Transactions of the Japan Society for Industrial and Applied Mathematics
Online ISSN : 2424-0982
ISSN-L : 0917-2246
Search
Advanced search
OR
Browse
Search
Current issue
Displaying 1-1 of 1 articles from this issue
Show all abstracts
    • |<
    • <
    • 1
    • >
    • >|
Theory
  • A Relationship between Orthogonal Lattice Polyhedron and Pick’s Theorem
    Sawa Komatuda, Riro Ishida, Sou Kurosawa, Seishirou Matui, Atushi Taka ...
    2025 Volume 35 Issue 2 Pages 19-56
    Published: 2025
    Released on J-STAGE: June 25, 2025
    DOIhttps://doi.org/10.11540/jsiamt.35.2_19
    JOURNAL FREE ACCESS
    Show abstractHide abstract

    Abstract. A lattice point is a point each of whose coordinates is integer. A lattice polygon is a polygon each of whose vertex is a lattice point. Pick’s theorem claims that the area M2(P) of a lattice polygon P equals to I+B/2−1, where I is the number of lattice points contained in the inner region of P, and B is the number of lattice points contained in the boundary of P. In this paper, we give some formulas like Pick’s theorem, one of which calculates volume of a orthogonal polyhedron in R3 using ratio of solid angles.

    View full abstract
    Download PDF (1722K)
    • |<
    • <
    • 1
    • >
    • >|
feedback
 Top