Чвор — разлика између измена

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Чвор је сплет или задевљање које настаје када се делови нечега савитљивог (конца, ужета, жице и сл.)^[1] чврсто вежу или замрсе на једном месту.^[2] Чворови се могу користити у озбиљне или у декоративне сврхе. Када оштећено уже пукне, везује се у чвор ради даљег одржавања своје функције. Понекад се уже кваси како би се додатно ојачало и чвор био снажнији. Чворови се такође користе и код транспорта. Разне врсте камиона, трактора и других превозних средстава користе чвор како би своје возило повезали са приколицом.

bend fastens two ends of a rope to each another; a loop knot is any knot creating a loop; and splice denotes any multi-strand knot, including bends and loops.^[3] A knot may also refer, in the strictest sense, to a stopper or knob at the end of a rope to keep that end from slipping through a grommet or eye.^[4] Knots have excited interest since ancient times for their practical uses, as well as their topological intricacy, studied in the area of mathematics known as knot theory.

Својства

Јачина

Knots weaken the rope in which they are made.^[5] When knotted rope is strained to its breaking point, it almost always fails at the knot or close to it, unless it is defective or damaged elsewhere. The bending, crushing, and chafing forces that hold a knot in place also unevenly stress rope fibers and ultimately lead to a reduction in strength. The exact mechanisms that cause the weakening and failure are complex and are the subject of continued study. Special fibers that show differences in color in response to strain are being developed and used to study stress as it relates to types of knots.^[6]^[7]

Relative knot strength, also called knot efficiency, is the breaking strength of a knotted rope in proportion to the breaking strength of the rope without the knot. Determining a precise value for a particular knot is difficult because many factors can affect a knot efficiency test: the type of fiber, the style of rope, the size of rope, whether it is wet or dry, how the knot is dressed before loading, how rapidly it is loaded, whether the knot is repeatedly loaded, and so on. The efficiency of common knots ranges between 40 and 80% of the rope's original strength.^[8] ^[9]

In most situations forming loops and bends with conventional knots is far more practical than using rope splices, even though the latter can maintain nearly the rope's full strength. Prudent users allow for a large safety margin in the strength of rope chosen for a task due to the weakening effects of knots, aging, damage, shock loading, etc. The working load limit of a rope is generally specified with a significant safety factor, up to 15:1 for critical applications.^[10]

Теорија чворова

Knot theory is a branch of topology. It deals with the mathematical analysis of knots, their structure and properties, and with the relationships between different knots. In topology, a knot is a figure consisting of a single loop with any number of crossing or knotted elements: a closed curve in space which may be moved around so long as its strands never pass through each other. As a closed loop, a mathematical knot has no proper ends, and cannot be undone or untied; however, any physical knot in a piece of string can be thought of as a mathematical knot by fusing the two ends. A configuration of several knots winding around each other is called a link. Various mathematical techniques are used to classify and distinguish knots and links. For instance, the Alexander polynomial associates certain numbers with any given knot; these numbers are different for the trefoil knot, the figure-eight knot, and the unknot (a simple loop), showing that one cannot be moved into the other (without strands passing through each other).^[11]

Физичка теорија фрикционих чворова

A simple mathematical theory of hitches has been proposed by Bayman^[12] and extended by Maddocks and Keller.^[13] It makes predictions that are approximately correct when tested empirically.^[14] No similarly successful theory has been developed for knots in general.

Референце

^ Ashley, Clifford W. (1944), The Ashley Book of Knots, New York: Doubleday, стр. 12, „"The word knot has three distinct meanings in common use. In the broadest sense it applies to all complications in cordage, except accidental ones, such as snarls and kinks, and complications adapted for storage, such as coils, hanks, skeins, balls, etc."”
^ Речник српскога језика. Нови Сад: Матица српска. 2011. стр. 1475.
^ Ashley, Clifford W. (1944), The Ashley Book of Knots, New York: Doubleday, стр. 12
^ Ashley, Clifford W. (1944), The Ashley Book of Knots, New York: Doubleday, стр. 12, „"In its second sense it does not include bends, hitches, splices, and sinnets, and in its third and narrowest sense the term applies only to a knob tied in a rope to prevent unreeving, to provide a handhold, or (in small material only) to prevent fraying."”
^ Richards, Dave (2005). „Knot Break Strength vs Rope Break Strength”. Nylon Highway. Vertical Section of the National Speleological Society (50). Приступљено 2010-10-11.
^ Greenfieldboyce, Nell (2. 1. 2020). „A Knotty Problem Solved”. All Things Considered. Приступљено 3. 1. 2020.
^ Patil, Vishal P.; Sandt, Joseph D.; Kolle, Mathias; Dunkel, Jörn (3. 1. 2020). „Topological Mechanics of Knots and Tangles”. Science. 367 (6473): 71—75. Bibcode:2020Sci...367...71P. PMID 31896713. S2CID 209677605. doi:10.1126/science.aaz0135 .
^ Warner, Charles (1996), „Studies on the Behaviour of Knots”, Ур.: Turner, J.C.; van de Griend, P., History and Science of Knots, K&E Series on Knots and Everything, 11, Singapore: World Scientific Publishing, стр. 181—203, ISBN 978-981-02-2469-1
^ Šimon; Dekýš, V.; Palček, P. (2020). „Revision of Commonly Used Loop Knots Efficiencies”. Acta Physica Polonica A. 138 (3): 404—420. doi:10.12693/APhysPolA.138.404 .
^ „Knot & Rope Safety”. Animated Knots by Grog. 2010. Архивирано из оригинала 7. 4. 2015. г. Приступљено 2010-09-14. . "Knot & Rope Safety", AnimatedKnots.com. Accessed April 2016.
^ Nakanishi, Yasutaka; Okada, Yuki (2012). „Differences of Alexander polynomials for knots caused by a single crossing change”. Topology and Its Applications. 159 (4): 1016—1025. doi:10.1016/j.topol.2011.11.023 .
^ Bayman, "Theory of hitches," Am J Phys, 45 (1977) 185
^ Maddocks, J.H. and Keller, J. B., "Ropes in Equilibrium," SIAM J Appl. Math., 47 (1987), pp. 1185–1200.
^ „The physics of knots”. www.lightandmatter.com.

Литература

Clifford W. Ashley. The Ashley Book of Knots. Doubleday, New York. ISBN 0-385-04025-3.
Geoffrey Budworth (1999). The Ultimate Encyclopedia of Knots & Ropework. Annes Publishing Limited. ISBN 1-55267-986-1.
John Cassidy (1985). The Klutz Book of Knots. Klutz Press, Palo Alto, California. ISBN 0-932592-10-4.
Paul Hasluck with foreward by Des Pawson (2018) The Art of Tying Knots. Endless Mountains Publishing Company. ISBN 0-998852-73-2.
Cyrus L. Day. Knots & Splices. International Marine/McGraw-Hill Companies. ISBN 0-87742-252-4.
Raoul Graumont. Handbook of Knots. Cornell Maritime Press/Tidewater Publishers. ISBN 0-87033-030-6.
R.S. Lee. All The Knots You Need. Algrove Publishing. ISBN 0-921335-47-4.
Allen Padgett and Bruce Smith. On Rope. National Speleological Society. ISBN 0-9615093-2-5.
Des Pawson (2001). Pocket Guide to Knots & Splices. Produced for Propsero Books by RPC Publishing Ltd., London. ISBN 1-55267-218-2.
Brion Toss. The Complete Rigger's Apprentice. International Marine/McGraw-Hill Companies. ISBN 0-07-064840-9.
J. C. Turner and P. van de Griend (ed.) (1996). History and Science of Knots. World Scientific. ISBN 981-02-2469-9.
Šimon; Dekýš, V.; Palček, P. (2020). „Revision of Commonly Used Loop Knots Efficiencies”. Acta Physica Polonica A. 138 (3): 404—420. doi:10.12693/APhysPolA.138.404.
Aldridge, Arthur F. (1918). Knots, a study of marlinespike seamanship which embraces bends, hitches, ties, fastenings and splices and their practical application. New York City: Rudder. OCLC 1047502131. OL 18970340M.
Burgess, J. Tom (1884). Knots, ties and splices; a handbook for seafarers, travellers, and all who use cordage; with historical, heraldic, and practical notes. London: George Routledge and sons. OL 24176273M.
Dana, Homer Jackson; Pearl, William Armour (1922). The use of ropes and tackle. Pullman, WA: Washington State College. OCLC 1158196429.
Hasluck, Paul Nooncree (1907). Knotting and splicing ropes and cordage. Philadelphia: David McKay. OL 6954703M.
Verrill, Alpheus Hyatt (1917). Knots, Splices and Rope Work. Norman W. Henley Publishing.
Thomson, Sir William (1867), „On Vortex Atoms”, Proceedings of the Royal Society of Edinburgh, VI: 94—105
Silliman, Robert H. (децембар 1963), „William Thomson: Smoke Rings and Nineteenth-Century Atomism”, Isis, 54 (4): 461—474, JSTOR 228151, S2CID 144988108, doi:10.1086/349764
Adams, Colin (2004), The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots, American Mathematical Society, ISBN 978-0-8218-3678-1
Adams, Colin; Crawford, Thomas; DeMeo, Benjamin; Landry, Michael; Lin, Alex Tong; Montee, MurphyKate; Park, Seojung; Venkatesh, Saraswathi; Yhee, Farrah (2015), „Knot projections with a single multi-crossing”, Journal of Knot Theory and Its Ramifications, 24 (3): 1550011, 30, MR 3342136, S2CID 119320887, arXiv:1208.5742 , doi:10.1142/S021821651550011X
Adams, Colin; Hildebrand, Martin; Weeks, Jeffrey (1991), „Hyperbolic invariants of knots and links”, Transactions of the American Mathematical Society, 326 (1): 1—56, JSTOR 2001854, doi:10.1090/s0002-9947-1991-0994161-2 
Akbulut, Selman; King, Henry C. (1981), „All knots are algebraic”, Comm. Math. Helv., 56 (3): 339—351, S2CID 120218312, doi:10.1007/BF02566217
Bar-Natan, Dror (1995), „On the Vassiliev knot invariants”, Topology, 34 (2): 423—472, doi:10.1016/0040-9383(95)93237-2 
Burton, Benjamin A. (2020). „The Next 350 Million Knots”. 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz Int. Proc. Inform. 164. Schloss Dagstuhl–Leibniz-Zentrum für Informatik. стр. 25:1—25:17. doi:10.4230/LIPIcs.SoCG.2020.25 .
Collins, Graham (април 2006), „Computing with Quantum Knots”, Scientific American, 294 (4): 56—63, Bibcode:2006SciAm.294d..56C, PMID 16596880, doi:10.1038/scientificamerican0406-56
Dehn, Max (1914), „Die beiden Kleeblattschlingen”, Mathematische Annalen, 75 (3): 402—413, S2CID 120452571, doi:10.1007/BF01563732
Conway, John H. (1970), „An enumeration of knots and links, and some of their algebraic properties”, Computational Problems in Abstract Algebra, Pergamon, стр. 329—358, ISBN 978-0-08-012975-4, doi:10.1016/B978-0-08-012975-4.50034-5
Doll, Helmut; Hoste, Jim (1991), „A tabulation of oriented links. With microfiche supplement”, Math. Comp., 57 (196): 747—761, Bibcode:1991MaCom..57..747D, doi:10.1090/S0025-5718-1991-1094946-4 
Flapan, Erica (2000), When topology meets chemistry: A topological look at molecular chirality, Outlook, Cambridge University Press, ISBN 978-0-521-66254-3
Haefliger, André (1962), „Knotted (4k − 1)-spheres in 6k-space”, Annals of Mathematics, Second Series, 75 (3): 452—466, JSTOR 1970208, doi:10.2307/1970208
Hass, Joel (1998), „Algorithms for recognizing knots and 3-manifolds”, Chaos, Solitons and Fractals, 9 (4–5): 569—581, Bibcode:1998CSF.....9..569H, S2CID 7381505, arXiv:math/9712269 , doi:10.1016/S0960-0779(97)00109-4
Hoste, Jim; Thistlethwaite, Morwen; Weeks, Jeffrey (1998), „The First 1,701,935 Knots”, Math. Intelligencer, 20 (4): 33—48, S2CID 18027155, doi:10.1007/BF03025227
Hoste, Jim (2005), „The enumeration and classification of knots and links”, Handbook of Knot Theory (PDF), Amsterdam: Elsevier
Levine, Jerome (1965), „A classification of differentiable knots”, Annals of Mathematics, Second Series, 1982 (1): 15—50, JSTOR 1970561, doi:10.2307/1970561
Kontsevich, Maxim (1993), „Vassiliev's knot invariants”, I. M. Gelfand Seminar, Adv. Soviet Math., 2, Providence, RI: American Mathematical Society, 16: 137—150, ISBN 9780821841174, doi:10.1090/advsov/016.2/04
Lickorish, W. B. Raymond (1997), An Introduction to Knot Theory, Graduate Texts in Mathematics, 175, Springer-Verlag, ISBN 978-0-387-98254-0, S2CID 122824389, doi:10.1007/978-1-4612-0691-0
Perko, Kenneth (1974), „On the classification of knots”, Proceedings of the American Mathematical Society, 45 (2): 262—6, JSTOR 2040074, doi:10.2307/2040074 
Rolfsen, Dale (1976), Knots and Links, Mathematics Lecture Series, 7, Berkeley, California: Publish or Perish, ISBN 978-0-914098-16-4, MR 0515288
Schubert, Horst (1949), „Die eindeutige Zerlegbarkeit eines Knotens in Primknoten”, Heidelberger Akad. Wiss. Math.-Nat. Kl. (3): 57—104
Silver, Dan (2006), „Knot theory's odd origins” (PDF), American Scientist, 94 (2), стр. 158—165, doi:10.1511/2006.2.158
Simon, Jonathan (1986), „Topological chirality of certain molecules”, Topology, 25 (2): 229—235, doi:10.1016/0040-9383(86)90041-8 
Sossinsky, Alexei (2002), Knots, mathematics with a twist, Harvard University Press, ISBN 978-0-674-00944-8
Turaev, Vladimir G. (1994), „Quantum invariants of knots and 3-manifolds”, De Gruyter Studies in Mathematics, Berlin: Walter de Gruyter & Co., 18, Bibcode:1994hep.th....9028T, ISBN 978-3-11-013704-0, arXiv:hep-th/9409028 
Weisstein, Eric W. (2013). „Reduced Knot Diagram”. MathWorld. Wolfram. Приступљено 8. 5. 2013.
Weisstein, Eric W. (2013a). „Reducible Crossing”. MathWorld. Wolfram. Приступљено 8. 5. 2013.
Witten, Edward (1989), „Quantum field theory and the Jones polynomial”, Comm. Math. Phys., 121 (3): 351—399, Bibcode:1989CMaPh.121..351W, S2CID 14951363, doi:10.1007/BF01217730
Zeeman, Erik C. (1963), „Unknotting combinatorial balls”, Annals of Mathematics, Second Series, 78 (3): 501—526, JSTOR 1970538, doi:10.2307/1970538
Burde, Gerhard; Zieschang, Heiner (1985), Knots, De Gruyter Studies in Mathematics, 5, Walter de Gruyter, ISBN 978-3-11-008675-1
Crowell, Richard H.; Fox, Ralph (1977). Introduction to Knot Theory. ISBN 978-0-387-90272-2.
Kauffman, Louis H. (1987), On Knots, ISBN 978-0-691-08435-0
Kauffman, Louis H. (2013), Knots and Physics (4th изд.), World Scientific, ISBN 978-981-4383-00-4
Cromwell, Peter R. (2004), Knots and Links, Cambridge University Press, ISBN 978-0-521-54831-1
Menasco, William W.; Thistlethwaite, Morwen, ур. (2005), Handbook of Knot Theory, Elsevier, ISBN 978-0-444-51452-3
Livio, Mario (2009), „Ch. 8: Unreasonable Effectiveness?”, Is God a Mathematician?, Simon & Schuster, стр. 203—218, ISBN 978-0-7432-9405-8

Спољашње везе

Knots на сајту Curlie
KnotInfo: Table of Knot Invariants and Knot Theory Resources
The Knot Atlas — detailed info on individual knots in knot tables
KnotPlot — software to investigate geometric properties of knots
Knotscape — software to create images of knots
Knoutilus — online database and image generator of knots
KnotData.html — Wolfram Mathematica function for investigating knots
Regina — software for low-dimensional topology with native support for knots and links. Tables of prime knots with up to 19 crossings
Movie of a modern recreation of Tait's smoke ring experiment
History of knot theory (on the home page of Andrew Ranicki)

[1] Ashley, Clifford W. (1944), The Ashley Book of Knots, New York: Doubleday, стр. 12, „"The word knot has three distinct meanings in common use. In the broadest sense it applies to all complications in cordage, except accidental ones, such as snarls and kinks, and complications adapted for storage, such as coils, hanks, skeins, balls, etc."”

[2] Речник српскога језика. Нови Сад: Матица српска. 2011. стр. 1475.

[3] Ashley, Clifford W. (1944), The Ashley Book of Knots, New York: Doubleday, стр. 12

[4] Ashley, Clifford W. (1944), The Ashley Book of Knots, New York: Doubleday, стр. 12, „"In its second sense it does not include bends, hitches, splices, and sinnets, and in its third and narrowest sense the term applies only to a knob tied in a rope to prevent unreeving, to provide a handhold, or (in small material only) to prevent fraying."”

[Richards2005-5] Richards, Dave (2005). „Knot Break Strength vs Rope Break Strength”. Nylon Highway. Vertical Section of the National Speleological Society (50). Приступљено 2010-10-11.

[Greenfieldboyce-6] Greenfieldboyce, Nell (2. 1. 2020). „A Knotty Problem Solved”. All Things Considered. Приступљено 3. 1. 2020.

[Patil-7] Patil, Vishal P.; Sandt, Joseph D.; Kolle, Mathias; Dunkel, Jörn (3. 1. 2020). „Topological Mechanics of Knots and Tangles”. Science. 367 (6473): 71—75. Bibcode:2020Sci...367...71P. PMID 31896713. S2CID 209677605. doi:10.1126/science.aaz0135 .

[hsok-ch10-8] Warner, Charles (1996), „Studies on the Behaviour of Knots”, Ур.: Turner, J.C.; van de Griend, P., History and Science of Knots, K&E Series on Knots and Everything, 11, Singapore: World Scientific Publishing, стр. 181—203, ISBN 978-981-02-2469-1

[9] Šimon; Dekýš, V.; Palček, P. (2020). „Revision of Commonly Used Loop Knots Efficiencies”. Acta Physica Polonica A. 138 (3): 404—420. doi:10.12693/APhysPolA.138.404 .

[grog-reliability-10] „Knot & Rope Safety”. Animated Knots by Grog. 2010. Архивирано из оригинала 7. 4. 2015. г. Приступљено 2010-09-14. . "Knot & Rope Safety", AnimatedKnots.com. Accessed April 2016.

[11] Nakanishi, Yasutaka; Okada, Yuki (2012). „Differences of Alexander polynomials for knots caused by a single crossing change”. Topology and Its Applications. 159 (4): 1016—1025. doi:10.1016/j.topol.2011.11.023 .

[12] Bayman, "Theory of hitches," Am J Phys, 45 (1977) 185

[13] Maddocks, J.H. and Keller, J. B., "Ropes in Equilibrium," SIAM J Appl. Math., 47 (1987), pp. 1185–1200.

[14] „The physics of knots”. www.lightandmatter.com.

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@@ Ред 1: / Ред 1: @@
+{{Short description|Начин причвршћивања или причвршћивања линеарног материјала}}{{рут}}
 {{друге употребе}}
 [[Датотека:Nf knots.png|300п|мини|десно|Разне врсте чворова]]
-'''Чвор''' је сплет или задевљање које настаје када се делови нечега савитљивог (конца, ужета, жице и сл.) чврсто вежу или замрсе на једном месту.<ref>{{cite book |title=Речник српскога језика |date=2011 |publisher=Матица српска |location=Нови Сад |pages=1475}}</ref> Чворови се могу користити у озбиљне или у декоративне сврхе.
+'''Чвор''' је сплет или задевљање које настаје када се делови нечега савитљивог (конца, ужета, жице и сл.)<ref>{{citation |last=Ashley |first=Clifford W. |title=The Ashley Book of Knots |year= 1944 |publisher=Doubleday |location=New York |page=12 |quote="The word knot has three distinct meanings in common use. In the broadest sense it applies to all complications in cordage, except accidental ones, such as snarls and kinks, and complications adapted for storage, such as coils, hanks, skeins, balls, etc." }}</ref>  чврсто вежу или замрсе на једном месту.<ref>{{cite book |title=Речник српскога језика |date=2011 |publisher=Матица српска |location=Нови Сад |pages=1475}}</ref> Чворови се могу користити у озбиљне или у декоративне сврхе. Када оштећено уже пукне, везује се у чвор ради даљег одржавања своје функције. Понекад се уже кваси како би се додатно ојачало и чвор био снажнији. Чворови се такође користе и код транспорта. Разне врсте камиона, трактора и других превозних средстава користе чвор како би своје возило повезали са [[Приколица|приколицом]].
-Када оштећено уже пукне, везује се у чвор ради даљег одржавања своје функције. Понекад се уже кваси како би се додатно ојачало и чвор био снажнији.
+''bend'' fastens two ends of a rope to each another; a ''loop knot'' is any knot creating a loop; and ''splice'' denotes any multi-strand knot, including bends and loops.<ref>{{citation|last=Ashley|first=Clifford W.|title=The Ashley Book of Knots|page=12|year=1944|location=New York|publisher=Doubleday}}</ref> A knot may also refer, in the strictest sense, to a stopper or knob at the end of a rope to keep that end from slipping through a grommet or eye.<ref>{{citation |last=Ashley |first=Clifford W. |title=The Ashley Book of Knots |year= 1944 |publisher=Doubleday |location=New York |page=12 |quote="In its second sense it does not include bends, hitches, splices, and sinnets, and in its third and narrowest sense the term applies only to a knob tied in a rope to prevent unreeving, to provide a handhold, or (in small material only) to prevent fraying." }}</ref> Knots have excited interest since ancient times for their practical uses, as well as their [[Topology|topological]] intricacy, studied in the area of mathematics known as [[knot theory]].
-Чворови се такође користе и код транспорта. Разне врсте камиона, трактора и других превозних средстава користе чвор како би своје возило повезали са [[Приколица|приколицом]].
+== Својства ==
+=== Јачина ===
+Knots weaken the rope in which they are made.<ref name="Richards2005">{{Cite journal|title=Knot Break Strength vs Rope Break Strength|last=Richards|first=Dave|journal=Nylon Highway|number=50|publisher=Vertical Section of the [[National Speleological Society]]|year=2005|url=http://www.caves.org/section/vertical/nh/50/knotrope.html|access-date=2010-10-11}}</ref> When knotted rope is strained to its breaking point, it almost always fails at the knot or close to it, unless it is defective or damaged elsewhere. The bending, crushing, and chafing forces that hold a knot in place also unevenly stress rope fibers and ultimately lead to a reduction in strength. The exact mechanisms that cause the weakening and failure are complex and are the subject of continued study. Special fibers that show differences in color in response to strain are being developed and used to study stress as it relates to types of knots.<ref name="Greenfieldboyce">{{cite news |last1=Greenfieldboyce |first1=Nell |title=A Knotty Problem Solved |url=https://www.npr.org/2020/01/02/793050811/a-knotty-problem-solved |access-date=3 January 2020 |work=All Things Considered |date=January 2, 2020}}</ref><ref name="Patil">{{Cite journal |last1=Patil |first1=Vishal P. |last2=Sandt |first2=Joseph D. |last3=Kolle |first3=Mathias |last4=Dunkel |first4=Jörn |date=3 January 2020 |title=Topological Mechanics of Knots and Tangles |journal=[[Science (journal)|Science]] |volume=367 |issue=6473 |pages=71–75 |doi=10.1126/science.aaz0135 |pmid=31896713 |bibcode=2020Sci...367...71P |s2cid=209677605 |doi-access=free }}</ref>
+Relative '''knot strength''', also called '''knot efficiency''', is the breaking strength of a knotted rope in proportion to the breaking strength of the rope without the knot. Determining a precise value for a particular knot is difficult because many factors can affect a knot efficiency test: the type of [[fiber]], the [[Rope#Styles of rope construction|style of rope]], the size of rope, whether it is wet or dry, how the knot is dressed before loading, how rapidly it is loaded, whether the knot is repeatedly loaded, and so on. The efficiency of common knots ranges between 40 and 80% of the rope's original strength.<ref name="hsok-ch10">{{Citation| last=Warner| first=Charles| year=1996| contribution=Studies on the Behaviour of Knots| editor-last=Turner| editor-first=J.C.| editor2-last=van de Griend| editor2-first=P.| title=History and Science of Knots| series=K&E Series on Knots and Everything| location=Singapore| publisher=World Scientific Publishing| volume=11| pages=181–203| isbn=978-981-02-2469-1}}</ref> <ref>{{Cite journal |last1=Šimon |first2=V. |last2=Dekýš |first3=P. |last3=Palček |title=Revision of Commonly Used Loop Knots Efficiencies |journal=Acta Physica Polonica A |volume=138 |issue=3 |pages=404-420 |doi=10.12693/APhysPolA.138.404|year=2020 |doi-access=free }}</ref>
+In most situations forming loops and bends with conventional knots is far more practical than using [[Rope splicing|rope splices]], even though the latter can maintain nearly the rope's full strength. Prudent users allow for a large [[factor of safety|safety margin]] in the strength of rope chosen for a task due to the weakening effects of knots, aging, damage, shock loading, etc.  The [[safe working load|working load limit]] of a rope is generally specified with a significant safety factor, up to 15:1 for critical applications.<ref name="grog-reliability">{{Cite web|url=http://www.animatedknots.com/reliability.php? |title=Knot & Rope Safety |publisher=Animated Knots by Grog |year=2010 |access-date=2010-09-14 |url-status=dead |archive-url=https://web.archive.org/web/20150407023208/http://www.animatedknots.com/reliability.php |archive-date=April 7, 2015 }}. "[http://www.animatedknots.com/safety.php?Categ=ropecare&LogoImage=LogoGrog.png&Website=www.animatedknots.com#ScrollPoint Knot & Rope Safety]", ''AnimatedKnots.com''. Accessed April 2016.</ref>
+== Теорија чворова ==
+{{main|Теорија чворова}}
+[[Датотека:TrefoilKnot 01.svg|thumb|right|150px|A [[trefoil knot]] is a mathematical version of an [[overhand knot]].]]
+Knot theory is a branch of [[topology]]. It deals with the [[mathematics|mathematical]] analysis of knots, their structure and properties, and with the relationships between different knots. In topology, a [[knot (mathematics)|knot]] is a figure consisting of a single loop with any number of crossing or knotted elements: a closed curve in space which may be moved around so long as its strands never pass through each other. As a closed loop, a mathematical knot has no proper ends, and cannot be undone or untied; however, any physical knot in a piece of string can be thought of as a mathematical knot by fusing the two ends. A configuration of several knots winding around each other is called a ''link''. Various mathematical techniques are used to classify and distinguish knots and links. For instance, the [[Alexander polynomial]] associates certain numbers with any given knot; these numbers are different for the [[trefoil knot]], the [[Figure-eight knot (mathematics)|figure-eight knot]], and the [[unknot]] (a simple loop), showing that one cannot be moved into the other (without strands passing through each other).<ref>{{Cite journal |last1=Nakanishi |first1=Yasutaka |last2=Okada |first2=Yuki |title=Differences of Alexander polynomials for knots caused by a single crossing change |journal=Topology and Its Applications |volume=159 |issue=4 |pages=1016–1025 |doi=10.1016/j.topol.2011.11.023|year=2012 |doi-access=free }}</ref>
+== Физичка теорија фрикционих чворова ==
+A simple mathematical theory of hitches has been proposed by Bayman<ref>Bayman, "Theory of hitches," Am J Phys, 45 (1977) 185</ref> and extended by Maddocks and Keller.<ref>Maddocks, J.H. and Keller, J. B., "Ropes in Equilibrium," SIAM J Appl. Math., 47 (1987), pp. 1185–1200.</ref> It makes predictions that are approximately correct when tested empirically.<ref>{{cite web|url=http://www.lightandmatter.com/article/knots.html|title=The physics of knots|website=www.lightandmatter.com}}</ref> No similarly successful theory has been developed for knots in general.
 == Референце ==
-{{Извори}}
+{{reflist|}}
 == Литература ==
-{{refbegin}}
+{{refbegin|30em}}
-* [[Clifford Ashley|Clifford W. Ashley]]. ''[[The Ashley Book of Knots]]''. Doubleday, New York. {{ISBN|0-385-04025-3}}
+* [[Clifford Ashley|Clifford W. Ashley]]. ''[[The Ashley Book of Knots]]''. Doubleday, New York. {{ISBN|0-385-04025-3}}.
-* Geoffrey Budworth (1999). ''The Ultimate Encyclopedia of Knots & Ropework''. Annes Publishing Limited. {{ISBN|1-55267-986-1}}
+* Geoffrey Budworth (1999). ''The Ultimate Encyclopedia of Knots & Ropework''. Annes Publishing Limited. {{ISBN|1-55267-986-1}}.
-* John Cassidy (1985). ''The Klutz Book of Knots''. Klutz Press, [[Palo Alto, California]]. {{ISBN|0-932592-10-4}}
+* John Cassidy (1985). ''The Klutz Book of Knots''. Klutz Press, [[Palo Alto, California]]. {{ISBN|0-932592-10-4}}.
+* Paul Hasluck with foreward by Des Pawson (2018) ''The Art of Tying Knots.'' Endless Mountains Publishing Company. {{ISBN|0-998852-73-2}}.
-* Cyrus L. Day. ''Knots & Splices''. International Marine/McGraw-Hill Companies. {{ISBN|0-87742-252-4}}
-* Raoul Graumont. ''Handbook of Knots''. Cornell Maritime Press/Tidewater Publishers. {{ISBN|0-87033-030-6}}
+* Cyrus L. Day. ''Knots & Splices''. International Marine/McGraw-Hill Companies. {{ISBN|0-87742-252-4}}.
-* R.S. Lee. ''All The Knots You Need''. Algrove Publishing. {{ISBN|0-921335-47-4}}
+* Raoul Graumont. ''Handbook of Knots''. Cornell Maritime Press/Tidewater Publishers. {{ISBN|0-87033-030-6}}.
-* Allen Padgett and Bruce Smith. ''On Rope''. National Speleological Society. {{ISBN|0-9615093-2-5}}
+* R.S. Lee. ''All The Knots You Need''. Algrove Publishing. {{ISBN|0-921335-47-4}}.
+* Allen Padgett and Bruce Smith. ''On Rope''. National Speleological Society. {{ISBN|0-9615093-2-5}}.
-* Des Pawson (2001). ''Pocket Guide to Knots & Splices''. Produced for Propsero Books by RPC Publishing Ltd., London. {{ISBN|1-55267-218-2}}
+* Des Pawson (2001). ''Pocket Guide to Knots & Splices''. Produced for Propsero Books by RPC Publishing Ltd., London. {{ISBN|1-55267-218-2}}.
-* Brion Toss. ''The Complete Rigger's Apprentice''. International Marine/McGraw-Hill Companies. {{ISBN|0-07-064840-9}}
+* Brion Toss. ''The Complete Rigger's Apprentice''. International Marine/McGraw-Hill Companies. {{ISBN|0-07-064840-9}}.
-* J.C. Turner and P. van de Griend (ed.) (1996). ''History and Science of Knots''. World Scientific. {{ISBN|981-02-2469-9}}
+* J. C. Turner and P. van de Griend (ed.) (1996). ''History and Science of Knots''. World Scientific. {{ISBN|981-02-2469-9}}.
+* {{cite journal |last1=Šimon |first2=V. |last2=Dekýš |first3=P. |last3=Palček |title=Revision of Commonly Used Loop Knots Efficiencies |journal=Acta Physica Polonica A |date=2020 |volume=138 |issue=3 |pages=404-420 |doi=10.12693/APhysPolA.138.404}}
+* {{cite book
+ |last= Aldridge
+ |first= Arthur F.
+ |date= 1918
+ |title= Knots, a study of marlinespike seamanship which embraces bends, hitches, ties, fastenings and splices and their practical application
+ |url= https://archive.org/details/knotsstudyofmarl00aldr
+ |location= New York City
+ |publisher= Rudder
+ | oclc = 1047502131
+ | ol = 18970340M
+}}
+* {{cite book
+ |last = Burgess
+ |first = J. Tom
+ |author-link = Joseph Tom Burgess
+ |date = 1884
+ |title = Knots, ties and splices; a handbook for seafarers, travellers, and all who use cordage; with historical, heraldic, and practical notes
+ |url = https://archive.org/details/cu31924014519940
+ |location = London
+ |publisher = George Routledge and sons
+ |ol = 24176273M
+}}
+* {{cite book
+ | last1 = Dana
+ | first1 = Homer Jackson
+ | last2 = Pearl
+ | first2 = William Armour
+ |date= 1922
+ |title= The use of ropes and tackle
+ |url= https://archive.org/details/useofropestackle00danarich
+ |location= Pullman, WA
+ |publisher= Washington State College
+ | oclc = 1158196429
+}}
+* {{cite book
+ |last= Hasluck
+ |first= Paul Nooncree
+ |author-link= Paul Nooncree Hasluck
+ |date= 1907
+ |title= Knotting and splicing ropes and cordage
+ |url= https://archive.org/details/gri_33125000664421
+ |location= Philadelphia
+ |publisher= David McKay
+ | ol = 6954703M
+}}
+* {{cite book
+ |last= Verrill
+ |first= Alpheus Hyatt
+ |author-link = Alpheus Hyatt Verrill
+ |date= 1917
+ |title= Knots, Splices and Rope Work
+ |url= https://www.gutenberg.org/ebooks/13510
+ |publisher= Norman W. Henley Publishing
+}}
+* {{citation |last=Thomson |first=Sir William  |author-link=Lord Kelvin |title=On Vortex Atoms |journal=Proceedings of the Royal Society of Edinburgh |volume=VI |pages=94–105 |year=1867 |url=http://zapatopi.net/kelvin/papers/on_vortex_atoms.html}}
+* {{citation |last=Silliman |first=Robert H. |title=William Thomson: Smoke Rings and Nineteenth-Century Atomism |journal=Isis |volume=54 |issue=4 |pages=461–474 |date=December 1963 |jstor=228151 |doi=10.1086/349764|s2cid=144988108 }}
+* {{Citation|first=Colin |last= Adams|author-link=Colin Adams (mathematician)|title=The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots |publisher=[[American Mathematical Society]]|year=2004|isbn=978-0-8218-3678-1}}
+* {{citation
+ | last1 = Adams | first1 = Colin
+ | last2 = Crawford | first2 = Thomas
+ | last3 = DeMeo | first3 = Benjamin
+ | last4 = Landry | first4 = Michael
+ | last5 = Lin | first5 = Alex Tong
+ | last6 = Montee | first6 = MurphyKate
+ | last7 = Park | first7 = Seojung
+ | last8 = Venkatesh | first8 = Saraswathi
+ | last9 = Yhee | first9 = Farrah
+ | arxiv = 1208.5742
+ | doi = 10.1142/S021821651550011X
+ | issue = 3
+ | journal = Journal of Knot Theory and Its Ramifications
+ | mr = 3342136
+ | page = 1550011, 30
+ | title = Knot projections with a single multi-crossing
+ | volume = 24
+ | year = 2015| s2cid = 119320887
+ }}
+* {{Citation|first1=Colin|last1=Adams|first2=Martin|last2=Hildebrand|first3=Jeffrey|last3=Weeks|author3-link= Jeffrey Weeks (mathematician)|title=Hyperbolic invariants of knots and links|journal=Transactions of the American Mathematical Society|year=1991|volume=326|pages=1–56|issue=1 |jstor=2001854|doi=10.1090/s0002-9947-1991-0994161-2|doi-access=free}}
+* {{Citation|first1=Selman|last1=Akbulut|author-link1=Selman Akbulut|first2=Henry C.|last2=King|title= All knots are algebraic|journal=Comm. Math. Helv.|year=1981|volume=56|pages=339–351|issue=3|doi=10.1007/BF02566217|s2cid=120218312}}
+* {{Citation|first=Dror|last=Bar-Natan|author-link=Dror Bar-Natan|title=On the Vassiliev knot invariants|journal=[[Topology (journal)|Topology]]|volume=34|year=1995|pages=423–472|issue=2|doi=10.1016/0040-9383(95)93237-2|doi-access=free}}
+* {{cite conference |url=https://drops.dagstuhl.de/opus/volltexte/2020/12183/|title=The Next 350 Million Knots|last=Burton|first=Benjamin A.|date=2020|publisher=Schloss Dagstuhl–Leibniz-Zentrum für Informatik|series=Leibniz Int. Proc. Inform.|volume=164|book-title=36th International Symposium on Computational Geometry (SoCG 2020)|pages=25:1–25:17|doi=10.4230/LIPIcs.SoCG.2020.25|doi-access=free}}
+* {{Citation|first=Graham|last=Collins|journal=[[Scientific American]]|title=Computing with Quantum Knots|date=April 2006|bibcode=2006SciAm.294d..56C|volume=294|pages=56–63|doi=10.1038/scientificamerican0406-56|issue=4|pmid=16596880}}
+* {{Citation|first=Max|last=Dehn|author-link=Max Dehn|title=Die beiden Kleeblattschlingen|journal=Mathematische Annalen|volume=75|year=1914|issue=3|pages=402–413|doi=10.1007/BF01563732|s2cid=120452571}}
+* {{Citation|first=John H.|last=Conway|author-link=John Horton Conway|chapter=An enumeration of knots and links, and some of their algebraic properties|publisher=Pergamon|year=1970|pages=329–358|title=Computational Problems in Abstract Algebra|doi=10.1016/B978-0-08-012975-4.50034-5|isbn=978-0-08-012975-4}}
+* {{Citation|first1=Helmut|last1=Doll|first2=Jim|last2=Hoste|title=A tabulation of oriented links. With microfiche supplement|journal=Math. Comp.|volume=57|year=1991|pages=747–761|issue=196|doi=10.1090/S0025-5718-1991-1094946-4|bibcode=1991MaCom..57..747D|doi-access=free}}
+* {{Citation|first=Erica|last=Flapan|author-link=Erica Flapan|title=When topology meets chemistry: A topological look at molecular chirality|title-link= When Topology Meets Chemistry |series=Outlook|publisher=[[Cambridge University Press]]|year=2000|isbn=978-0-521-66254-3}}
+* {{Citation|first=André|last=Haefliger|author-link=André Haefliger|title=Knotted (4''k''&nbsp;&minus;&nbsp;1)-spheres in 6''k''-space|journal=Annals of Mathematics |series=Second Series|year=1962|volume=75|pages=452–466|issue=3|jstor=1970208|doi=10.2307/1970208}}
+* {{Citation|first=Joel|last=Hass|author-link=Joel Hass|title=Algorithms for recognizing knots and 3-manifolds|journal=[[Chaos, Solitons and Fractals]]|year=1998|pages=569–581|volume=9|doi=10.1016/S0960-0779(97)00109-4|issue=4–5 |arxiv=math/9712269|bibcode = 1998CSF.....9..569H |s2cid=7381505}}
+* {{Citation|first1=Jim|last1=Hoste|first2=Morwen|last2=Thistlethwaite|author-link2=Morwen Thistlethwaite|first3=Jeffrey|last3=Weeks|title= The First 1,701,935 Knots|journal=[[Math. Intelligencer]]| volume=20|year=1998|pages=33–48|doi=10.1007/BF03025227|issue=4|s2cid=18027155}}
+* {{Citation|first=Jim|last=Hoste|contribution=The enumeration and classification of knots and links|year=2005|title=Handbook of Knot Theory|place= Amsterdam|publisher=Elsevier|url=http://pzacad.pitzer.edu/~jhoste/HosteWebPages/downloads/Enumeration.pdf}}
+* {{Citation|first=Jerome|last=Levine|author-link=Jerome Levine|title=A classification of differentiable knots|journal=[[Annals of Mathematics]] |series=Second Series|year=1965|volume=1982|issue=1|pages=15–50|jstor=1970561|doi=10.2307/1970561}}
+* {{Citation|first=Maxim|last=Kontsevich|author-link=Maxim Kontsevich|title=Vassiliev's knot invariants|pages=137–150|journal= I. M. Gelfand Seminar, Adv. Soviet Math.|volume=16|series=2|publisher=American Mathematical Society |place=Providence, RI|year=1993|doi=10.1090/advsov/016.2/04|isbn=9780821841174}}
+* {{Citation|first=W. B. Raymond|last=Lickorish|author-link=W. B. R. Lickorish|title=An Introduction to Knot Theory|publisher=Springer-Verlag|series=Graduate Texts in Mathematics|volume=175|year=1997|isbn=978-0-387-98254-0|url=https://books.google.com/books?id=PhHhw_kRvewC|doi=10.1007/978-1-4612-0691-0|s2cid=122824389 }}
+* {{Citation|first=Kenneth|last=Perko|title=On the classification of knots|journal=[[Proceedings of the American Mathematical Society]] |year=1974|volume=45|pages=262–6 |issue=2|jstor=2040074|doi=10.2307/2040074|doi-access=free}}
+* {{Citation|first=Dale|last=Rolfsen|title=Knots and Links|publisher=Publish or Perish|location=[[Berkeley, California]]|
+year=1976|series=Mathematics Lecture Series| volume= 7|
+isbn=978-0-914098-16-4 |url=https://books.google.com/books?id=naYJBAAAQBAJ|mr=0515288}}
+* {{Citation|last=Schubert|first=Horst|author-link=Horst Schubert|year=1949|title=Die eindeutige Zerlegbarkeit eines Knotens in Primknoten|journal=Heidelberger Akad. Wiss. Math.-Nat. Kl.|pages = 57–104|issue = 3}}
+* {{Citation|first=Dan|last=Silver|title=Knot theory's odd origins|periodical=American Scientist|volume=94|pages=158–165|year=2006|url=http://www.southalabama.edu/mathstat/personal_pages/silver/scottish.pdf|issue=2|doi=10.1511/2006.2.158}}
+* {{Citation| last=Simon|first=Jonathan| year = 1986| journal = Topology|volume = 25|pages=229–235|title=Topological chirality of certain molecules| doi=10.1016/0040-9383(86)90041-8| issue=2|doi-access=free}}
+* {{Citation | last =Sossinsky | first =Alexei | year =2002 | title =Knots, mathematics with a twist | publisher =Harvard University Press | isbn =978-0-674-00944-8 }}
+* {{Citation|last=Turaev|first=Vladimir G.|author-link=Vladimir Turaev|title=Quantum invariants of knots and 3-manifolds|journal= De Gruyter Studies in Mathematics|volume= 18|publisher=Walter de Gruyter & Co.|place=Berlin|year=1994|isbn=978-3-11-013704-0|title-link=Quantum invariant|arxiv=hep-th/9409028|bibcode=1994hep.th....9028T}}
+* {{cite web |url=http://mathworld.wolfram.com/ReducedKnotDiagram.html |title=Reduced Knot Diagram |last1=Weisstein |first1=Eric W. |author-link=Eric W. Weisstein| work=MathWorld |publisher=Wolfram |access-date=8 May 2013 |year=2013 }}
+* {{cite web |url=http://mathworld.wolfram.com/ReducibleCrossing.html |title=Reducible Crossing |last1=Weisstein |first1=Eric W. |work=MathWorld |publisher=[[Wolfram Research|Wolfram]] |access-date=8 May 2013 |year=2013a}}
+* {{Citation|last=Witten|first=Edward|author-link=Edward Witten|title=Quantum field theory and the Jones polynomial|journal=Comm. Math. Phys.|volume=121|year=1989|pages=351–399|issue=3|doi=10.1007/BF01217730|bibcode=1989CMaPh.121..351W|s2cid=14951363|url=http://projecteuclid.org/euclid.cmp/1104178138}}
+* {{Citation|first=Erik C.|last=Zeeman|author-link=E. C. Zeeman|title=Unknotting combinatorial balls|journal=Annals of Mathematics |series=Second Series|year=1963|volume=78|pages=501–526|issue=3|jstor=1970538|doi=10.2307/1970538}}
+* {{citation |first1=Gerhard |last1=Burde |author-link=Gerhard Burde |author2-link=Heiner Zieschang |first2=Heiner |last2=Zieschang |title=Knots |publisher=Walter de Gruyter |series=De Gruyter Studies in Mathematics |volume=5 |year=1985 |isbn=978-3-11-008675-1 |url=https://books.google.com/books?id=DJHI7DpgIbIC}}
+* {{cite book |first1=Richard H. |last1=Crowell |author-link=Richard H. Crowell |first2=Ralph |last2=Fox |author-link2=Ralph Fox| title=Introduction to Knot Theory |year=1977 |isbn=978-0-387-90272-2 }}
+* {{citation |first=Louis H. |last=Kauffman |author-link=Louis H. Kauffman |title=On Knots |year=1987 |isbn=978-0-691-08435-0 |url=https://books.google.com/books?id=BLvGkIY8YzwC }}
+* {{citation |first=Louis H. |last=Kauffman |author-link=Louis H. Kauffman |title=Knots and Physics |publisher=World Scientific |year=2013 |isbn=978-981-4383-00-4 |edition=4th |url=https://books.google.com/books?id=fSKrRQ77FMkC }}
+* {{citation |first=Peter R. |last=Cromwell |title=Knots and Links |publisher=Cambridge University Press |year=2004 |isbn=978-0-521-54831-1 |url=https://books.google.com/books?id=djvbTNR2dCwC }}
+* {{citation |editor-first=William W. |editor-last=Menasco |editor2-first=Morwen |editor2-last=Thistlethwaite |editor2-link=Morwen Thistlethwaite |title=Handbook of Knot Theory |publisher=Elsevier |year=2005 |isbn=978-0-444-51452-3 }}
+* {{citation |last=Livio |first=Mario |chapter=Ch. 8: Unreasonable Effectiveness? |chapter-url=https://books.google.com/books?id=ebd6QofqY6QC&pg=PA203 |title=Is God a Mathematician? |publisher=Simon & Schuster |year=2009 |isbn=978-0-7432-9405-8 |pages=203–218 }}
 {{refend}}
 == Спољашње везе ==
 {{commons category|Knots}}
-*{{Dmoz|/Reference/Knots/|Knots}}
+* {{Dmoz|/Reference/Knots/|Knots}}
+* [https://knotinfo.math.indiana.edu/ '''KnotInfo''': ''Table of Knot Invariants and Knot Theory Resources'']
+* [http://katlas.math.toronto.edu/wiki/Main_Page The Knot Atlas] — detailed info on individual knots in knot tables
+* [http://knotplot.com/ KnotPlot] — software to investigate geometric properties of knots
+* [http://www.math.utk.edu/~morwen/knotscape.html Knotscape] — software to create images of knots
+* [http://knotilus.math.uwo.ca/ Knoutilus] — online database and image generator of knots
+* [https://reference.wolfram.com/language/ref/KnotData.html KnotData.html] — [[Wolfram Mathematica]] function for investigating knots
+* [https://regina-normal.github.io/index.html/ Regina] — software for low-dimensional topology with native support for knots and links. [https://regina-normal.github.io/data.html#knots Tables] of prime knots with up to 19 crossings
+* [http://www.southalabama.edu/mathstat/personal_pages/silver/smoke%20rings.mpg Movie] of a modern recreation of Tait's smoke ring experiment
+* [http://www.maths.ed.ac.uk/~aar/knots History of knot theory] (on the home page of [[Andrew Ranicki]])
-{{клица}}
 {{Authority control}}

Нормативна контрола
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Остале	Енциклопедија Британика