Pi: Perbedaan antara revisi
Konten dihapus Konten ditambahkan
Alex Neman (bicara | kontrib) kTidak ada ringkasan suntingan |
Add 3 books for Wikipedia:Pemastian (20231209)) #IABot (v2.0.9.5) (GreenC bot |
||
Baris 19:
{{pi}} umumnya didefinisikan sebagai [[rasio]] [[keliling]] [[lingkaran]] {{math|''C''}} dengan [[diameter]]nya {{math|''d''}}:<ref name="Arndt">{{harvnb|Arndt|Haenel|2006|p=8}}</ref>
:<math> \pi = \frac{C}{d}</math>
Rasio {{math|''C''/''d''}} bernilai konstan tak tergantung pada ukuran lingkaran. Contohnya, jika suatu lingkaran memiliki diameter dua kali lipat daripada lingkaran lainnya, ia juga akan memiliki keliling yang dua kali lipat lebih besar, sehingganya nilai rasio {{math|''C''/''d''}} akan tetap sama. Definisi {{pi}} seperti ini secara implisit menggunakan [[geometri Euklides]]. Walaupun gagasan akan lingkaran juga dapat diperluas ke dalam geometri non-Euklides, namun lingkaran yang baru ini tidak akan lagi memenuhi rumus {{math|{{pi}} {{=}} ''C''/''d''}}.<ref name="Arndt" /> Terdapat pula definisi {{pi}} lainnya yang tidak menyebut-nyebut lingkaran sama sekali, yakni: {{pi}} adalah bilangan yang bernilai dua kali lipat dari bilangan positif terkecil {{math|''x''}} yang mana {{math|[[Kosinus|cos]](''x'')}} sama dengan 0.<ref name="Arndt" /><ref>{{cite book|last=Rudin|first=Walter|title=Principles of Mathematical Analysis|url=https://archive.org/details/principlesofmath00rudi|publisher=McGraw-Hill|year=1976|isbn=0-07-054235-X|ref=harv}}, p 183.</ref>
=== Ciri-ciri ===
Baris 349:
* {{cite book|last=Beckmann|first=Peter|title=History of Pi|url=https://archive.org/details/historyofpisymbo00beck|publisher=St. Martin's Press|year=1989|origyear=1974|isbn=978-0-88029-418-8|ref=harv}}
* {{cite book|last=Borwein|first=Jonathan|author1-link=|last2=Borwein|first2=Peter|author2-link=|title=Pi and the AGM: a Study in Analytic Number Theory and Computational Complexity|publisher=Wiley|year=1987|isbn=978-0-471-31515-5|ref=harv}}
* {{cite book|last=Boyer|first=Carl B.|last2=Merzbach|first2=Uta C.|year=1991|title=A History of Mathematics|url=https://archive.org/details/historyofmathema00boye|edition=2|publisher=Wiley|isbn=978-0-471-54397-8|ref=harv}}<!-- Year from ISBN. Original citatation was just to Boyer. Possible that edition is wrong and therefore page is wrong. Editions: Boyer 1968, Boyer/Merzbach 1989, Boyer/Merzbach 1991, Merzbach/Boyer 2010, Merzbach/Boyer 2011. Verify second: Hui and 3072-sided polygon is on cited page 202 of 1991 edition; page 228 of 1968 edition. Google snippet has a hit for 3.1456 on page 168 for 1991, but does not show the number. -->
* {{cite book|last=Bronshteĭn|first=Ilia|last2=Semendiaev|first2=K. A.|title=A Guide Book to Mathematics|publisher=H. Deutsch|year=1971|isbn= 978-3-871-44095-3|ref=harv}}
* {{cite book|last=Eymard, Pierre, Lafon, Jean Pierre|year=1999|title=The Number Pi|url=https://archive.org/details/numberpi0000eyma|publisher=American Mathematical Society|isbn=978-0-8218-3246-2|ref=harv}}, English translation by Stephen Wilson.
* {{cite book|last=Joseph|first=George Gheverghese|title=The Crest of the Peacock: Non-European Roots of Mathematics|publisher=Princeton University Press|year=1991|isbn=978-0-691-13526-7|url=http://books.google.com/?id=c-xT0KNJp0cC&printsec=frontcover#v=onepage&q&f=false%7C|ref=harv|accessdate=2013-06-05}}<!-- This ISBN is for the third edition from 2011! -->
* {{cite book|last=Posamentier|first=Alfred S.|last2=Lehmann|first2=Ingmar|title=Pi: A Biography of the World's Most Mysterious Number|url=https://archive.org/details/pi00alfr_0|publisher=Prometheus Books|year=2004|isbn=978-1-59102-200-8|ref=harv}}
* {{cite journal|last=Reitwiesner|first=George|title=An ENIAC Determination of pi and e to 2000 Decimal Places|journal=Mathematical Tables and Other Aids to Computation|year=1950|volume=4|issue= 29|pages=11–15|doi=10.2307/2002695|ref=harv }}
* {{cite journal|last=Roy|first=Ranjan|title=The Discovery of the Series Formula for pi by Leibniz, Gregory, and Nilakantha|url=https://archive.org/details/sim_mathematics-magazine_1990-12_63_5/page/291|journal=Mathematics Magazine|volume=63|issue= 5|year=1990|pages=291–306|doi=10.2307/2690896|ref=harv }}
| |||