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On the Intersection Equation of a Hyperboloid and a Plane

机译:关于双曲面和平面的相交方程

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In this note, the ideas employed in [1] to treat the problem of an ellipsoid intersected by a plane are applied to the analogous problem of a hyperboloid being intersected by a plane. The curves of intersection resulting in this case are not only ellipses but rather all types of conics: ellipses, hyperbolas and parabolas. In text books of mathematics usually only cases are treated, where the planes of intersection are parallel to the coordinate planes. Here the general case is illustrated with intersecting planes which are not necessarily parallel to the coordinate planes.
机译:在本说明中,将[1]中所用的想法用来解决一个椭圆与一个平面相交的问题,将其应用于类似一个双曲面与一个平面相交的问题。在这种情况下产生的相交曲线不仅是椭圆,而且是所有圆锥形:椭圆,双曲线和抛物线。在数学教科书中,通常只处理交集平面平行于坐标平面的情况。在此,一般情况以相交平面示出,该相交平面不必平行于坐标平面。

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