Affiliation:
1. Faculty of Mathematics and Computer Science, FernUniversität in Hagen, Germany
Abstract
Consider two paths ϕ , ψ : [ 0 ; 1 ] → [ 0 ; 1 ] 2 in the unit square such that ϕ ( 0 ) = ( 0 , 0 ), ϕ ( 1 ) = ( 1 , 1 ), ψ ( 0 ) = ( 0 , 1 ) and ψ ( 1 ) = ( 1 , 0 ). By continuity of ϕ and ψ there is a point of intersection. We prove that from ϕ and ψ we can compute closed intervals S ϕ , S ψ ⊆ [ 0 ; 1 ] such that ϕ ( S ϕ ) = ψ ( S ψ ).
Subject
Artificial Intelligence,Computational Theory and Mathematics,Computer Science Applications,Theoretical Computer Science
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