Citation
Rearick, David Francis (1960) Some Visibility Problems in Point Lattices. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/AH509D92. https://resolver.caltech.edu/CaltechETD:etd06232006133908
Abstract
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. We say that one lattice point is visible from another if no third lattice point lies on the line joining them. A lattice point visible from the origin is called a visible point. We study the manner in which the visible points are distributed throughout the lattice and show that, in a kdimensional lattice, the fraction of such points in an expanding region "usually" tends to [...]. On the other hand there exist arbitrarily large "gaps" containing no visible points. The following is a typical theorem: The maximum number of lattice points mutually visible in pairs is [...], and if [...], the "density" of points visible from each of a fixed set of n points, themselves mutually visible in pairs, is [...]. The last section is devoted to a study of the function [...], which is defined to be the number of distinct solutions of the congruence [...] having [...]. A special case of this function arises in connection with a certain visibility problem. A typical result is that [...].
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  (Mathematics) 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Mathematics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  1 January 1960 
Record Number:  CaltechETD:etd06232006133908 
Persistent URL:  https://resolver.caltech.edu/CaltechETD:etd06232006133908 
DOI:  10.7907/AH509D92 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  2705 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  30 Jun 2006 
Last Modified:  07 Nov 2023 22:55 
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