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An interesting pair of identically distributed random tessellations, with vertices of Y‐type, which always cross orthogonally
Author(s) -
MILES R. E.
Publication year - 1988
Publication title -
journal of microscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.569
H-Index - 111
eISSN - 1365-2818
pISSN - 0022-2720
DOI - 10.1111/j.1365-2818.1988.tb04679.x
Subject(s) - independent and identically distributed random variables , vertex (graph theory) , combinatorics , type (biology) , mathematics , plane (geometry) , distribution (mathematics) , geometry , line (geometry) , random variable , mathematical analysis , statistics , geology , graph , paleontology
SUMMARY It is shown that the skeletons of the polygons determined by a line process in the plane form two identically distributed tessellations I′, I″ with all vertices of Y‐type, such that wherever I′, I″ cross, they do so at a right angle. The characteristics N̄, B̄, Ā for I′ or I″ are derived, along with the joint distribution of the random angles, at a random vertex. The space‐filling three‐dimensional versions are also considered.