创建数学模型
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①本范例演示如何使用 GeoGebra 创建和操作数学模型,包括多边形、线段、函数图像等;②涉及的核心数学概念有函数、解析几何、优化问题、概率统计等;③作图要点提炼自构造摘要,使用了 Polygon(多边形)、Line(线)、Midpoint(中点)、Segment(线段)、FitPoly(拟合多项式)等命令和对象;④适合高中及以上学生学习和教师教学使用。
GeoGebra 命令及参数
Polygon(A, E, D) → poly1, d_4, a_4, e_{16}Polygon(C, E, B) → poly2, b_4, c_2, e_1Polygon(I, E, F) → poly3, f_9, i_9, e_2Polygon(G, E, H) → poly4, h_4, g_4, e_3Polygon(A, B, E) → poly5, e_4, a_1, b_1Polygon(C, F, E) → poly6, e_5, c_1, f_6Polygon(I, H, E) → poly7, e_6, i_6, h_1Polygon(G, D, E) → poly8, e_7, g_1, d_1Polygon(A, D, E) → poly9, e_8, a_2, d_2Polygon(C, B, E) → poly10, e_9, c_3, b_2Polygon(I, F, E) → poly11, e_{10}, i_7, f_7Polygon(G, H, E) → poly12, e_{11}, g_2, h_2Polygon(A, B, E) → poly13, e_{12}, a_3, b_3Polygon(F, C, E) → poly14, e_{13}, f_8, c_4Polygon(H, I, E) → poly15, e_{14}, h_3, i_8Polygon(D, G, E) → poly16, e_{15}, d_3, g_3Textfield(a) → InputBox1Line(L, M) → c_{answer}Line(J, K) → b_{answer}Textfield(b) → InputBox2Textfield(c) → InputBox3Textfield(d_{a1}) → InputBox4Textfield(d_{b1}) → InputBox5Textfield(d_{c1}) → InputBox6Polygon(W_1, W_2, W_3, W_4) → poly17, w_1, w_2, w_3, w_4Midpoint(W_1, W_2) → NMidpoint(W_3, W_2) → OMidpoint(W_3, W_4) → PMidpoint(W_1, W_4) → QSegment(O, Q) → jMidpoint(W_1, N) → RMidpoint(N, W_2) → SMidpoint(W_3, P) → TMidpoint(W_4, P) → USegment(R, U) → kSegment(N, P) → lSegment(S, T) → mFitPoly(list11, 2) → qTextfield(e) → InputBox7Textfield(f) → InputBox8Textfield(g) → InputBox9Textfield(h) → InputBox10Polygon(A_1, C_1, B_1, D_1) → poly18, a_5, c_6, b_5, d_5Line(A_1, C_1) → i_{line3}Line(A_1, D_1) → i_{line4}Line(B_1, C_1) → i_{line1}Line(B_1, D_1) → i_{line2}Textfield(i_{answer1}) → InputBox11Textfield(i_{answer2}) → InputBox12Textfield(i_{answer3}) → InputBox13Textfield(i_{answer4}) → InputBox14Segment(A_1, C_1) → iSegment(A_1, D_1) → sSegment(B_1, C_1) → tSegment(B_1, D_1) → j_1
AI 绘图提示语参考
画多个多边形,它们共享一个公共顶点,并按顺序连接顶点形成封闭形状。再画几条线段连接多边形的顶点,并标出线段的中点。最后,用一条曲线拟合这些中点,展示函数与统计的应用。
以上提示语为根据原始绘图命令整理而来,仅供参考。