B, f) → hPoint(g) → COrthogonalLine(C, g) → iIntersect(h, i) → DSegment(A, B) → jSegment(A, C) → kSegment(C, D) → lSegment(B, D) → mSegment(A, E) → nSegment(F, E) → pSegment(F, G) → qSegment(H, G) → rSegment(H, B) → sVector(A, C) → uTranslate(A, u) → A'Translate(E, u) → E'Segment(A', E') → n'Translate(F, u) → F'Translate(E, u) → E'_1Segment(F', E'_1) → p'Translate(F, u) → F'_1Translate(G, u) → G'Segment(F'_1, G') → q'Translate(H, u) → H'Translate(G, u) → G'_1Segment(H', G'_1) → r'Translate(H, u) → H'_1Translate(B, u) → B'Segment(H'_1, B') → s'Segment(A, I) → tSegment(I, J) → aSegment(J, K) → bSegment(K, L) → cSegment(L, M) → dSegment(N, O) → eSegment(P, C) → f_1Vector(A, B) → vTranslate(A, v) → A'_1Translate(I, v) → I'Segment(A'_1, I') → t'Translate(I, v) → I'_1Translate(J, v) → J'Segment(I'_1, J') → a'Translate(J, v) → J'_1Translate(K, v) → K'Segment(J'_1, K') → b'Translate(K, v) → K'_1Translate(L, v) → L'Segment(K'_1, L') → c'Translate(L, v) → L'_1Translate(M, v) → M'Segment(L'_1, M') → d'Translate(N, v) → N'Translate(O, v) → O'Segment(N', O') → e'Translate(P, v) → P'Translate(C, v) → C'Segment(P', C') → g_1Segment(M, N) → h_1Segment(M, N) → i_1Segment(O, P) → j_1Segment(M, N) → k_1Segment(M', N') → l_1Segment(P', O') → m_1Polygon(F, E, P, C, E', F', G', H', D, P', O', N', A, M', L', K', J', I', B, H, G, I, J, K, L, M, N, O) → poly1, f_2, o, p_1, c_1, e'_1, f', g', h', d_1, p'_1, o', e_1, n'_1, m', l', k', j', i', b_1, h_2, g_2, a_1, i_2, j_2, k_2, l_2, m_2, n_1Circle(Q, S) → q_1Circle(R, T) → r_1Semicircle(U, V) → s_1Segment(V, U) → t_1Segment(V, U) → n_{2}Vector(A, B) → wTranslate(F, w) → F'_2Translate(E, w) → E'_2Translate(A, w) → A'_2Translate(I, w) → I'_2Translate(J, w) → J'_2Translate(K, w) → K'_2Translate(L, w) → L'_2Translate(M, w) → M'_1Translate(N, w) → N'_1Translate(O, w) → O'_1Translate(P, w) → P'_1Translate(C, w) → C'_1Translate(E', w) → E''Translate(F', w) → F''Translate(G', w) → G''Translate(H', w) → H''Translate(D, w) → D'Translate(P', w) → P''Translate(O', w) → O''Translate(N', w) → N''Translate(M', w) → M''Translate(L', w) → L''Translate(K', w) → K''Translate(J', w) → J''Translate(I', w) → I''Translate(B, w) → B'_1Translate(H, w) → H'_2Translate(G, w) → G'_2Polygon(F'_2, E'_2, P'_1, C'_1, E'', F'', G'', H'', D', P'', O'', N'', A'_2, M'', L'', K'', J'', I'', B'_1, H'_2, G'_2, I'_2, J'_2, K'_2, L'_2, M'_1, N'_1, O'_1) → poly1', f'_2, o'_1, p'_2, c'_1, e'', f'', g'', h'', d'_1, p'', o'', e'_2, n'', m'', l'', k'', j'', i'', b'_1, h'_2, g'_2, a'_2, i'_2, j'_2, k'_2, l'_2, m'_1, n'_2Translate(q_1, w) → c_2Translate(r_1, w) → d_2Translate(s_1, w) → e_2Translate(A, w) → A'_3Translate(E, w) → E'_3Segment(A'_3, E'_3) → n'_3Translate(F, w) → F'_3Translate(E, w) → E'_4Segment(F'_3, E'_4) → p'_3Translate(F, w) → F'_4Translate(G, w) → G'_3Segment(F'_4, G'_3) → q'_1Translate(H, w) → H'_3Translate(G, w) → G'_4Segment(H'_3, G'_4) → r'_1Translate(H, w) → H'_4Translate(B, w) → B'_2Segment(H'_4, B'_2) → s'_1Translate(A', w) → A''Translate(E', w) → E''_1Segment(A'', E''_1) → n''_1Translate(F', w) → F''_1Translate(E'_1, w) → WSegment(F''_1, W) → p''_1Translate(F'_1, w) → ZTranslate(G', w) → G''_1Segment(Z, G''_1) → q''Translate(H', w) → H''_1Translate(G'_1, w) → A_1Segment(H''_1, A_1) → r''Translate(H'_1, w) → B_1Translate(B', w) → B''Segment(B_1, B'') → s''Translate(A, w) → A'_4Translate(I, w) → I'_3Segment(A'_4, I'_3) → t'_1Translate(I, w) → I'_4Translate(J, w) → J'_3Segment(I'_4, J'_3) → a'_1Translate(J, w) → J'_4Translate(K, w) → K'_3Segment(J'_4, K'_3) → b'_2Translate(K, w) → K'_4Translate(L, w) → L'_3Segment(K'_4, L'_3) → c'_2Translate(L, w) → L'_4Translate(M, w) → M'_2Segment(L'_4, M'_2) → d'_2Translate(N, w) → N'_2Translate(O, w) → O'_2Segment(N'_2, O'_2) → e'_3Translate(P, w) → P'_2Translate(C, w) → C'_2Segment(P'_2, C'_2) → n_2Translate(A'_1, w) → C_1Translate(I', w) → I''_1Segment(C_1, I''_1) → t''Translate(I'_1, w) → D_1Translate(J', w) → J''_1Segment(D_1, J''_1) → a''Translate(J'_1, w) → E_1Translate(K', w) → K''_1Segment(E_1, K''_1) → b''Translate(K'_1, w) → F_1Translate(L', w) → L''_1Segment(F_1, L''_1) → c''Translate(L'_1, w) → G_1Translate(M', w) → M''_1Segment(G_1, M''_1) → d''Translate(N', w) → N''_1Translate(O', w) → O''_1Segment(N''_1, O''_1) → e''_1Translate(P', w) → P''_1Translate(C', w) → C''Segment(P''_1, C'') → p_2Translate(M, w) → M'_3Translate(N, w) → N'_3Segment(M'_3, N'_3) → q_2Translate(M, w) → M'_4Translate(N, w) → N'_4Segment(M'_4, N'_4) → r_2Translate(O, w) → O'_3Translate(P, w) → P'_3Segment(O'_3, P'_3) → s_2Translate(M, w) → M'_5Translate(N, w) → N'_5Segment(M'_5, N'_5) → t_2Translate(M', w) → M''_2Translate(N', w) → N''_2Segment(M''_2, N''_2) → a_2Translate(P', w) → P''_2Translate(O', w) → O''_2Segment(P''_2, O''_2) → b_2Translate(V, w) → V'Translate(U, w) → U'Segment(V', U') → f_3Translate(A, Vector[(0, -0.027146446191190776)]) → A'_5
AI 绘图提示语参考
画一个动态展示函数图像、向量变换和积分计算的图形。首先绘制一条线段,然后在线段两端分别作出垂线,交点连接形成新的图形。接着以线段为向量,平移线段和图形,展示变换效果。最后添加多个线段连接平移后的点,构成复杂的几何结构,体现坐标几何和积分的应用。
以上提示语为根据原始绘图命令整理而来,仅供参考。