The argument below was incomplete: another possibility is that the quadric degenerates to a point, where all 4 altitudes meet: such tetrahedra are called "orthocentric" in Richard's paper. WFL On 10/30/11, Fred lunnon <fred.lunnon@gmail.com> wrote:
This would follow almost immediately from the theorem I quoted: if two altitudes meet, the quadric must degenerate to a pair of planes; then either the other two altitudes lie on the other plane, or else three are coplanar and the tetrahedron degenerates to a prism. WFL
On 10/30/11, Joshua Zucker <joshua.zucker@gmail.com> wrote:
On Sat, Oct 29, 2011 at 5:27 PM, Fred lunnon <fred.lunnon@gmail.com> wrote:
Richard's paper mentions mentions that the 4 altitude lines of a tetrahedron, through vertices and perpendicular to faces, do not necessarily concur in a common point.
I seem to recall that if one pair of altitudes is intersecting, then the other pair is as well. Does anyone know an easy proof or counterexample?
--Joshua Zucker
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