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What is the name of the point of intersection of a line drawn from an apex of a...

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etotheeyepi | Student, Undergraduate | (Level 1) Valedictorian

Posted October 13, 2012 at 3:26 PM via web

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What is the name of the point of intersection of a line drawn from an apex of a tetrahedron such that it is perpendicular to the opposite face?

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etotheeyepi | Student, Undergraduate | (Level 1) Valedictorian

Posted October 14, 2012 at 5:43 PM (Answer #1)

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A line drawn from a tetrahedorn's apex to the opposite face, which I suppose would be called the base, should be called the height. That all seems more or less straight forward.  What should one call the point of intersection between the height and the base?  If there is no standard word, maybe I'll make up a name, like maybe "Eto's Point" for want of a better name.

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etotheeyepi | Student, Undergraduate | (Level 1) Valedictorian

Posted November 17, 2012 at 2:58 AM (Answer #2)

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I'm going to answer my own question.  The point of intersection between the altitude and the opposite plane of an tetrahedron should be called the center of the face.  Any triangle has four centers, in center, orthocenter, circumcienter, and centrod depending on how the center is defined.  With an equilateral triangle, all of the centers are in the same place, so I figure i should call it the center.

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