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GeoGebra 3D 立体几何作图示例

GeoGebra 3D 立体几何作图示例
几何画板及绘图内容加载中，请稍等……
2025-03-12 16:02
所属专题 FLINKe Bedienung
本范例演示了如何使用GeoGebra 3D工具构建三角形与圆的立体几何图形。核心数学概念包括三角形、圆、角和立体几何。作图要点涉及使用CornerThreeD、PointIn、Intersect等GeoGebra命令，以及viewStart、quader等对象。适合高中生或大学低年级学生用于学习立体几何和几何作图。

GeoGebra 命令及参数

  1. CornerThreeD(-1, 11) → viewActual
  2. PointIn(xOyPlane) → quaderA
  3. PointIn(xOyPlane) → quaderB
  4. Point(OrthogonalLine[quaderB, Plane[Segment[quaderA, quaderB], OrthogonalLine[quaderA, xOyPlane]]]) → quaderC
  5. Intersect(Line[quaderA, Segment[quaderB, quaderC]], Line[quaderC, Segment[quaderA, quaderB]]) → quaderD
  6. Point(OrthogonalLine[quaderA, xOyPlane]) → quaderE
  7. If(x(speechBubbleStart) < x((0.5 * (speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0)))), {PolyLine[(0.5 * (speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0))) + ((sqrt((x(speechBubbleB) - x(speechBubbleA))^(2) / 4 + (y((0.5 * (speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0))) + (0, (1.1 * (y(speechBubbleC) - y(speechBubbleB))))) - y(speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0)))^(2)) * cos((6 / 5 * pi))), ((y((0.5 * (speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0))) + (0, (1.1 * (y(speechBubbleC) - y(speechBubbleB))))) - y(speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0))) * sin((6 / 5 * pi)))), speechBubbleStart, (0.5 * (speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0))) + ((sqrt((x(speechBubbleB) - x(speechBubbleA))^(2) / 4 + (y((0.5 * (speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0))) + (0, (1.1 * (y(speechBubbleC) - y(speechBubbleB))))) - y(speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0)))^(2)) * cos((2 / 3 * pi))), ((-(y((0.5 * (speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0))) + (0, (1.1 * (y(speechBubbleC) - y(speechBubbleB))))) - y(speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0)))) * sin((2 / 3 * pi))))], CurveCartesian[(0.5 * (speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0))) + ((sqrt((x(speechBubbleB) - x(speechBubbleA))^(2) / 4 + ((0.5 * (y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2 + y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2)) + (1.1 * (y(speechBubbleC) - y(speechBubbleB))) - (y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2))^(2)) * cos(t)), ((-((0.5 * (y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2 + y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2)) + (1.1 * (y(speechBubbleC) - y(speechBubbleB))) - (y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2))) * sin(t))), t, 0, (2 / 3 * pi)], CurveCartesian[(0.5 * (speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0))) + ((sqrt((x(speechBubbleB) - x(speechBubbleA))^(2) / 4 + ((0.5 * (y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2 + y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2)) + (1.1 * (y(speechBubbleC) - y(speechBubbleB))) - (y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2))^(2)) * cos(t)), (((0.5 * (y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2 + y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2)) + (1.1 * (y(speechBubbleC) - y(speechBubbleB))) - (y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2)) * sin(t))), t, 0, (6 * pi / 5)]}, {PolyLine[(0.5 * (speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0))) + ((sqrt((x(speechBubbleB) - x(speechBubbleA))^(2) / 4 + (y((0.5 * (speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0))) + (0, (1.1 * (y(speechBubbleC) - y(speechBubbleB))))) - y(speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0)))^(2)) * cos((5 / 3 * pi))), ((y((0.5 * (speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0))) + (0, (1.1 * (y(speechBubbleC) - y(speechBubbleB))))) - y(speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0))) * sin((5 / 3 * pi)))), speechBubbleStart, (0.5 * (speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0))) + ((sqrt((x(speechBubbleB) - x(speechBubbleA))^(2) / 4 + (y((0.5 * (speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0))) + (0, (1.1 * (y(speechBubbleC) - y(speechBubbleB))))) - y(speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0)))^(2)) * cos((1 / 5 * pi))), ((-(y((0.5 * (speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0))) + (0, (1.1 * (y(speechBubbleC) - y(speechBubbleB))))) - y(speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0)))) * sin((1 / 5 * pi))))], CurveCartesian[(0.5 * (speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0))) + ((sqrt((x(speechBubbleB) - x(speechBubbleA))^(2) / 4 + ((0.5 * (y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2 + y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2)) + (1.1 * (y(speechBubbleC) - y(speechBubbleB))) - (y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2))^(2)) * cos(t)), ((-((0.5 * (y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2 + y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2)) + (1.1 * (y(speechBubbleC) - y(speechBubbleB))) - (y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2))) * sin(t))), t, 0, (1 / 5 * pi)], CurveCartesian[(0.5 * (speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + speechBubbleA + (0, (y(speechBubbleC) - y(speechBubbleB)) / 2) + (x(speechBubbleB) - x(speechBubbleA), 0))) + ((sqrt((x(speechBubbleB) - x(speechBubbleA))^(2) / 4 + ((0.5 * (y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2 + y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2)) + (1.1 * (y(speechBubbleC) - y(speechBubbleB))) - (y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2))^(2)) * cos(t)), (((0.5 * (y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2 + y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2)) + (1.1 * (y(speechBubbleC) - y(speechBubbleB))) - (y(speechBubbleA) + (y(speechBubbleC) - y(speechBubbleB)) / 2)) * sin(t))), t, 0, (5 * pi / 3)]}) → speechBubble