From Homma's theorem to Pick's theorem

От теоремы Хоммы к теореме Пика
Tetsunori Kurogi, Osami Yasukura
2005-12-01
SCID:  54.1/z5w6eh39 Discuss with AI
Homma's theoremPL Gauss-Bonnet theoremPL-complexPick's theoremlattice PL-figure
Abstract (AI)
From Homma's PL Gauss-Bonnet theorem applied on a PL-complex in a plane, many generalizations of Pick's theorem on a lattice PL-figure are obtained in a unified geometric way.
Key Findings
1
Homma's PL Gauss–Bonnet theorem, applied to planar PL-complexes, provides a unified geometric framework for deriving generalizations of Pick's theorem.
2
Multiple generalizations of Pick's theorem for lattice PL-figures are obtained from Homma's theorem.
3
The work connects a planar piecewise-linear Gauss–Bonnet result with Pick-type formulas for lattice polygonal figures.
Research Object

lattice PL-figure

Research Subject

generalizations of Pick's theorem derived via Homma's PL Gauss–Bonnet theorem

Publication Details
Publication Date
2005-12-01
Journal
Publisher
ISSN
Access Type
Author Information
Authors
Tetsunori Kurogi
Osami Yasukura
Explore further
Open the scid.ai AI chat with a ready-made request: it will find papers on a similar topic and help build a literature review.
Find similar papers in the chat →
Make a presentation
100%