恒星轨迹探索
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所属专题
Regular Polygons
本范例展示了恒星在特定条件下的轨迹,探讨了单个恒星的连续轨迹与两个恒星轨迹的重叠情况。涉及的核心数学概念包括几何变换和轨迹。通过使用旋转、镜像、多边形等 GeoGebra 命令,可以构造出复杂的几何图形。适合高中及以上学生或数学爱好者学习和探索。
GeoGebra 命令及参数
Intersect(xAxis, yAxis) → ACircle(A, u) → c_3Intersect(c_3, yAxis) → B, CRotate(B, 360 * ° / (2 * a), A) → B'Mirror(B', yAxis) → B''Polygon(B'', B', a) → poly1, b_3, l_2, m, n, D, E, F, G, H, I, J, d_3, K, L, M, e_3, f_3, g_3, h_3, i_3, j_3, k_2Dilate(poly1, o, A) → poly1'Dilate(c_3, o, A) → c'Ray(A, E) → dRay(A, F) → eRay(A, G) → fRay(A, B'') → bRay(A, B') → cRay(A, D) → a_1Intersect(c', d) → N,Intersect(c', b) → O,Intersect(c', e, 1) → PIntersect(c', f, 1) → QIntersect(c', c, 1) → RIntersect(c', a_1, 1) → SRay(A, H) → gRay(A, I) → hRay(A, J) → iRay(A, K) → jRay(A, L) → kRay(A, M) → lIntersect(c', g, 1) → TIntersect(c', h, 1) → UIntersect(c', i, 1) → VIntersect(c', j, 1) → WIntersect(c', k, 1) → ZIntersect(c', l, 1) → A_1Polygon(O, R, a) → poly2, h_1, j_2, s_1, e_2, B_1, C_1, D_1, E_1, F_1, G_1, H_1, i_1, I_1, J_1, K_1, j_1, k_1, l_1, m_1, g_2, h_2, i_2Segment(F, N) → n_1Segment(N, D) → p_1Segment(D, R) → q_1Segment(R, B'') → r_1Segment(Q, F) → t_1Segment(P, E) → a_2Segment(E, S) → b_2Segment(S, B') → c_2Segment(B', O) → d_2Segment(G, P) → f_2Segment(K_1, B'') → pSegment(M, O) → qSegment(K_1, L) → rSegment(M, Z) → sSegment(L, I_1) → tSegment(Z, K) → b_1Segment(K, V) → c_1Segment(I_1, J) → d_1Segment(J, U) → e_1Segment(V, I) → f_1Segment(I, T) → g_1Segment(U, H) → m_2Segment(H, Q) → n_2Segment(G, T) → p_2Segment(S, B'') → q_2Segment(O, D) → r_2Mirror(N, d) → N'Mirror(D, d) → D'Segment(N', D') → s_2Mirror(E, d) → E'Mirror(S, d) → S'Segment(E', S') → t_2Mirror(F, e) → F'Mirror(N, e) → N'_1Segment(F', N'_1) → a_3Mirror(E', e) → E''Mirror(S', e) → S''Segment(E'', S'') → k_3Mirror(E'', f) → E'''Mirror(S'', f) → S'''Segment(E''', S''') → l_3Mirror(F', f) → F''Mirror(N'_1, f) → L_1Segment(F'', L_1) → m_3Mirror(F'', g) → F'''Mirror(L_1, g) → M_1Segment(F''', M_1) → n_3Mirror(G, g) → G'Mirror(T, g) → T'Segment(G', T') → p_3Mirror(I, h) → I'Mirror(T, h) → T'_1Segment(I', T'_1) → q_3Mirror(U, h) → U'Mirror(H, h) → H'Segment(U', H') → r_3Mirror(J, i) → J'Mirror(U, i) → U'_1Segment(J', U'_1) → s_3Mirror(V, i) → V'Mirror(I, i) → I'_1Segment(V', I'_1) → t_3Mirror(K, j) → K'Mirror(V, j) → V'_1Segment(K', V'_1) → a_4Mirror(I_1, j) → N_1Mirror(J, j) → J'_1Segment(N_1, J'_1) → b_4Mirror(L, k) → L'Mirror(I_1, k) → O_1Segment(L', O_1) → t'Mirror(Z, k) → Z'Mirror(K, k) → K'_1Segment(Z', K'_1) → c_4
AI 绘图提示语参考
绘制一个星体轨迹探索图形,包含一个圆c_3,圆心为A,与y轴相交于B和C两点。通过旋转、镜像和多边形命令,构造B'和B'',并使用多边形命令构建poly1。接着,通过缩放和相交命令,构造c'、d、e、f、b、c、a_1等对象,以及N、O、P、Q、R、S、T、U、V、W、Z、A_1等点,最后使用多边形命令构建poly2。
以上提示语为根据原始绘图命令整理而来,仅供参考。