Kubus satuan: Perbedaan antara revisi

Revisi terkini sejak 27 Agustus 2026 14.01

Kubus satuan, lebih formalnya kubus dengan sisi 1, adalah kubus yang panjang sisi-sisinya 1 satuan.^[1]^[2] Volume kubus satuan 3 dimensi adalah 1 satuan kubik, dan luas permukaan totalnya adalah 6 satuan persegi.^[3]

Satuan hiperkubus

Istilah kubus satuan atau hiperkubus satuan juga digunakan untuk hiperkubus, atau "kubus" dalam ruang berdimensi n, untuk nilai n selain 3 dan panjang rusuk 1.^[4]^[5]

Kadang-kadang istilah "kubus satuan" merujuk secara khusus pada himpunan [0, 1] ⁿ dari semua n -tupel angka dalam interval [0, 1].^[6]

Panjang diagonal terpanjang suatu hiperkubus satuan berdimensi n adalah $\sqrt{n}$ , akar kuadrat dari n dan panjang (Euclidean) dari vektor (1,1,1,....1,1) dalam ruang berdimensi n.^[7]

Lihat juga

Menggandakan kubus
sel-K
Konstanta Robbins, jarak rata-rata antara dua titik acak dalam satuan kubus
Kubus Tychonoff, analog berdimensi tak hingga dari kubus satuan
Satuan persegi
Bola satuan

Pranala luar

Referensi

↑ Keith Ball. The Princeton Companion to Mathematics. Princeton University Press. 2010. hlm. 670–680. ISBN 9781400830398.. See in particular p. 671.
↑ Martin Gardner. The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems : Number Theory, Algebra, Geometry, Probability, Topology, Game Theory, Infinity, and Other Topics of Recreational Mathematics. W. W. Norton & Company. 2001. hlm. 162–174. ISBN 9780393020236..
↑ Geometry: Reteaching Masters. Holt Rinehart & Winston. 2001. hlm. 74. ISBN 9780030543289..
↑ Keith Ball. The Princeton Companion to Mathematics. Princeton University Press. 2010. hlm. 670–680. ISBN 9781400830398. Ball, Keith (2010), "High-dimensional geometry and its probabilistic analogues", in Gowers, Timothy (ed.), The Princeton Companion to Mathematics, Princeton University Press, pp. 670–680, ISBN 9781400830398 . See in particular p. 671.
↑ Martin Gardner. The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems : Number Theory, Algebra, Geometry, Probability, Topology, Game Theory, Infinity, and Other Topics of Recreational Mathematics. W. W. Norton & Company. 2001. hlm. 162–174. ISBN 9780393020236. Gardner, Martin (2001), "Chapter 13: Hypercubes", The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems : Number Theory, Algebra, Geometry, Probability, Topology, Game Theory, Infinity, and Other Topics of Recreational Mathematics, W. W. Norton & Company, pp. 162–174, ISBN 9780393020236 .
↑ Keith Ball. The Princeton Companion to Mathematics. Princeton University Press. 2010. hlm. 670–680. ISBN 9781400830398. Ball, Keith (2010), "High-dimensional geometry and its probabilistic analogues", in Gowers, Timothy (ed.), The Princeton Companion to Mathematics, Princeton University Press, pp. 670–680, ISBN 9781400830398 . See in particular p. 671.
↑ Martin Gardner. The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems : Number Theory, Algebra, Geometry, Probability, Topology, Game Theory, Infinity, and Other Topics of Recreational Mathematics. W. W. Norton & Company. 2001. hlm. 162–174. ISBN 9780393020236. Gardner, Martin (2001), "Chapter 13: Hypercubes", The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems : Number Theory, Algebra, Geometry, Probability, Topology, Game Theory, Infinity, and Other Topics of Recreational Mathematics, W. W. Norton & Company, pp. 162–174, ISBN 9780393020236 .

Sumber dan atribusi

Konten artikel ini diadaptasi dari Wikipedia bahasa Indonesia, revisi 26923841 (2025-02-14T16:56:26Z), yang tersedia berdasarkan lisensi Creative Commons Atribusi-BerbagiSerupa (CC BY-SA). Gambar pada artikel ini bersumber dari Wikimedia Commons dan mengikuti ketentuan lisensi masing-masing berkas. Mohon gunakan konten dan media secara bijak serta sesuai dengan ketentuan lisensi yang berlaku.

[1] Keith Ball. The Princeton Companion to Mathematics. Princeton University Press. 2010. hlm. 670–680. ISBN 9781400830398.. See in particular p. 671.

[2] Martin Gardner. The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems : Number Theory, Algebra, Geometry, Probability, Topology, Game Theory, Infinity, and Other Topics of Recreational Mathematics. W. W. Norton & Company. 2001. hlm. 162–174. ISBN 9780393020236..

[3] Geometry: Reteaching Masters. Holt Rinehart & Winston. 2001. hlm. 74. ISBN 9780030543289..

[4] Keith Ball. The Princeton Companion to Mathematics. Princeton University Press. 2010. hlm. 670–680. ISBN 9781400830398. Ball, Keith (2010), "High-dimensional geometry and its probabilistic analogues", in Gowers, Timothy (ed.), The Princeton Companion to Mathematics, Princeton University Press, pp. 670–680, ISBN 9781400830398 . See in particular p. 671.

[5] Martin Gardner. The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems : Number Theory, Algebra, Geometry, Probability, Topology, Game Theory, Infinity, and Other Topics of Recreational Mathematics. W. W. Norton & Company. 2001. hlm. 162–174. ISBN 9780393020236. Gardner, Martin (2001), "Chapter 13: Hypercubes", The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems : Number Theory, Algebra, Geometry, Probability, Topology, Game Theory, Infinity, and Other Topics of Recreational Mathematics, W. W. Norton & Company, pp. 162–174, ISBN 9780393020236 .

[6] Keith Ball. The Princeton Companion to Mathematics. Princeton University Press. 2010. hlm. 670–680. ISBN 9781400830398. Ball, Keith (2010), "High-dimensional geometry and its probabilistic analogues", in Gowers, Timothy (ed.), The Princeton Companion to Mathematics, Princeton University Press, pp. 670–680, ISBN 9781400830398 . See in particular p. 671.

[7] Martin Gardner. The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems : Number Theory, Algebra, Geometry, Probability, Topology, Game Theory, Infinity, and Other Topics of Recreational Mathematics. W. W. Norton & Company. 2001. hlm. 162–174. ISBN 9780393020236. Gardner, Martin (2001), "Chapter 13: Hypercubes", The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems : Number Theory, Algebra, Geometry, Probability, Topology, Game Theory, Infinity, and Other Topics of Recreational Mathematics, W. W. Norton & Company, pp. 162–174, ISBN 9780393020236 .

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@@ Baris 1: / Baris 1: @@
-'''Kubus satuan''', lebih formalnya '''kubus dengan sisi 1''', adalah [[kubus]] yang panjang sisi-sisinya 1 satuan. Volume kubus satuan [[Ruang dimensi tiga|3 dimensi]] adalah 1 satuan kubik, dan [[luas permukaan]] totalnya adalah 6 satuan persegi.
+[[File:Unitcube.svg|thumb|right|280px|Kubus satuan]]
+'''Kubus satuan''', lebih formalnya '''kubus dengan sisi 1''', adalah [[kubus]] yang panjang sisi-sisinya 1 satuan.<ref>Keith Ball. ''The Princeton Companion to Mathematics''. Princeton University Press. 2010. hlm. 670–680. ISBN 9781400830398.. See in particular [https://books.google.com/books?id=ZOfUsvemJDMC&pg=PA671 p. 671].</ref><ref>Martin Gardner. [https://books.google.com/books?id=orz0SDEakpYC&pg=PA162 The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems : Number Theory, Algebra, Geometry, Probability, Topology, Game Theory, Infinity, and Other Topics of Recreational Mathematics]. W. W. Norton & Company. 2001. hlm. 162–174. ISBN 9780393020236..</ref> Volume kubus satuan [[Ruang dimensi tiga|3 dimensi]] adalah 1 satuan kubik, dan [[luas permukaan]] totalnya adalah 6 satuan persegi.<ref>''Geometry: Reteaching Masters''. Holt Rinehart & Winston. 2001. hlm. 74. ISBN 9780030543289..</ref>
 == Satuan hiperkubus ==
-Istilah ''kubus satuan'' atau '''hiperkubus satuan''' juga digunakan untuk [[hiperkubus]], atau "kubus" dalam [[Dimensi|ruang berdimensi ''n'']], untuk nilai ''n'' selain 3 dan panjang rusuk 1.
+Istilah ''kubus satuan'' atau '''hiperkubus satuan''' juga digunakan untuk [[hiperkubus]], atau "kubus" dalam [[Dimensi|ruang berdimensi ''n'']], untuk nilai ''n'' selain 3 dan panjang rusuk 1.<ref>Keith Ball. ''The Princeton Companion to Mathematics''. Princeton University Press. 2010. hlm. 670–680. ISBN 9781400830398. Ball, Keith (2010), "High-dimensional geometry and its probabilistic analogues", in Gowers, Timothy (ed.), ''The Princeton Companion to Mathematics'', Princeton University Press, pp. 670–680, ISBN 9781400830398 . See in particular [https://books.google.com/books?id=ZOfUsvemJDMC&pg=PA671 p. 671].</ref><ref>Martin Gardner. [https://books.google.com/books?id=orz0SDEakpYC&pg=PA162 The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems : Number Theory, Algebra, Geometry, Probability, Topology, Game Theory, Infinity, and Other Topics of Recreational Mathematics]. W. W. Norton & Company. 2001. hlm. 162–174. ISBN 9780393020236. Gardner, Martin (2001), "Chapter 13: Hypercubes", [https://books.google.com/books?id=orz0SDEakpYC&pg=PA162 ''The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems : Number Theory, Algebra, Geometry, Probability, Topology, Game Theory, Infinity, and Other Topics of Recreational Mathematics''], W. W. Norton & Company, pp. 162–174, ISBN 9780393020236 .</ref>
-Kadang-kadang istilah "kubus satuan" merujuk secara khusus pada himpunan [0,&nbsp;1] <sup>''n''</sup> dari semua ''n'' -tupel angka dalam interval [0,&nbsp;1].
+Kadang-kadang istilah "kubus satuan" merujuk secara khusus pada himpunan [0,&nbsp;1] <sup>''n''</sup> dari semua ''n'' -tupel angka dalam interval [0,&nbsp;1].<ref>Keith Ball. ''The Princeton Companion to Mathematics''. Princeton University Press. 2010. hlm. 670–680. ISBN 9781400830398. Ball, Keith (2010), "High-dimensional geometry and its probabilistic analogues", in Gowers, Timothy (ed.), ''The Princeton Companion to Mathematics'', Princeton University Press, pp. 670–680, ISBN 9781400830398 . See in particular [https://books.google.com/books?id=ZOfUsvemJDMC&pg=PA671 p. 671].</ref>
-Panjang diagonal terpanjang suatu hiperkubus satuan berdimensi ''n'' adalah <math>\sqrt n</math>, [[akar kuadrat]] dari ''n'' dan panjang (Euclidean) dari vektor (1,1,1,....1,1) dalam ruang berdimensi ''n''.
+Panjang diagonal terpanjang suatu hiperkubus satuan berdimensi ''n'' adalah <math>\sqrt n</math>, [[akar kuadrat]] dari ''n'' dan panjang (Euclidean) dari vektor (1,1,1,....1,1) dalam ruang berdimensi ''n''.<ref>Martin Gardner. [https://books.google.com/books?id=orz0SDEakpYC&pg=PA162 The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems : Number Theory, Algebra, Geometry, Probability, Topology, Game Theory, Infinity, and Other Topics of Recreational Mathematics]. W. W. Norton & Company. 2001. hlm. 162–174. ISBN 9780393020236. Gardner, Martin (2001), "Chapter 13: Hypercubes", [https://books.google.com/books?id=orz0SDEakpYC&pg=PA162 ''The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems : Number Theory, Algebra, Geometry, Probability, Topology, Game Theory, Infinity, and Other Topics of Recreational Mathematics''], W. W. Norton & Company, pp. 162–174, ISBN 9780393020236 .</ref>
 == Lihat juga ==
 * Menggandakan kubus
 * sel-K
@@ Baris 16: / Baris 17: @@
 * [[Persegi satuan|Satuan persegi]]
 * Bola satuan
-== Referensi ==
 == Pranala luar ==
 *
+== Referensi ==
+<references />
+== Sumber dan atribusi ==
-== Sumber dan atribusi ==
+Konten artikel ini diadaptasi dari [https://id.wikipedia.org/w/index.php?title=Kubus+satuan&oldid=26923841 Wikipedia bahasa Indonesia], revisi 26923841 (2025-02-14T16:56:26Z), yang tersedia berdasarkan lisensi Creative Commons Atribusi-BerbagiSerupa (CC BY-SA). Gambar pada artikel ini bersumber dari Wikimedia Commons dan mengikuti ketentuan lisensi masing-masing berkas. Mohon gunakan konten dan media secara bijak serta sesuai dengan ketentuan lisensi yang berlaku.
-Konten artikel ini diadaptasi dari [https://id.wikipedia.org/w/index.php?title=Kubus+satuan&oldid=26923841 Wikipedia bahasa Indonesia], revisi 26923841 (2025-02-14T16:56:26Z), yang tersedia berdasarkan lisensi Creative Commons Atribusi-BerbagiSerupa (CC BY-SA). Mohon gunakan konten ini secara bijak serta sesuai dengan ketentuan lisensi yang berlaku.
+<!-- WIKI_UNISSULA_PRESENTATION_V4 -->