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Lines tangent to four triangles in three-dimensional space

Identifieur interne : 005E90 ( Main/Exploration ); précédent : 005E89; suivant : 005E91

Lines tangent to four triangles in three-dimensional space

Auteurs : Hervé Brönnimann ; Olivier Devillers ; Sylvain Lazard ; Frank Sottile

Source :

RBID : CRIN:brönnimann05d

English descriptors

Abstract

We investigate the lines tangent to four triangles in three-dimensional space. By a construction, there can be as many as 62 tangents. We show that there are at most 162 connected components of tangents, and at most 156 if the triangles are disjoint. In addition, if the triangles are in (algebraic) general position, then the number of tangents is finite and it is always even.


Affiliations:

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Le document en format XML

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<div type="abstract" xml:lang="en" wicri:score="1877">We investigate the lines tangent to four triangles in three-dimensional space. By a construction, there can be as many as 62 tangents. We show that there are at most 162 connected components of tangents, and at most 156 if the triangles are disjoint. In addition, if the triangles are in (algebraic) general position, then the number of tangents is finite and it is always even.</div>
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   |texte=   Lines tangent to four triangles in three-dimensional space
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