Editing Pick's theorem (section)

{{good article}}
{{short description|Formula for area of a grid polygon}}
{{for|the theorem in complex analysis|Schwarz lemma#Schwarz–Pick theorem}}
[[File:Farey_sunburst_6.svg|thumb|[[Farey sunburst]] of order 6, with 1 interior {{color|red|(red)}} and 96 boundary {{color|green|(green)}} points giving an area of {{nowrap|{{color|red|1}} + {{sfrac|{{color|green|96}}|2}} − 1 {{=}} 48}}{{r|kiradjiev}}]]
In [[geometry]], '''Pick's theorem''' provides a formula for the [[area]] of a [[simple polygon]] with integer [[vertex (geometry)|vertex]] coordinates, in terms of the number of integer points within it and on its boundary. The result was first described by [[Georg Alexander Pick]] in 1899.{{r|pick}} It was popularized in English by [[Hugo Steinhaus]] in the 1950 edition of his book ''Mathematical Snapshots''.{{r|gs|steinhaus}} It has multiple proofs, and can be generalized to formulas for certain kinds of non-simple polygons.