互动多边形正弦曲线
几何画板及绘图内容加载中,请稍等……
这个范例展示了互动多边形正弦曲线的动态变化。它涉及三角函数和随机过程的核心概念。通过使用GeoGebra命令如Circle, Point, Rotate, Segment, Polygon等,可以构造出一系列多边形,并观察其正弦曲线的变化。适合高中数学教学和学习,特别是三角函数和几何作图的内容。
GeoGebra 命令及参数
Circle(A, 1) → cPoint(c) → BRotate(B, t, A) → B'Segment(A, B') → gPolygon(B, Rotate[B, (2 * π / n), A], n) → poly1, a, p, q, r, s, a_1, b_1, c_1, d_1, e_1, f_1, b, g_1, h_1, i_1, j_1, k_1, l_1, m_1, q_1, r_1, s_1, d, t_1, C, H, I, J, K, L, M, N, O, h, P, Q, R, S, T, U, V, W, Z, A_1, i, B_1, C_1, D_1, E_1, F_1, G_1, H_1, I_1, J_1, j, k, l, mIntersect(g, poly1) → DPoint(poly1) → EAngle(B, A, D) → αSegment(A, D) → eLocus(G, t) → lieu2Segment(D, G) → fSegment(A, B) → n_1Segment(F, G) → p_1Segment((6.283185307179586, 1), (6.283185307179586, -1)) → a_2Segment(B, K_1) → b_2Circle(N_1, 1) → c_2Point(c_2) → CCPolygon(CC, Rotate[CC, 0.12566370614359174, N_1], 50) → poly2, d_2, m_2, n_2, p_2, q_2, r_2, s_2, t_2, a_3, b_3, c_3, e_2, d_3, e_3, f_3, g_3, h_3, i_3, j_3, k_3, l_3, m_3, f_2, n_3, p_3, q_3, r_3, s_3, t_3, a_4, b_4, c_4, d_4, g_2, e_4, f_4, g_4, h_4, i_4, j_4, k_4, l_4, m_4, n_4, h_2, p_4, O_1, P_1, Q_1, R_1, S_1, T_1, U_1, V_1, W_1, i_2, Z_1, A_2, B_2, C_2, D_2, E_2, F_2, G_2, H_2, I_2, j_2, J_2, K_2, L_2, M_2, N_2, O_2, P_2, Q_2, R_2, S_2, k_2, T_2, U_2, V_2, W_2, Z_2, A_3, B_3, C_3, D_3, E_3, l_2, F_3, G_3, H_3, I_3, J_3, K_3, L_3, M_3, N_3Rotate(CC, t, N_1) → CC'Locus(GG, t) → lieu1Vector((0, -1.25), (0, 1.25)) → uVector(OO + (0, -1.25), OO + (0, 1.25)) → vSegment(N_1, CC') → q_4Segment(CC, N_1) → r_4Segment(CC', GG) → s_4Ray(OO, OO + (15, 0)) → t_4Segment(CC, O_3) → a_5Angle(CC, N_1, CC') → βSegment(GG, P_3) → b_5Segment(N_1, QQ) → c_5Angle(QQ, N_1, CC) → γSegment((6.28319, -2), (6.28319, -4)) → d_5Sequence(OO + (i, 0), i, 0, 12.566370614359172, 1.5707963267948966) → liste1
AI 绘图提示语参考
绘制一个交互式多边形正弦波演示图。先画一个单位圆,在圆上取一点,并绕圆心旋转该点形成动态角。以该点为顶点构造一个正多边形,并让多边形的一条边与圆上的旋转点相交。从圆心到交点作线段,并追踪交点的轨迹形成正弦曲线。再画第二个单位圆,在其上构造一个边数更多的正多边形,同样旋转一个点,并连接旋转点与轨迹点,形成另一条正弦曲线。添加坐标轴、向量和刻度点,展示两个正弦波的动态变化。
以上提示语为根据原始绘图命令整理而来,仅供参考。