角侦探
几何画板及绘图内容加载中,请稍等……
这个范例通过一个有趣的侦探游戏,演示了菱形的性质。核心数学概念包括角的性质和几何变换。通过使用GeoGebra命令如Point、Angle、Segment等,可以动态地探索菱形的角和对称性。适合初中及以上学生学习几何变换和菱形的性质。
GeoGebra 命令及参数
Point(Circle[A, (2.5 * zr)]) → C'Angle(C, A, C') → angSegment(F, E) → lSegment(A, C') → aCircleSector(A, F, Rotate[F, t1, A]) → cCircle(B, arr) → ePolygon(F + v_1 / 5, F + h / 10, F - h / 10) → fth, b, f, gPolygon(E + v_1 / 5, E + h / 10, E - h / 10) → bth, i, j, kSequence(Rotate[fth, t1 + ((i * 2) * pi / freq), A], i, 1, freq) → liste3Sequence(Rotate[bth, t2 + ((i * 2) * pi / rap), B], i, 1, rap) → liste4Segment(Mirror[F, A], Mirror[E, B]) → mVector(E, F) → wMirror(F, A) → F'CircleSector(B, E, Rotate[E, t2, B]) → dMirror(E, B) → E'Vector(F', E') → uPolyLine(A, B, G, A, H, G) → nTranslate(e, Vector[B, I]) → e'Sequence(Segment[Rotate[D, t2 + ((i * 2) * pi / av), B], Rotate[E, t2 + ((i * 2) * pi / av), B]], i, 1, av) → liste1Sequence(Segment[I, Rotate[J, t2 + ((i * 2) * pi / av), I]], i, 1, av) → liste2Polygon(G + (0.1 * v_1) + h, G + (0.9 * v_1) + h, G + (0.5 * v_1) - (2 * h)) → poly1, q, r, sCircle(M, (5 * zr)) → d_1Circle(K, (6 * zr)) → c_1Intersect(c_1, d_1, 2) → LPolygon(C' + (0.5 * h) + (0.25 * v_1), C' + (0.5 * h) - (0.25 * v_1), C' - (0.5 * h) - (0.25 * v_1), C' - (0.5 * h) + (0.25 * v_1)) → poly2, b_1, e_1, f_1, g_1PolyLine(K, L, M) → a_1Mirror(C', A) → C''Mirror(poly2, A) → poly2'Circle(N, (5 * zr)) → h_1Intersect(c_1, h_1, 2) → OPolyLine(K, O, N) → i_1Segment(A, C'') → j_1Circle(A, r1) → k_1Circle(B, r2) → p_1Sequence(Arc[k_1, Rotate[F, Min[3.141592653589793, Max[0, (((chaine * i) + posass) / cc1 * pi)]], A], Rotate[F, Max[0, Min[3.141592653589793, (((chaine * i) + posass + chaine / 2) / cc1 * pi)]], A]], i, 0, round(cc1 / chaine)) → liste5Sequence(Arc[p_1, Rotate[E', Min[3.141592653589793, Max[0, (((chaine * i) + posdr) / cc2 * pi)]], B], Rotate[E', Max[0, Min[3.141592653589793, (((chaine * i) + posdr + chaine / 2) / cc2 * pi)]], B]], i, 0, round(cc2 / chaine)) → liste7Sequence(Segment[F' + (u * Min[1, Max[0, ((chaine * i) + posdeb) / l]]), F' + (u * Min[1, Max[0, ((chaine * i) + posdeb + chaine / 2) / l]])], i, 0, If[(chaine * lien) + posdeb > l, lien - 1, lien]) → liste6Sequence(Segment[E + (w * Min[1, Max[0, ((chaine * i) + poslet) / l]]), E + (w * Min[1, Max[0, ((chaine * i) + poslet + chaine / 2) / l]])], i, 0, If[(chaine * lien) + posdeb > l, lien - 1, lien]) → liste8Element(liste1, Length[liste1]) → l_1CircumcircleArc(H, H - v_1, I) → pPoint(n) → QSegment(P, Q) → m_1Point(a_1) → TSegment(S, A_1) → r_1Segment(R, S) → q_1Circle(U, 1.32) → s_1Segment(R, V) → t_1Segment(R, K) → n_1CircumcircleArc(H, Z, P) → c_2Point(s_1) → C_1Point(s_1) → D_1Segment(F_1, C_1) → b_2CircleArc(U, D_1, C_1) → d_2Segment(R, U) → e_2Segment(A_1 + (-0.15, 0.5), V) → a_2Segment(H_1, I_1) → f_2Sequence(K_1 + ((10 * i), 0), i, 0, 12) → liste9Vector(K_1, L_1) → zSequence(Translate[image5, Vector[(i * z)]], i, -2, 12) → liste10Line(J_1, xAxis) → g_2Polygon(J_1, J_1 + (120, 0), J_1 + (120, -30), J_1 + (0, -30)) → poly3, j_2, h_2, i_2, k_2
AI 绘图提示语参考
绘制一个以菱形为核心的几何侦探主题图形。菱形由两条对角线分割,顶点处有旋转的扇形和圆弧,周围分布着多个小三角形和多边形,形成对称的装饰图案。从菱形中心向外延伸出若干条线段和向量,连接着圆、圆弧和交点。图形中包含多个圆,其中两个较大的圆相交,交点与菱形顶点相连。整体构图强调角度关系、对称性和几何变换,适合用于探索菱形性质的互动教学场景。
以上提示语为根据原始绘图命令整理而来,仅供参考。