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Poughkeepsie Chapter of the Association For Computing Machinery

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Program: Minimal Angular Determinations for Convex Polygons

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

Where: Presentation Room (2 nd floor, Rm 2023)

Hancock Center, Marist College

Directions: Building #16 on the map at http://www.marist.edu/welcome/map.html

Parking: Please park at black dot #11 on http://www.marist.edu/welcome/map.html (the lot North of the Hancock Center #16) or in the lot East of Route 9, S/E of the former Main Entrance.

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, "minimal angular determination", for U(n) and for interesting subsets of U(n).

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

In 2010, a paper by Disser, Mihalak, and Widmeyer shows 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: Dr. Silberger is an Emeritus in the SUNY-NewPaltz Mathematics Dept., & a retired Head of its Graduate Program. He received his AB in physics from Harvard, and his MS & PhD in mathematics from the University of Washington. He's taught 2 years in high school and 50 years in colleges & universities in the Americas. He's directed 14 Masters theses, several of which resulted in papers that appeared in the research literature. He's published with a large number of his colleagues & students. So far, 3 dozen of his articles occur in refereed journals, and, at age 85, he is still producing new results. All 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.

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Cost: Our meeting is Free and open to the public

Dinner: 6:00 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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