动画演示几何变换与图形构造
几何画板及绘图内容加载中,请稍等……
所属专题
Geometry Review
①本范例通过动画演示了点、圆、向量等几何元素的动态变换与交点构造;②涉及核心数学概念包括角度、解析几何、参数方程、几何变换等;③作图要点运用了Circle, Point, Segment, Intersect, Rotate, Translate, Vector等GeoGebra命令;④适合高中及以上学生用于理解几何变换、参数方程及解析几何的应用。
GeoGebra 命令及参数
Circle(A, B) → c_3Point(c_3) → CPoint(c_3) → DCircleArc(A, C, D) → d_3CircleArc(A, D, C) → ePoint(d_3) → EPoint(e) → FSegment(E, F) → fSegment(C, D) → gIntersect(f, g) → GSegment(A, B) → hSegment(D, E) → iSegment(F, C) → jCircle(D, (0.2 * h)) → kCircle(F, (0.2 * h)) → pIntersect(k, g, 1) → HIntersect(k, i, 1) → IIntersect(p, j, 1) → JIntersect(p, f, 1) → KCircleSector(D, H, I) → qLine(F, g) → lIntersect(p, l, 1) → LAngle(L, F, C) → αCircleArc(A, C, E) → rCircleArc(A, D, F) → sCircleArc(A, F, C) → tCircleArc(A, E, D) → c_1Segment(E, G) → cSegment(G, F) → dSegment(D, G) → bSegment(G, C) → aCircle(E, (0.2 * h)) → d_1Circle(C, (0.2 * h)) → e_1Intersect(e_1, a, 1) → MIntersect(d_1, i, 1) → NIntersect(d_1, f, 1) → OLine(C, i) → f_1Intersect(e_1, f_1) → P, QAngle(M, C, P) → βCircleSector(E, N, O) → g_1Dilate(D, If[0 < o ≤ 1, 1 - o, 0], F) → D'Vector(D, D') → uDilate(D, If[0 < o ≤ 1, 1 - o, 0], E) → D'_1Segment(D, D'_1) → h_1Dilate(F, If[1 < o ≤ 2, 2 - o, 0], C) → D'_2Segment(F, D'_2) → i_1CircleArc(A, D, F) → k_1CircleArc(A, C, E) → p_1Polygon(F, G, C) → poly1, c_2, f_2, g_2Polygon(E, D, G) → poly2, g_3, e_2, d_2Dilate(D, If[2 < o ≤ 3, 3 - o, 0], F) → D'_3Vector(D, D'_3) → vTranslate(q, v) → q'Rotate(q', If[3 < o ≤ 4, ((o - 3) * α), α], F) → q''Dilate(E, If[4 < o ≤ 5, 5 - o, 0], C) → E'Vector(E, E') → wTranslate(g_1, w) → q_1Rotate(q_1, If[5 < o ≤ 6, ((-(o - 5)) * β), (-β)], C) → r_1
AI 绘图提示语参考
画一个动态演示几何变换和交点构造的动画图形,包含点、圆、线段和向量。展示圆的相交、旋转和平移,以及参数方程的应用。关键对象有两条线段的交点,通过旋转和平移生成的圆弧,以及这些圆弧的交点。最终形成多个圆和线段构成的复杂几何结构,体现坐标几何和几何变换的核心概念。
以上提示语为根据原始绘图命令整理而来,仅供参考。