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矩形在抛物线下的几何构造

矩形在抛物线下的几何构造
几何画板及绘图内容加载中，请稍等……
2015-02-13 23:26
解析几何
这个范例展示了矩形位于抛物线下方的几何图形。核心数学概念包括抛物线方程、矩形面积计算以及坐标几何中的图形关系。作图要点涉及使用GeoGebra命令如Intersect、Segment、Polygon等来构造抛物线、矩形和面积计算。适合高中生或大学低年级学生用于学习解析几何和面积计算。

GeoGebra 命令及参数

  1. Intersect(f, a, (0.75, 3.4375)) → B
  2. Segment(C, B) → b
  3. Segment(B, A) → c
  4. Segment(A, D) → d
  5. Segment(D, C) → e
  6. LaTeX(AREA, true, true) → AREA_1
  7. Polygon(C, B, A, D) → poly1, c_1, b_1, a_1, d_1
  8. LaTeX(AREA, true, true) → text1
  9. AttachCopyToView(PolyLine[(1.2702033364061383, 3.032105433015351), (1.2976093029177909, 3.0869173660386564), (1.3524212359410963, 3.1417292990619616), (1.4072331689644018, 3.182838248829441), (1.4620451019877072, 3.2102442153410933), (1.530560018266839, 3.2650561483643985), (1.571668968034318, 3.2924621148760513), (1.6264809010576236, 3.3061650981318778), (1.6675898508251028, 3.3198680813877037), (1.7086988005925818, 3.33357106464353), (1.7498077503600609, 3.360977031155183), (1.7909167001275401, 3.3883829976668354), (1.8320256498950191, 3.415788964178488), (1.8731345996624982, 3.429491947434314), (1.9142435494299774, 3.4431949306901406), (1.9690554824532829, 3.4431949306901406), (2.0375703987324147, 3.4706008972017934), (2.0786793484998936, 3.4843038804576194), (2.1334912815231992, 3.4843038804576194), (2.1883032145465044, 3.4843038804576194), (2.24311514756981, 3.4843038804576194), (2.2979270805931153, 3.4843038804576194), (2.3664419968722474, 3.4843038804576194), (2.4075509466397267, 3.5117098469692722), (NaN, NaN), (1.3250152694294437, 3.2650561483643985), (1.3250152694294437, 3.2102442153410933), (1.3250152694294437, 3.155432282317788), (1.3113122861736173, 3.100620349294483), (1.3524212359410963, 3.1143233325503092), (1.4072331689644018, 3.1143233325503092), (1.4620451019877072, 3.1143233325503092), true], 1, (-6.362358337089147, -2.298355053501084), (8.35464567966837, 6.15638561534375), (-126, 575), (948, -42.00000000000001)) → stroke1

AI 绘图提示语参考

画一个抛物线，并在其下方画一个矩形，矩形的一边与抛物线相切，另一边与x轴平行，计算并显示矩形的面积，展示抛物线与矩形的几何关系，从抛物线与x轴的交点到矩形顶点的连线构成矩形，最后用平滑曲线连接矩形顶点形成闭合图形。
以上提示语为根据原始绘图命令整理而来，仅供参考。