91.70 An elementary proof of Pick's theorem

  title={91.70 An elementary proof of Pick's theorem},
  author={J. Trainin},
  journal={The Mathematical Gazette},
  pages={536 - 540}
  • J. Trainin
  • Published 1 November 2007
  • Mathematics
  • The Mathematical Gazette
6 Citations
Flipping Geometric Triangulations on Hyperbolic Surfaces
It is proved that the flip graph of geometric triangulations with fixed vertices of a flat torus or a closed hyperbolic surface is connected and upper bounds are given on the number of edge flips that are necessary to transform any geometric Triangulation on such a surface into a Delaunay triangulation.
On teaching sets for 2-threshold functions of two variables
We consider k-threshold functions of n variables, i.e. the functions representable as the conjunction of k threshold functions. For n = 2, k = 2, we give upper bounds for the cardinality of the
An Algorithmic Approach to Pick's Theorem
We give an algorithmic proof of Pick's theorem which calculates the area of a lattice-polygon in terms of the lattice-points.
On a Relation Between the Integral Image Algorithm and Calculus
Theoretical aspects of the Integral Image algorithm's continuous version are discussed, including a novel integration method over curves in the plane and a theorem that extends the algorithm to general continuous domains.
Euler's characteristics and Pick's theorem
A very general definition of a Polygon is presented to obtain the definition of faces and holes of a polygon and a generalization of Pick’s Theorem is proved for very general lattice polygons.