运动对称 = 保持质心
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该 GeoGebra 范例直观演示了运动对称性下质心的不变性。通过点、线、圆弧、射线等几何构造,展示了在特定运动变换中,质心位置保持不变的数学原理。核心概念涉及对称性、质心、几何变换与三角函数关系。作图要点包括使用 Point、Segment、CircleArc、Intersect、Ray、OrthogonalLine、Angle、Line、Polygon 等命令,以及 E_k、E_ob、E_oa 等几何对象的组合应用。适合高中数学、物理及几何变换单元的教学与探究。
GeoGebra 命令及参数
Point(yAxis) → RPoint(yAxis) → ASegment(A, S) → iPoint(xAxis) → CPoint(yAxis) → BCircleArc(A, R, B) → cIntersect(c, i) → T,Ray(A, C) → bOrthogonalLine(C, b) → dCircleArc(A, C, T) → ArcPoint(d) → KAngle(C, A, Rotate[C, alfa, A]) → αOrthogonalLine(T, yAxis) → jOrthogonalLine(T, xAxis) → lIntersect(j, yAxis) → UIntersect(l, xAxis) → VSegment(A, V) → cosinusSegment(A, U) → sinusSegment(U, T) → sSegment(V, T) → tSegment(C, S) → tangensPoint(yAxis) → DPoint(yAxis) → LPoint(d) → MSegment(A, J) → mIntersect(c, m) → O,OrthogonalLine(O, yAxis) → nOrthogonalLine(O, xAxis) → pIntersect(p, xAxis) → PIntersect(n, yAxis) → QSegment(C, J) → qSegment(A, Q) → rSegment(A, P) → b_1Angle(J, A, V) → βSegment(P, O) → eSegment(O, Q) → fPoint(xAxis) → WCircleArc(A, O, C) → gSegment(T, S) → aSegment(J, O) → hSegment(V, Q) → kLine(C, k) → a_1Intersect(a_1, yAxis) → FLine(F, xAxis) → c_1Line(S, xAxis) → d_1Point(d_1) → GLine(G, yAxis) → e_1Intersect(e_1, c_1) → HSegment(G, H) → v_{ab}Segment(G, S) → g_1Segment(H, F) → h_1Segment(F, C) → i_1Polygon(A, B_1, N, U) → p_{ea}, a_2, b_2, E_{a}, uPolygon(C_1, Z, Q, A) → p_{eb}, c_2, E_{b}, q_1, a_3Polygon(C, S, D_1, D_2) → p_{ia}, c_3, E_{0a}, d_2, d_3Polygon(C, F_2, F_1, J) → p_{ib}, c_4, f_2, E_{0b}, j_1