旋转对称性演示 by juliacyng
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①本范例演示图形绕中心点旋转一定角度后与原图重合的现象;②涉及核心数学概念为旋转对称性、角度、几何变换;③作图要点:使用 GeoGebra 命令 Circle(画圆)、Point(创建点)、Angle(设置角度)、Rotate(旋转对象)等构建图形;④适合初中及以上学生学习几何变换与对称性知识,也可用于数学演示。
GeoGebra 命令及参数
Circle(O, A) → cPoint(c) → BAngle(A, O, B) → αRotate(pic1, α, O) → pic1'Circle(D, C) → dPoint(d) → EAngle(C, D, E) → βRotate(pic2, β, D) → pic2'Circle(G, F) → ePoint(e) → HAngle(F, G, H) → γRotate(pic15, γ, G) → pic15'Circle(I, J) → fPoint(f) → KAngle(J, I, K) → δRotate(pic9, δ, I) → pic9'Circle(L, M) → gPoint(g) → NAngle(M, L, N) → εRotate(pic18, ε, L) → pic18'Circle(P, Q) → hPoint(h) → RAngle(Q, P, R) → ζRotate(pic5, ζ, P) → pic5'Circle(S, T) → kPoint(k) → UAngle(T, S, U) → ηRotate(pic6, η, S) → pic6'Circle(V, W) → pPoint(p) → ZAngle(W, V, Z) → θRotate(pic11, θ, V) → pic11'Circle(A_1, B_1) → qPoint(q) → C_1Angle(B_1, A_1, C_1) → ιRotate(pic13, ι, A_1) → pic13'Circle(D_1, E_1) → rPoint(r) → F_1Angle(E_1, D_1, F_1) → κRotate(pic10, κ, D_1) → pic10'Circle(G_1, H_1) → sPoint(s) → I_1Angle(H_1, G_1, I_1) → λRotate(pic7, λ, G_1) → pic7'Circle(J_1, K_1) → tPoint(t) → L_1Angle(K_1, J_1, L_1) → μRotate(pic17, μ, J_1) → pic17'Circle(M_1, N_1) → c_1Point(c_1) → O_1Angle(N_1, M_1, O_1) → νRotate(pic8, ν, M_1) → pic8'Circle(P_1, Q_1) → d_1Point(d_1) → R_1Angle(Q_1, P_1, R_1) → ξRotate(pic16, ξ, P_1) → pic16'Circle(S_1, T_1) → e_1Point(e_1) → U_1Angle(T_1, S_1, U_1) → οRotate(pic14, Angle[T_1, S_1, U_1], S_1) → pic14'Circle(V_1, W_1) → f_1Point(f_1) → Z_1Rotate(pic4, Angle[W_1, V_1, Z_1], V_1) → pic4'Circle(A_2, B_2) → g_1Point(g_1) → C_2Rotate(pic3, Angle[B_2, A_2, C_2], A_2) → pic3'Circle(D_2, E_2) → h_1Point(h_1) → F_2Rotate(pic12, Angle[E_2, D_2, F_2], D_2) → pic12'
AI 绘图提示语参考
绘制一个中心对称图形,围绕一个点旋转。首先画一个圆,然后在圆上取一个点,测量该点与圆心的夹角。接着,以圆心为中心,将圆旋转该角度。重复此过程,每次旋转不同的角度,直到形成一个具有多个旋转对称性的图形。
以上提示语为根据原始绘图命令整理而来,仅供参考。