几何均值 by olperocchi02
几何画板及绘图内容加载中,请稍等……
这个范例演示了如何通过几何均值的概念来构造图形。它涉及的核心数学概念包括几何均值、圆和角度。通过使用GeoGebra命令如Segment、Semicircle、Point等,可以构造出几何均值相关的图形。适合高中数学教学和学习。
GeoGebra 命令及参数
Segment(Z, A_1) → t_1Semicircle(Z, A_1) → d_1Point(d_1) → B_1OrthogonalLine(B_1, t_1) → a_1Intersect(t_1, a_1) → C_1Segment(C_1, A_1) → h_2Segment(Z, C_1) → g_2Line(A, B) → fOrthogonalLine(C, f) → gRotate(A, (-(90°)), C) → A'Angle(A', C, A) → αLine(C, A') → hIntersect(f, h) → DIntersect(f, g) → EPolygon(A, C, E) → poly1, e, a, cPolygon(E, C, D) → poly2, d, e_1, c_1Segment(E, C) → iSegment(E, C) → jSegment(A, E) → kSegment(E, D) → lTableText({{A1, B1, C1, D1, E1}, {A2, B2, C2, D2, E2}, {A3, B3, C3, D3, E3}, {A4, B4, C4, D4, E4}, {A5, B5, C5, D5, E5}, {A6, B6, C6, D6, E6}, {A7, B7, C7, D7, E7}}, "|_") → text4TableText({{A9, B9, C9, D9, E9}, {A10, B10, C10, D10, E10}, {A11, B11, C11, D11, E11}, {A12, B12, C12, D12, E12}, {A13, B13, C13, D13, E13}, {A14, B14, C14, D14, E14}, {A15, B15, C15, D15, E15}, {A16, B16, C16, D16, E16}, {A17, B17, C17, D17, E17}, {A18, B18, C18, D18, E18}, {A19, B19, C19, D19, E19}}, "|_") → text6Semicircle(F, G) → pPoint(p) → HSegment(F, G) → nMidpoint(n) → IPolygon(H, F, G) → poly3, g_1, h_1, f_1Semicircle(R, S) → rPoint(r) → TPolygon(R, T, S) → poly6, s, r_1, tOrthogonalLine(T, t) → i_1Intersect(i_1, t) → USegment(U, T) → q_1Polygon(N, O, 4) → poly5, q, n_1, p_1, s_1, P, QPolygon(Z, B_1, A_1) → poly7, a_2, z_1, b_1Segment(B_1, C_1) → f_2Textfield(u) → InputBox1Segment(A_1, D) → i_2Segment(B_1, C_1) → GeometricMean_1Segment(D_1, H) → GeometricMeanSegment(E_1, H) → MeanOrthogonalLine(H, n) → l_2Intersect(n, h_1) → F_1Intersect(l_2, n) → G_1Midpoint(n) → H_1Segment(F, G_1) → m_2Segment(G_1, G) → n_2Segment(U, R) → j_2Segment(U, S) → k_2Rotate(R, 90°, U) → R'OrthogonalLine(R', i_1) → j_1OrthogonalLine(S, j_1) → k_1Intersect(j_1, k_1) → JPolygon(U, R', J, S) → ab, u_1, r', j_3, s_2CircleArc(U, R, R') → c_2Segment(R, U) → l_1Line(F, G) → m_1OrthogonalLine(H, m_1) → p_2Intersect(m_1, p_2) → KSegment(F, K) → q_2Segment(K, G) → r_2Segment(H, K) → t_2
AI 绘图提示语参考
画一个几何平均数的图形,包含一条线段和其半圆,在线段上找到中点并画出垂线,与半圆相交得到一个点,连接该点与线段两端,形成两个三角形。再画出线段的垂线并旋转得到另一个点,连接该点与线段的一端,形成另一个三角形。最后标注出几何平均数相关的线段和角度,展示几何平均数的概念。
以上提示语为根据原始绘图命令整理而来,仅供参考。