变换游戏
几何画板及绘图内容加载中,请稍等……
这个范例通过游戏的形式演示了图形的变换,包括平移、镜像和旋转等。它涉及的核心数学概念是坐标几何中的变换。通过使用GeoGebra命令如Point、Rotate、Mirror等,可以构造出动态的几何图形。适合初中及以上学生学习几何变换和相关概念。
GeoGebra 命令及参数
Point(yAxis) → CCircle(C, D) → cPoint(c) → RotateRotate(Rotate, 120*°, C) → E'Rotate(Rotate, 90*°, C) → E'_1Mirror(Rotate, C) → E'_2Mirror(E'_1, C) → V_1Point(c) → C_2CircleArc(C, C_2, Rotate) → dAngle(C_2, C, Rotate) → αPoint(c) → U_2Rotate(U_2, 90*°, C) → V_2Rotate(U_2, -90*°, C) → W_2LaTeX(right, true, true) → text5Textfield(B1) → inputBox1Element(list1, a) → βPolygon(J, K, L) → poly1, l, j, kPolygon(J', K', L') → poly2, l_1, j_1, k_1Rotate(J, 90*°, C) → J'_3Rotate(K, 90*°, C) → K'_3Rotate(L, 90*°, C) → L'_3Polygon(J'_3, K'_3, L'_3) → poly1', l', j', k'Rotate(J, 180*°, C) → J'_1Rotate(K, 180*°, C) → K'_1Rotate(L, 180*°, C) → L'_1Polygon(J'_1, K'_1, L'_1) → poly1'_1, l'_1, j'_1, k'_1Rotate(J, -90*°, C) → J'_2Rotate(K, -90*°, C) → K'_2Rotate(L, -90*°, C) → L'_2Polygon(J'_2, K'_2, L'_2) → poly1'_2, l'_2, j'_2, k'_2Circle(C, K) → pCircle(C, L) → qCircle(C, J) → rRotate(K, γ, C) → K'_4Angle(K, C, K'_4) → δRotate(L, γ, C) → L'_4Angle(L, C, L'_4) → εRotate(J, γ, C) → J'_4Angle(J, C, J'_4) → ζPolygon(L'_4, K'_4, J'_4) → poly3, j'_4, l'_4, k'_4Mirror(K, xAxis) → K'_5Mirror(J, xAxis) → J'_5Mirror(L, xAxis) → L'_5Mirror(K, yAxis) → K'_6Mirror(J, yAxis) → J'_6Mirror(L, yAxis) → L'_6Midpoint(J, J'_5) → J_1Midpoint(K, K'_5) → K_1Midpoint(L, L'_5) → E_3Circle(K_1, K) → sCircle(J_1, J) → tCircle(E_3, L) → c_1Rotate(K, η, K_1) → K'_7Angle(K, K_1, K'_7) → θRotate(J, η, J_1) → J'_7Angle(J, J_1, J'_7) → ιRotate(L, η, E_3) → L'_7Angle(L, E_3, L'_7) → κSegment(K, K'_5) → mSegment(J, J'_5) → nSegment(L, L'_5) → a_1Line(K'_7, xAxis) → b_1Line(J'_7, xAxis) → d_1Line(L'_7, xAxis) → e_1Intersect(b_1, m) → F_3Intersect(n, d_1) → G_3Intersect(a_1, e_1) → H_3Polygon(F_3, G_3, H_3) → poly4, h_3, f_3, g_3Midpoint(K'_6, K) → I_3Circle(I_3, K) → f_1Rotate(K, η, I_3) → K'_8Angle(K, I_3, K'_8) → λSegment(K'_6, K) → g_1Line(K'_8, yAxis) → h_1Intersect(h_1, g_1) → M_3Midpoint(J, J'_6) → N_3Circle(N_3, J) → p_1Rotate(J, η, N_3) → J'_8Angle(J, N_3, J'_8) → μSegment(J'_6, J) → i_1Line(J'_8, yAxis) → m_1Intersect(i_1, m_1) → O_3Midpoint(L'_6, L) → P_3Circle(P_3, L) → q_1Rotate(L, η, P_3) → L'_8Angle(L, P_3, L'_8) → νSegment(L'_6, L) → n_1Line(L'_8, yAxis) → r_1Intersect(r_1, n_1) → Q_3Polygon(Q_3, M_3, O_3) → poly5, o_3, q_3, m_3LaTeX(wrong, true, true) → text11Point(xAxis) → L_1Mirror(pic1, xAxis) → pic1'Mirror(pic1', xAxis) → pic1''Rotate(pic1'', 90*°, C) → pic1'''Rotate(pic1', 90*°, C) → pic1''_1Textfield(Date) → inputBox2Textfield(Name) → inputBox3
AI 绘图提示语参考
画一个坐标系,包含y轴上的一个点,以该点为圆心画一个圆,圆上取一点并旋转120度和90度得到两个新点,再将这两个点关于圆心对称得到另外两个点,最后将圆上的一点和旋转后的点连接成线段,并标注角度和线段长度。
以上提示语为根据原始绘图命令整理而来,仅供参考。