Cone SymmetryDate: 7/17/96 at 4:34:34 From: Kang hui min Subject: Symmetry for a cone Hi! Why is it that a circular cone has infinite lines of symmetry? Thanks! Date: 9/27/96 at 16:47:12 From: Doctor Jerry Subject: Re: Symmetry for a Cone Dear Kang hui min, I'll try to answer your question by first asking what does it mean for an object O to be symmetric relative to a plane P? This is like a mirror image of an object. For each point of the object in front of the mirror, there is a corresponding point in the mirror image. The object and the corresponding point are at equal distances from the mirror but on opposite sides of the mirror. So, for an object O to be symmetric relative to a plane P, for any line L perpendicular to P, if (a,b,c) is a point belonging to both L and O, then there will be a second point of O on L and at the same distance from P as the first point. I'll assume that an object O is symmetric relative to a line LL if for any line L intersecting LL and perpendicular to LL, if (a,b,c) is a point belonging to both L and O, then there will be a second point of O on L and at the same distance from LL as the first point. With this definition, a right circular cone is symmetric relative to the plane through its vertex and perpendicular to its axis. It is also symmetric relative to any plane containing its axis. A right circular cone is symmetric to its axis. It is also symmetric relative to any line passing through the vertex and perpendicular to the axis of the cone. There are infinitely many such lines. -Doctor Jerry, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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