Geometri proyektif: Perbedaan antara revisi
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Pada bagian akhir abad ke-19, kajian rinci tentang geometri projektif menjadi kurang bergaya lagi, meski pustaka yang membahasnya sangat banyak. Beberapa karya penting telah dibikin dalam bidang [[geometri enumeratif]] khususnya, oleh Schubert, yang kini dipandang sebagai antisipasi teori [[kelas Chern]], diambil untuk menyajikan [[topologi aljabar]] [[Grassmannian]].
[[Paul Dirac]] mengkaji geometri projektif dan menggunakannya sebagai basis untuk pengembangan konsep-konsepnya mengenai [[mekanika kuantum]], meskipun karya-karyanya yang diterbitkan selalu berbentuk aljabar. Lihatlah [http://www.math.columbia.edu/~woit/wordpress/?p=262 sebuah artikel blog] {{Webarchive|url=https://web.archive.org/web/20201020122652/http://www.math.columbia.edu/~woit/wordpress/?p=262 |date=2020-10-20 }} yang merujuk pada sebuah artikel dan buku tentang pokok bahasan ini, juga pada ceramah Dirac yang disajikan dalam audiensi umum tahun 1972 di Boston mengenai geometri projektif, tanpa menspesifikasi aplikasi dalam fisikanya.
== Deskripsi ==
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=== Aksioma untuk bidang projektif ===
{{utama|Bidang projektif}}
Dalam [[geometri insidensi]], sebagian besar penulis<ref>{{harvnb|Bennett|1995|loc=pg. 4}}, {{harvnb|Beutelspacher|Rosenberg|1998|loc=pg. 8}}, {{harvnb|Casse|2006|loc=pg. 29}}, {{harvnb|Cederberg|2001|loc=pg. 9}}, {{harvnb|Garner|1981|loc=pg. 7}}, {{harvnb|Hughes|Piper|1973|loc=pg. 77}}, {{harvnb|Mihalek|1972|loc=pg. 29}}, {{harvnb|Polster|1998|loc=pg. 5}}, dan {{harvnb|Samuel|1988|loc= pg. 21}} adalah di antara referensi-referensi yang diberikan.</ref> memberikan suatu perlakuan yang melingkupi [[bidang Fano]] PG(2, 2) sebagai bidang projektif berhingga minimal. Sebuah [[sistem aksioma]] yang menerimanya adalah yang berikut ini:
* (P1) Sembarang dua titik yang berbeda terletak pada sebuah garis unik.
* (P2) Sembarang dua garis yang berbeda bertemu di sebuah titik unik.
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== Referensi ==
* <cite id=refBachmann1959>F. Bachmann, 1959. ''Aufbau der Geometrie aus dem Spiegelungsbegriff'', Springer, Berlin.</cite>
* {{cite book|last=Baer|first=Reinhold|title=Linear Algebra and Projective Geometry|url=https://archive.org/details/linearalgebrapro0000rein|year=2005|publisher=Dover|location=Mineola NY|isbn=0-486-44565-8}}
* {{cite book|last=Bennett|first=M.K.|title=Affine and Projective Geometry|url=https://archive.org/details/affineprojective0000benn|year=1995|publisher=Wiley|location=New York|isbn=0-471-11315-8}}
* {{cite book|last1=Beutelspacher|first1=Albrecht|last2=Rosenbaum|first2=Ute|title=Projective Geometry: from foundations to applications|year=1998|publisher=Cambridge University Press|location=Cambridge|isbn=0-521-48277-1}}
* {{cite book|last=Casse|first=Rey|title=Projective Geometry: An Introduction|year=2006|publisher=Oxford University Press|location=New York|isbn=0-19-929886-6}}
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|first=Judith N.
|title=A Course in Modern Geometries
|url=https://archive.org/details/courseinmodernge0002cede
|location=New York
|publisher=Springer-Verlag
Baris 206 ⟶ 207:
|first=H. S. M.
|title=Introduction to Geometry
|url=https://archive.org/details/introductiontoge0002coxe
|location=New York
|publisher=John Wiley & Sons
Baris 214 ⟶ 216:
* {{cite book|last=Garner|first=Lynn E.|title=An Outline of Projective Geometry|year=1981|publisher=North Holland|location=New York|isbn=0-444-00423-8}}
* Greenberg, M.J., 2007. ''Euclidean and non-Euclidean geometries'', 4th ed. Freeman.
* Richard Hartley and Andrew Zisserman, 2003. ''Multiple view geometry in computer vision'', 2nd ed. [[Cambridge University Press]]. ISBN 0-521-54051-8
* [[Robin Hartshorne|Hartshorne, Robin]], 2009. ''Foundations of Projective Geometry'', 2nd ed. Ishi Press. ISBN 978-4-87187-837-1
* Hartshorne, Robin, 2000. ''Geometry: Euclid and Beyond''. Springer.
* [[David Hilbert|Hilbert, D.]] and Cohn-Vossen, S., 1999. ''Geometry and the imagination'', 2nd ed. Chelsea.
* <cite id=refHughes1973>D. R. Hughes and F. C. Piper, 1973. ''Projective Planes'', Springer.</cite>
* {{cite book|last=Mihalek|first=R.J.|title=Projective Geometry and Algebraic Structures|url=https://archive.org/details/projectivegeomet0000miha|year=1972|publisher=Academic Press|location=New York|isbn=0-12-495550-9}}
* <cite id=refPolster1998>{{cite book
|last=Polster
|first=Burkard
|title=A Geometrical Picture Book
|url=https://archive.org/details/geometricalpictu0000pols
|location=New York
|publisher=Springer-Verlag
Baris 240 ⟶ 243:
|pages=87–94
|date=August 1997 }}
* {{cite book|last=Samuel|first=Pierre|title=Projective Geometry|url=https://archive.org/details/projectivegeomet0000samu|year=1988|publisher=Springer-Verlag|location=New York|isbn=0-387-96752-4}}
* {{Cite book|first=Oswald|last=Veblen|first2=J. W. A.|last2= Young|title=Projective geometry|year=1938|place=Boston|publisher= Ginn & Co.|url=http://www.archive.org/details/117714799_001|isbn=978-1-4181-8285-4|postscript=<!--None-->}}
== Pranala luar ==
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* [http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.17.1329 Projective Geometry for Machine Vision] {{Webarchive|url=https://web.archive.org/web/20141207043642/http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.17.1329 |date=2014-12-07 }} — tutorial by Joe Mundy and Andrew Zisserman.
* [http://xahlee.org/projective_geometry/projective_geometry.html Notes] {{Webarchive|url=https://web.archive.org/web/20120610062611/http://xahlee.org/projective_geometry/projective_geometry.html |date=2012-06-10 }} based on Coxeter's ''The Real Projective Plane''.
* [http://lear.inrialpes.fr/people/triggs/pubs/isprs96/isprs96.html Projective Geometry for Image Analysis] {{Webarchive|url=https://web.archive.org/web/20201209143644/http://lear.inrialpes.fr/people/triggs/pubs/isprs96/isprs96.html |date=2020-12-09 }} — free tutorial by Roger Mohr and Bill Triggs.
* [http://www.geometer.org/mathcircles/projective.pdf Projective Geometry.] {{Webarchive|url=https://web.archive.org/web/20190819095626/http://www.geometer.org/mathcircles/projective.pdf |date=2019-08-19 }} — free tutorial by Tom Davis.
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[[Kategori:Geometri| ]]
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