Talk:Pick's theorem

I submit to thee that the statement provided below is not an explanation, but merely a set of instructions. I won't make any changes myself due to the popularity of rote learning. A more intuitive explanation should be shown at the top of the page.

>A simple way to explain to middle school kids in 4 simple steps. 1) count the dots on the perimeter of the figure. 2) divide the number by 2. 3) subtract 1. 4) add the interior dots. The example above would be 14 / 2 = 7 − 1 = 6 + 39 = 45.

How do you compute the Euler characteristic? —Preceding unsigned comment added by 79.37.207.183 (talk) 20:06, 27 February 2009 (UTC)

:I've rewritten the article so that you don't need to. —David Eppstein (talk) 21:50, 27 February 2009 (UTC)

References are all from the web, it's pretty sad as this seems like it surely made it into a book somewhere. I'll try to find one. Cliff (talk) 05:48, 22 March 2011 (UTC)

The proof described on this page can be found in Chapter 2 of [Beck, Matthias; Robins, Sinai (2007), Computing the Continuous Discretely, Integer-point enumeration in polyhedra, Undergraduate Texts in Mathematics, New York: Springer-Verlag, {{ISBN|978-0-387-29139-0}}, MR 2271992]. --Mattbeck (talk) 07:55, 17 June 2013 (UTC)

{{Talk:Pick's theorem/GA1}}

{{Did you know nominations/Pick's theorem}}

This is my first time posting on a talk page, as far as I can remember, so I apologize if I'm doing this wrong! Please let me know if so.

The proof in the article that makes use of Voronoi diagrams isn't correct. It seems likely that there's a valid proof that works by using the Voronoi diagram of the integer lattice, but the version laid out in the article isn't right. It's fairly easy to construct counterexamples to both of these assertions:

- "For each interior grid point of the polygon, the entire Voronoi cell is covered by the polygon."

- "Grid points on an edge of the polygon have half of their Voronoi cell covered."

Does anyone see how to fix this proof while keeping it reasonably concise? I'm not seeing it at the moment. Hmkgx (talk) 21:34, 13 December 2021 (UTC)

:Removed. I agree that it has problems, and it isn't clearly formulated as a proof in the source. It would be nice if something like that could be made to work, but trying to fix it here is the wrong way to go; we should only include it if we have a source that formulates it properly. —David Eppstein (talk) 23:29, 13 December 2021 (UTC)