椭圆极坐标连接
几何画板及绘图内容加载中,请稍等……
所属专题
Ellipse Analysis
①本范例演示了椭圆的极坐标连接及其几何性质;②涉及核心数学概念包括椭圆、极坐标、相似三角形、向量与变换;③作图要点:使用 Circle, Point, Line, Midpoint, OrthogonalLine, Intersect, Locus, Segment, Distance, Angle, Vector, CurveCartesian, Length 等命令构建图形;④适合高中及以上学生及数学爱好者用于理解解析几何与几何变换。
GeoGebra 命令及参数
Circle(A, B) → cPoint(c) → CLine(A, C) → fPoint(xAxis) → DLine(C, D) → gMidpoint(D, C) → EOrthogonalLine(E, g) → hIntersect(f, h) → FLine(D, F) → iLocus(F, C) → loc1Midpoint(A, D) → GOrthogonalLine(G, xAxis) → jSegment(D, F) → kLine(F, xAxis) → lSegment(A, F) → mOrthogonalLine(E_d, l) → pIntersect(l, p) → HSegment(F, H) → qDistance(D, J) → distanceDJDistance(G, J) → distanceGJDistance(G, D) → distanceGDAngle(D, A, F) → αVector(A, F) → uCircle(I, 1) → dCircle(I, 2) → rCircle(I, 3) → c_1Circle(I, 4) → d_1Circle(I, 5) → e_1Circle(I, 6) → f_1Circle(I, 7) → g_1Circle(I, 8) → h_1Circle(I, 9) → k_1Circle(I, 10) → p_1Circle(I, 11) → q_1Circle(I, 12) → r_1Circle(I, 13) → s_1Circle(I, 14) → t_1Circle(I, 15) → c_2Segment(G, K) → bSegment(G, J) → i_1Segment(R, S) → j_1Segment(D, K) → l_1Midpoint(I, D) → TIntersect(p, q) → UAngle(D, I, F) → βCurveCartesian((cos(t) * E_b^(2) / E_a / (1 - (E_c / E_a * cos(t)))), (sin(t) * E_b^(2) / E_a / (1 - (E_c / E_a * cos(t)))), t, 0, (2 * π)) → wDistance(D, p) → distanceDpIntersect(p, xAxis) → VSegment(S, W) → m_1Length(u) → a_1Distance(I, F) → distanceIFTableText({{A2, B2}, {A3, B3}, {A4, B4}, {A5, B5}, {A6, B6}, {A7, B7}, {A8, B8}, {A9, B9}, {A10, B10}, {A11, B11}, {A12, B12}, {A13, B13}}, "|_") → text1
AI 绘图提示语参考
绘制一个椭圆,并通过极坐标连接椭圆上的点,展示椭圆的几何性质。首先画一个圆,然后在圆上取一点C,通过C点画一条直线f与x轴相交于D点,取D和C的中点E,画E的垂线h与f交于F点,通过F点画直线i,Locus(F, C)得到轨迹loc1。接着画D和F的中点G,画G的垂线j,画D到F的线段k,画F到x轴的线段l,画A到F的线段m,画F的垂线p,取p和l的交点H,画D到H的线段q,计算D到J的距离distanceDJ,G到J的距离distanceGJ,G到D的距离distanceGD,以及角DAF的度数α,画向量AF,画圆d、r、c1、d1、e1、f1、g1、h1、k1、p1、q1、r1、s1、t1、c2,画线段GK、GJ、RS、DK,取I的中点T,取p和q的交点U,计算角DAF的度数β,画曲线w,计算D到p的距离distanceDp,取p和x轴的交点V。
以上提示语为根据原始绘图命令整理而来,仅供参考。