Pengguna:Dedhert.Jr/Uji halaman 01/7: Perbedaan antara revisi
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{{Periksa terjemahan|en|Pick's theorem}}
[[Berkas:Pick-theorem.svg|jmpl|{{color|red|{{math|''i'' {{=}} 7}}}}, {{color|green|{{math|''b'' {{=}} 8}}}}, {{math|''A'' {{=}} {{color|red|''i''}} + {{sfrac|{{color|green|''b''}}|2}} − 1 {{=}} 10}}]]
Dalam [[geometri]], '''teorema Pick''' merupakan sebuah rumus luas [[poligon sederhana]] dengan koordinat simpul berupa bilangan bulat dengan menjumlahkan titik-titik bilangan bulat dalam poligon dan batasnya. Hasil teorema ini dijelaskan pertama kali oleh [[Georg Alexander Pick]] pada tahun 1899.
== Rumus ==
Baris 22:
== Topik yang berkaitan ==
Ada beberapa topik dalam matematika yang mengaitkan luas daerah dengan jumlah titik kisi, di antaranya: [[teorema Blichfeldt]], yang mengatakan bahwa setiap bentuk yang dapat ditranslasikan memiliki setidaknya luas bentuk tersebut dalam titik kisi;<ref name="olds">{{cite book|last1=Olds|first1=C. D.|last2=Lax|first2=Anneli|last3=Davidoff|first3=Giuliana P.|year=2000|title=The Geometry of Numbers|title-link=The Geometry of Numbers|publisher=Mathematical Association of America, Washington, DC|isbn=0-88385-643-3|series=Anneli Lax New Mathematical Library|volume=41|pages=119–127|contribution=Chapter 9: A new principle in the geometry of numbers|mr=1817689|author1-link=Carl D. Olds|author2-link=Anneli Cahn Lax|author3-link=Giuliana Davidoff}}</ref> [[masalah lingkaran Gauss]] yang melibatkan batas galat antara luas lingkaran dengan jumlah titik kisi dalam lingkaran;<ref name="guy">{{cite book|last=Guy|first=Richard K.|year=2004|title=Unsolved Problems in Number Theory|location=New York|publisher=Springer-Verlag|isbn=0-387-20860-7|edition=3rd|series=Problem Books in Mathematics|pages=365–367|contribution=F1: Gauß's lattice point problem|doi=10.1007/978-0-387-26677-0|mr=2076335|author-link=Richard K. Guy}}</ref> serta masalah menghitung [[Titik bilangan bulat dalam polihedron cembung|jumlah titik bilangan bulat dalam polihedron cembung]] yang muncul dalam cabang-cabang matematika dan ilmu komputer.<ref name="barvinok">{{cite book|last=Barvinok|first=Alexander|year=2008|title=Integer Points In Polyhedra|location=Zürich|publisher=European Mathematical Society|isbn=978-3-03719-052-4|series=Zurich Lectures in Advanced Mathematics|doi=10.4171/052|mr=2455889|authorlink=Alexander Barvinok}}</ref> Dalam cabang terapan, [[planimeter titik]] merupakan perangkat berbasis transparansi yang mengestimasi luas bentuk dengan menghitung jumlah titik yang terdapat dalam bentuk tersebut.
== Rujukan ==
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<ref name=funkenbusch>{{cite journal
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<ref name=pick>{{cite journal |last=Pick |first=Georg | author-link = Georg Alexander Pick |title=Geometrisches zur Zahlenlehre |journal=Sitzungsberichte des deutschen naturwissenschaftlich-medicinischen Vereines für Böhmen "Lotos" in Prag |series=(Neue Folge) |year=1899 |volume=19 |pages=311–319 |url=https://www.biodiversitylibrary.org/item/50207#page/327 |jfm=33.0216.01 }} [http://citebank.org/node/47270 CiteBank:47270]</ref>
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<ref name=wells>{{cite book | last = Wells | first = David | title = The Penguin Dictionary of Curious and Interesting Geometry | publisher = Penguin Books | year = 1991 | contribution = Pick's theorem | pages = 183–184}}</ref>
<ref name=wiedijk>{{cite web|first=Freek|last=Wiedijk|url=https://www.cs.ru.nl/~freek/100/|title=Formalizing 100 Theorems|publisher=Radboud University Institute for Computing and Information Sciences|access-date=2021-07-10}}</ref>
}}
== Pranala luar ==
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