六边形相位演示
几何画板及绘图内容加载中,请稍等……
①本范例演示六边形的几何构造与相关属性;②涉及核心概念包括角度、多边形、正弦函数、积分等;③构造过程中运用了画圆、射线、交点、线段、扇形、向量、平移、缩放、条件判断、多边形、点、中点、旋转、直线、圆弧等 GeoGebra 命令;④适合高中数学教学,用于理解多边形性质与函数图像关系。
GeoGebra 命令及参数
Circle(C, 1.5) → hRay(C, D) → cIntersect(h, c, 1) → PRay(A, B) → aRay(B, C) → bRay(E, A) → eCircle(A, 1.5) → fCircle(B, 1.5) → gCircle(D, 1.5) → kCircle(E, 1.5) → pSegment(C, A) → iSegment(C, E) → jIntersect(f, a, 1) → FIntersect(f, i, 1) → GIntersect(f, e, 1) → HIntersect(f, e, 2) → IIntersect(p, e) → J,Intersect(p, j) → K,Intersect(k, c, 2) → OIntersect(h, j, 1) → QIntersect(h, i, 1) → RIntersect(h, b, 1) → SIntersect(g, a, 2) → TIntersect(g, b, 1) → UIntersect(g, a, 1) → VCircleSector(A, F, G) → qCircleSector(A, G, H) → rCircleSector(B, U, V) → sCircleSector(C, Q, R) → c_1CircleSector(C, R, S) → d_1Intersect(k, c, 1) → WCircleSector(E, J, K) → h_1CircleSector(A, I, F) → p_1CircleSector(B, T, U) → q_1Intersect(h, b, 2) → ZCircleSector(C, Z, P) → r_1Vector(A, B) → uVector(C, B) → vVector(E, D) → wVector(C, D) → u_1Vector(C, E) → v_1Vector(A, E) → w_1Translate(d_1, v) → s_1Dilate(C, If[1 < l ≤ 2, 2 - l, 0], E) → C'_1Dilate(C, If[2 < l ≤ 3, 3 - l, 0], D) → C'_2Dilate(E, If[2 < l ≤ 3, 3 - l, 0], D) → E'Vector(A, B) → a_1Vector(E, E') → j_1Vector(C, C'_2) → l_1Vector(C, C'_1) → m_1Translate(r, w_1) → r'_2Translate(c_1, v_1) → f_2Translate(c_1, m_1) → g_2Translate(q, a_1) → r'Vector(D, C) → u_2Vector(E, C) → v_2Vector(A, C) → w_2Vector(B, C) → l_2Dilate(B, If[0 < o < 1, 1 - o, 0], C) → B'Dilate(A, If[1 < o < 2, 2 - o, 0], C) → A'_2Dilate(E, If[2 < o < 3, 3 - o, 0], C) → E'_1Dilate(D, If[3 < o < 4, 4 - o, 0], C) → D'Vector(B, B') → m_2Vector(A, A'_2) → n_2Vector(E, E'_1) → s_2Vector(D, D') → t_2Translate(q_1, m_2) → c_3Translate(q_1, l_2) → d_3Translate(p_1, w_2) → e_3If(1 < o < 2, Translate[p_1, n_2]) → h_3Ray(D, A_1) → a_3Ray(A_1, E) → b_3Circle(A_1, 1.5) → q_3Intersect(q_3, b_3, 1) → NIntersect(q_3, a_3, 2) → B_1Intersect(k, c, 2) → C_1Intersect(k, a_3, 1) → D_1Intersect(k, c, 1) → E_1Intersect(p, b_3, 1) → F_1Dilate(C, If[2 < l < 3, 3 - l, 0], A_1) → C'_3Vector(E, A_1) → f_1Vector(C, A_1) → g_1Vector(C, C'_3) → b_2Intersect(q_3, a_3, 1) → I_1CircleSector(D, D_1, E_1) → k_3Vector(C, D) → j_2Vector(A_1, D) → u_3Intersect(p, b_3, 2) → J_1Polygon(A, B, C) → poly1, c_4, a_4, b_4Polygon(A, C, E) → poly2, e_4, a_5, c_5Polygon(E, C, A_1) → poly3, a_6, e_5, c_6Polygon(A_1, C, D) → poly4, d_4, a_7, c_7Polygon(A, B, C, D, A_1, E) → poly5, a_8, b_5, c_8, d_5, a_9, e_6Intersect(e, e_6) → K_1Intersect(p, e, 1) → L_1CircleSector(E, J_1, L_1) → f_4CircleSector(A_1, B_1, N) → g_4CircleSector(D, C_1, D_1) → h_4Vector(E, C) → j_3Vector(A_1, C) → l_3Vector(D, C) → m_3Translate(f_4, j_3) → k_4Translate(g_4, l_3) → p_4Translate(h_4, m_3) → q_4Dilate(E, If[2 < o < 3, 3 - o, 0], C) → E'_3Dilate(A_1, If[3 < o < 4, 4 - o, 0], C) → M_7Dilate(D, If[4 < o < 5, 5 - o, 0], C) → D'_1Vector(E, E'_3) → n_3Vector(A_1, M_7) → u_4Vector(D, D'_1) → v_4If(2 < o < 3, Translate[f_4, n_3]) → r_4If(3 < o < 4, Translate[g_4, u_4]) → s_4If(4 < o < 5, Translate[h_4, v_4]) → t_4Ray(C, A_1) → l_4Ray(C, E) → m_4Point(l_4) → N_1Point(m_4) → O_1Segment(D, C) → n_4Segment(C, B) → f_5Segment(B, A) → g_5Segment(A, E) → h_5Segment(E, A_1) → i_5Segment(A_1, D) → j_5Midpoint(f_5) → M_2Midpoint(g_5) → M_1Rotate(d_1, If[0 < l ≤ 1, ((-l) * 180°), -180°], M_2) → dRotate(C, If[0 < l ≤ 1, ((-l) * 180°), -180°], M_2) → C'Segment(M_2, C') → tRotate(q, If[0 < l ≤ 1, (l * 180°), 180°], M_1) → q'Rotate(A, If[0 < l ≤ 1, (l * 180°), 180°], M_1) → A'Segment(M_1, A') → e_1Rotate(R, 180°, M_2) → R'Line(B, R') → k_1Ray(E, O_1) → i_1Midpoint(h_5) → M_6Rotate(r, If[1 < l ≤ 2, ((-(l - 1)) * 180°), -180°], M_6) → r'_1Rotate(A, If[1 < l ≤ 2, ((-(l - 1)) * 180°), -180°], M_6) → A'_1Segment(M_6, A'_1) → n_1CircleSector(E, K, F_1) → c_2Midpoint(i_5) → M_5Rotate(E, If[2 < l ≤ 3, ((-(l - 2)) * 180°), -180°], M_5) → E'_2Segment(M_5, E'_2) → a_2Rotate(c_2, If[2 < l ≤ 3, ((-(l - 2)) * 180°), -180°], M_5) → d_2Segment(A_1, C) → e_2Intersect(h, e_2, 1) → U_1CircleSector(C, U_1, Q) → h_2CircleSector(C, P, U_1) → k_2Vector(C, C'_3) → t_1Translate(h_2, t_1) → p_2Intersect(q_3, e_2, 1) → R_1CircleSector(A_1, N, R_1) → q_2CircleSector(A_1, R_1, I_1) → r_2Vector(C, A_1) → i_2Translate(U_1, i_2) → S_1Ray(A_1, S_1) → f_3Midpoint(j_5) → M_4Midpoint(n_4) → M_3Rotate(k_2, If[3 < l ≤ 4, ((l - 3) * 180°), 180°], M_3) → g_3Rotate(C, If[3 < l ≤ 4, ((l - 3) * 180°), 180°], M_3) → C'_4Rotate(U_1, 180°, M_3) → W_1Segment(M_3, C'_4) → i_3Rotate(r_2, If[3 < l ≤ 4, ((-(l - 3)) * 180°), -180°], M_4) → p_3Rotate(A_1, If[3 < l ≤ 4, ((-(l - 3)) * 180°), -180°], M_4) → Z_1Segment(M_4, Z_1) → r_3Line(D, W_1) → s_3CircleArc(C, R, S) → t_3CircleArc(A, F, G) → k_5CircleArc(C, Q, R) → p_5CircleArc(A, G, H) → q_5CircleArc(C, U_1, Q) → r_5CircleArc(E, K, F_1) → s_5CircleArc(C, P, U_1) → t_5CircleArc(A_1, R_1, I_1) → d_6
AI 绘图提示语参考
请绘制一个正六边形,包含六个等边三角形和六个圆弧。构造顺序是从中心开始,依次画出六个圆,然后连接圆的交点,形成六边形。确保图形对称,线条清晰,适用于数学教育。
以上提示语为根据原始绘图命令整理而来,仅供参考。