Zobrazeno 1 - 10
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pro vyhledávání: '"Pick's theorem"'
Autor:
Binder, Sage, Kosaian, Katherine
We formalize Pick's theorem for finding the area of a simple polygon whose vertices are integral lattice points. We are inspired by John Harrison's formalization of Pick's theorem in HOL Light, but tailor our proof approach to avoid a primary challen
Externí odkaz:
http://arxiv.org/abs/2405.01793
Autor:
ÖZ, Halil Rıdvan1 hridvan.oz@igdir.edu.tr
Publikováno v:
Journal of the Institute of Science & Technology / Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi. Dec2023, Vol. 13 Issue 4, p2915-2925. 11p.
Autor:
Si, Lin
In this note, we given a version of Pick's theorem for the simple lattice polygon in two-dimensional subspace of R^3.
Externí odkaz:
http://arxiv.org/abs/2111.15353
We add another brick to the large building comprising proofs of Pick's theorem. Although our proof is not the most elementary, it is short and reveals a connection between Pick's theorem and the pointwise convergence of multiple Fourier series of pie
Externí odkaz:
http://arxiv.org/abs/1909.03435
Autor:
Stephenson, Paul
Publikováno v:
Mathematics in School, 2018 Sep 01. 47(4), 35-38.
Externí odkaz:
https://www.jstor.org/stable/26534777
Publikováno v:
In Graphical Models May 2020 109
Autor:
Kowalski, Jacek M.
We review and possibly add some new variant to the existing derivations of the formula for the area of Jordan lattice polygons drawn on two-dimensional lattices. The formula is known as Pick's theorem and is related to the number theory elementary re
Externí odkaz:
http://arxiv.org/abs/1707.04808
Kniha
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Autor:
Levy, Karl, Nathanson, Melvyn B.
Publikováno v:
in: Connections in Discrete Mathematics, Cambridge University Press, 2018, pp. 278--282
Pick's theorem is used to prove that if $P$ is a lattice polygon (that is, the convex hull of a finite set of lattice points in the plane), then every lattice point in the $h$-fold sumset $hP$ is the sum of $h$ lattice points in $P$.
Comment: 4
Comment: 4
Externí odkaz:
http://arxiv.org/abs/1511.02747
Autor:
Rosner, Haim Shraga
We give an algorithmic proof of Pick's theorem which calculates the area of a lattice-polygon in terms of the lattice-points.
Externí odkaz:
http://arxiv.org/abs/1407.0586