移动点!
几何画板及绘图内容加载中,请稍等……
所属专题
My 3D Collection
本范例展示了如何通过移动点来探索空间中的位置关系。涉及的核心数学概念包括几何变换和函数。通过使用GeoGebra命令如PointIn、Polygon、FitPoly等,学生可以直观地理解几何变换和函数的概念。适合初中及以上学生进行几何作图和探索。
GeoGebra 命令及参数
PointIn(i) → APointIn(b) → IPointIn(a) → EPolygon((x(E), y(E)), (x(A), y(A)), (x(I), y(I)), (x(E), y(I))) → Polígon1, p, q, r, f_1PointIn(a) → BPointIn(a) → CPointIn(a) → DPointIn(b) → FPointIn(b) → GPointIn(b) → HFitPoly({(y(A), z(A)), (y(F), z(F)), (y(G), z(G)), (y(H), z(H)), (y(I), z(I))}, 4) → fFitPoly({(x(A), z(A)), (x(B), z(B)), (x(C), z(C)), (x(D), z(D)), (x(E), z(E))}, 4) → gCurveCartesian(x(A), t, f(t), t, y(A), y(I)) → cCurveCartesian(t, y(A), g(t), t, x(E), x(A)) → dSurface(u, v, g(u) + f(v), u, x(E), x(A), v, y(A), y(I)) → eOrthogonalLine(E, xOyPlane) → jOrthogonalLine(I, xOyPlane) → kIntersect(j, xOyPlane) → JIntersect(k, xOyPlane) → KSurface(t + x(M) - x(L), s + y(M) - y(L), g(t) + f(s), t, x(E), x(A), s, y(A), y(I)) → lSurface((2 * x(A)) - u, v, g(u) + f(v), u, x(E), x(A), v, y(A), y(I)) → e_xSurface(u, (2 * y(A)) - v, g(u) + f(v), u, x(E), x(A), v, y(A), y(I)) → e_ySequence(Sequence[Surface[u + ((2 * k) * s), v + ((2 * l) * t), g(u) + f(v), u, x(E), x(A), v, y(A), y(I)], k, -2, 2], l, -2, 2) → l1Sequence(Sequence[Surface[(2 * x(A)) - u + ((2 * k) * s), v + ((2 * l) * t), g(u) + f(v), u, x(E), x(A), v, y(A), y(I)], k, -2, 2], l, -2, 2) → l2Sequence(Sequence[Surface[u + ((2 * l) * s), (2 * y(A)) - v + ((2 * k) * t), g(u) + f(v), u, x(E), x(A), v, y(A), y(I)], k, -2, 2], l, -2, 2) → l3Surface((2 * x(A)) - u, (2 * y(A)) - v, g(u) + f(v), u, x(E), x(A), v, y(A), y(I)) → e_{xy}Sequence(Sequence[Surface[(2 * x(A)) - u + ((2 * l) * s), (2 * y(A)) - v + ((2 * k) * t), g(u) + f(v), u, x(E), x(A), v, y(A), y(I)], k, -2, 2], l, -2, 2) → l4PointIn(Polígon1) → PPSequence(Sequence[((2 * x(A)) - x(PP) + ((2 * k) * s), y(PP) + ((2 * l) * t), g(x(PP)) + f(y(PP))), k, -2, 2], l, -2, 2) → lp2Sequence(Sequence[(x(PP) + ((2 * l) * s), (2 * y(A)) - y(PP) + ((2 * k) * t), g(x(PP)) + f(y(PP))), k, -2, 2], l, -2, 2) → lp3Sequence(Sequence[((2 * x(A)) - x(PP) + ((2 * l) * s), (2 * y(A)) - y(PP) + ((2 * k) * t), g(x(PP)) + f(y(PP))), k, -2, 2], l, -2, 2) → lp4Sequence(Sequence[(x(PP) + ((2 * k) * s), y(PP) + ((2 * l) * t), g(x(PP)) + f(y(PP))), k, -2, 2], l, -2, 2) → lp1
AI 绘图提示语参考
绘制一个由点A、B、C、D、E、F、G、H、I构成的多边形,然后通过这些点拟合多项式函数f和g。接着,使用点E和I作为起点,分别绘制曲线c和d。最后,通过点E和I绘制曲面e,并围绕这些点绘制一系列曲面l1至l4。
以上提示语为根据原始绘图命令整理而来,仅供参考。