This page was last updated Mar 11, 2015.

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  Poughkeepsie Chapter of the Association For Computing Machinery

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  Program:  Minimal Angular Determinations for Convex Polygons

  Speaker:  Dr. Donald Silberger, donaldsilberger@gmail.com   


  About the Program:

  At each of the  n  vertices of a convex n-gon there are exactly 
(n-1)(n-2)  angles.  So the set  A(n)  of all "vertex-jointed" 
angles of such an n-gon is of size  n(n-1)(n-2)/2.  By an 
"angular determination" for the set  U(n)  of all convex n-gons 
we mean any subset  B  of  A(n)  such that every two convex n-
gons whose angle sizes agree throughout  B  will agree throughout 
A(n);  i.e., the two n-gons will be similar in the usual 
Euclidean sense.  We study the mads for  U(n)  and for 
interesting subsets of  U(n),  where the word "mad" is acronymic 
for "minimal angular determination".

Main Theorem:  Every mad for  U(n)  contains exactly  2n-4  angles.

In 2010, a paper by Disser, Mihalak, and Widmeyer showed that 
knowing the sizes of all  n(n-1)(n-2)/2  angles of a plane (not 
necessarily convex) n-gon enables the construction of a similar 
n-gon. Their paper alludes to others apparently authored by 
roboticists and other computer scientists.


  About the Speaker:

  Donald Silberger is an Emeritus in the SUNY-NewPaltz 
Mathematics Department, and a retired Head of its Graduate 
Program.  He received his AB in physics from Harvard, and his MS 
and PhD in mathematics from the University of Washington. He has 
taught a total of two years in high school and fifty years in 
colleges and universities in the Americas. He has directed 14 
Masters theses, several of which resulted in papers that appeared 
in the research literature. He has published with a large number 
of his colleagues and students. Thus far, three dozen of his 
articles occur in refereed journals, and -- at age 85 -- he is 
still producing new results. All of his work deals with down-to-
earth questions, which can be understood by a serious listener 
with little advanced mathematical background; he seeks live 
collaborators of all ages. His main mathematical interests 
include algebra, logic, number theory, combinatorics, topology, 
graph theory, and elementary Euclidean geometry.


  When:     7:30 pm, Monday, March 16, 2015  

  Where:    Presentation Room (2d floor, Rm 2023) 
            Hancock Center, Marist College   
            Directions:  Building 15 on the map at
            www.marist.edu/welcome/map.html

  Parking:  You can park at black dot Number 27 on the map at
            www.marist.edu/welcome/map.html or in the lot east
            of Route 9, southeast of the former Main Entrance.
            
  Cost:     Free and open to the public

  Dinner:   6 pm, Palace Diner, 845.473.1576
            Map and menu:  www.thepalacediner.com 
            All are welcome to join us for dinner.

  We thank Marist College for hosting the chapter's meetings.

  Refreshments are served after the meeting.  For further
information, email collier@acm.org or call 845.522.1971.

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