正多边形的三角函数
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本范例展示了正多边形与圆之间的关系,通过构造正多边形并无限增加边数,可以逼近圆。三角函数被定义为线段的长度。通过使用GeoGebra命令如Point, Circle, Intersect, Polygon, Rotate等,可以动态演示正多边形的性质。适合高中数学教学,特别是三角函数和几何作图的学习。
GeoGebra 命令及参数
Point(xAxis) → ACircle(A, 1) → cIntersect(c, xAxis, 2) → BCircle(B, (2 * sin(π / n))) → dIntersect(c, d, 1) → CPolygon(B, C, n) → poly1, a, l, m, p, q, r, s, t_2, a_1, b_1, c_1, b, d_1, e_1, f_1, g_1, h_1, i_1, j_1, k_1, l_1, m_1, e, n_1, p_1, q_1, r_1, s_1, t_1, a_2, b_2, c_2, d_2, f, e_2, f_2, g_2, h_2, i_2, j_2, k_2, l_2, m_2, n_2, g, p_2, D, E, F, G, H, I, J, K, L, h, M, N, O, P, Q, R, S, T, U, V, i, W, Z, A_1, B_1, C_1, D_1, E_1, F_1, G_1, H_1, j, I_1, J_1, K_1, L_1, M_1, N_1, O_1, P_1, Q_1, R_1, k, S_1, T_1, U_1, V_1, W_1, Z_1, A_2, B_2, C_2Rotate(B, t, A) → B'Angle(B, A, B') → αSegment(A, B') → q_2Intersect(q_2, poly1) → D_2Rotate(B, t + 90°, A) → B'_1Angle(B, A, B'_1) → βSegment(A, B'_1) → a_3Intersect(a_3, poly1) → G_2Segment(A, B'_1) → b_3Intersect(b_3, poly1) → H_2