Bimini Twist Knot Instructions
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Jones Polynomial for Graphs of Twist Knots
Available at Applications and Applied http://pvamu.edu/aam Mathematics: Appl. Appl. Math. An International Journal ISSN: 1932-9466 (AAM) Vol. 14, Issue 2 (December 2019), pp. 1269 – 1278 Jones Polynomial for Graphs of Twist Knots 1Abdulgani ¸Sahinand 2Bünyamin ¸Sahin 1Faculty of Science and Letters 2Faculty of Science Department Department of Mathematics of Mathematics Agrı˘ Ibrahim˙ Çeçen University Selçuk University Postcode 04100 Postcode 42130 Agrı,˘ Turkey Konya, Turkey [email protected] [email protected] Received: January 1, 2019; Accepted: March 16, 2019 Abstract We frequently encounter knots in the flow of our daily life. Either we knot a tie or we tie a knot on our shoes. We can even see a fisherman knotting the rope of his boat. Of course, the knot as a mathematical model is not that simple. These are the reflections of knots embedded in three- dimensional space in our daily lives. In fact, the studies on knots are meant to create a complete classification of them. This has been achieved for a large number of knots today. But we cannot say that it has been terminated yet. There are various effective instruments while carrying out all these studies. One of these effective tools is graphs. Graphs are have made a great contribution to the development of algebraic topology. Along with this support, knot theory has taken an important place in low dimensional manifold topology. In 1984, Jones introduced a new polynomial for knots. The discovery of that polynomial opened a new era in knot theory. In a short time, this polynomial was defined by algebraic arguments and its combinatorial definition was made. -
Sea Fishing Knots - from the Reel to the Hook Online
3x45F [Read free] Sea Fishing Knots - from the reel to the hook Online [3x45F.ebook] Sea Fishing Knots - from the reel to the hook Pdf Free Andy Steer ePub | *DOC | audiobook | ebooks | Download PDF Download Now Free Download Here Download eBook #4532368 in Books Ingramcontent 2016-08-31Original language:English 8.50 x .12 x 5.50l, #File Name: 907174727148 pagesSea Fishing Knots From the Reel to the Hook | File size: 72.Mb Andy Steer : Sea Fishing Knots - from the reel to the hook before purchasing it in order to gage whether or not it would be worth my time, and all praised Sea Fishing Knots - from the reel to the hook: 0 of 0 people found the following review helpful. Ok, basic, not many knots.By PLM, JRI bought it to see what it was about. There are better books and apps out there, with more knot options. The author has several books out on knots, I think he should combine them and sell them at the price of one.0 of 0 people found the following review helpful. EXCELLENT five stars easy...By gbJust downloaded "Sea Fishing Knots" on my iPhone and iPad -- has the exact knots I wanted (the knots are listed in the ad and I read the ad before I ordered) -- beautiful and clear information -- easy to follow -- great work!0 of 1 people found the following review helpful. Two StarsBy R. SnyderThe knot I need wasn't in it Sea Fishing Knots - From the reel to the hook Contains 39 clear, concise, easy to follow step-by-step knot-tying illustrations of recommended Sea and big game fishing knots and 2 set-ups. -
Splitting Numbers of Links
Splitting numbers of links Jae Choon Cha, Stefan Friedl, and Mark Powell Department of Mathematics, POSTECH, Pohang 790{784, Republic of Korea, and School of Mathematics, Korea Institute for Advanced Study, Seoul 130{722, Republic of Korea E-mail address: [email protected] Mathematisches Institut, Universit¨atzu K¨oln,50931 K¨oln,Germany E-mail address: [email protected] D´epartement de Math´ematiques,Universit´edu Qu´ebec `aMontr´eal,Montr´eal,QC, Canada E-mail address: [email protected] Abstract. The splitting number of a link is the minimal number of crossing changes between different components required, on any diagram, to convert it to a split link. We introduce new techniques to compute the splitting number, involving covering links and Alexander invariants. As an application, we completely determine the splitting numbers of links with 9 or fewer crossings. Also, with these techniques, we either reprove or improve upon the lower bounds for splitting numbers of links computed by J. Batson and C. Seed using Khovanov homology. 1. Introduction Any link in S3 can be converted to the split union of its component knots by a sequence of crossing changes between different components. Following J. Batson and C. Seed [BS13], we define the splitting number of a link L, denoted by sp(L), as the minimal number of crossing changes in such a sequence. We present two new techniques for obtaining lower bounds for the splitting number. The first approach uses covering links, and the second method arises from the multivariable Alexander polynomial of a link. Our general covering link theorem is stated as Theorem 3.2. -
Preparing Trolling Lines
CHAPTER 3 PREPARING TROLLING LINES A. TOOLS AND UTENSILS B. HOOKS -Hook types -Sharpening hooks -Ganging hooks C. 'TYPES OF FISHING LINE -Handling lines -Line characteristics D. END LOOPS IN LINE AND SINGLE-STRAND WIRE -Double figure-eight knot -Using end loops -End loops in wire E. .END LOOPS IN ROPE -Whipping and sealing rope ends -Bowline knot -Eye splice F. END LOOPS IN CABLE (MULTI-STRAND WIRE) -Wrapped end loops -Flemish eye -Crimping cable -Lazy splice G. KNOTS FOR HOOKS AND TACKLE -Palomar knot -Slip knot -Clinch knot -'Trilene' knot -Tying a hook rigid on wire H. JOINING LINES TOGETHER -Blood knot (Barrel knot) -Double slip knot -Using end loops -Connector rings and swivels I. THE ASSEMBLED TROLLING LINE -The mainline -The trace -Changing traces- Trace length -The backing J. SINKERS -Heavier line materials -Sinkers -Downriggers -Cannonballs K. DIVING DEVICES -Diving boards -Tripping -Diving lures -Trolling depth L. RIGGING FIXED LINES -Making shock absorbers -Rigging shock absorbers -Position -Backing cord and lazy line -Line storage M. RIGGING LINES ON HAND REELS -Loading the reel -Overloading -Adjustments -Using wire N. RIGGING HANDREELS FOR TROLLING -Rigging through a trolling boom -Rabbit line -Boom stays -Braking system (drag) -Lazy line 29 CHAPTER 3: PREPARING TROLLING LINES SECTION A: TOOLS AND UTENSILS Most of the preparation for trolling is normally done on shore before the fishing trip starts. This makes gear rigging easier and more comfortable, prevents new materials being contaminated with salt water before they are used, and avoids wasting time at sea which could better be used in fishing or carrying out other tasks on the boat. -
Transverse Unknotting Number and Family Trees
Transverse Unknotting Number and Family Trees Blossom Jeong Senior Thesis in Mathematics Bryn Mawr College Lisa Traynor, Advisor May 8th, 2020 1 Abstract The unknotting number is a classical invariant for smooth knots, [1]. More recently, the concept of knot ancestry has been defined and explored, [3]. In my research, I explore how these concepts can be adapted to study trans- verse knots, which are smooth knots that satisfy an additional geometric condition imposed by a contact structure. 1. Introduction Smooth knots are well-studied objects in topology. A smooth knot is a closed curve in 3-dimensional space that does not intersect itself anywhere. Figure 1 shows a diagram of the unknot and a diagram of the positive trefoil knot. Figure 1. A diagram of the unknot and a diagram of the positive trefoil knot. Two knots are equivalent if one can be deformed to the other. It is well-known that two diagrams represent the same smooth knot if and only if their diagrams are equivalent through Reidemeister moves. On the other hand, to show that two knots are different, we need to construct an invariant that can distinguish them. For example, tricolorability shows that the trefoil is different from the unknot. Unknotting number is another invariant: it is known that every smooth knot diagram can be converted to the diagram of the unknot by changing crossings. This is used to define the smooth unknotting number, which measures the minimal number of times a knot must cross through itself in order to become the unknot. This thesis will focus on transverse knots, which are smooth knots that satisfy an ad- ditional geometric condition imposed by a contact structure. -
Jones Polynomial of Knots
KNOTS AND THE JONES POLYNOMIAL MATH 180, SPRING 2020 Your task as a group, is to research the topics and questions below, write up clear notes as a group explaining these topics and the answers to the questions, and then make a video presenting your findings. Your video and notes will be presented to the class to teach them your findings. Make sure that in your notes and video you give examples and intuition, along with formal definitions, theorems, proofs, or calculations. Make sure that you point out what the is most important take away message, and what aspects may be tricky or confusing to understand at first. You will need to work together as a group. You should all work on Problem 1. Each member of the group must be responsible for one full example from problem 2. Then you can split up problem 3-7 as you wish. 1. Resources The primary resource for this project is The Knot Book by Colin Adams, Chapter 6.1 (page 147-155). An Introduction to Knot Theory by Raymond Lickorish Chapter 3, could also be helpful. You may also look at other resources online about knot theory and the Jones polynomial. Make sure to cite the sources you use. If you find it useful and you are comfortable, you can try to write some code to help you with computations. 2. Topics and Questions As you research, you may find more examples, definitions, and questions, which you defi- nitely should feel free to include in your notes and/or video, but make sure you at least go through the following discussion and questions. -
Taut Line Hitch Knot Instructions
Taut Line Hitch Knot Instructions Carbonic and systemic Rob never start-up doggedly when Spiro mineralizes his upholders. Rolando remains enfoldtendentious his heteronomy after Rowland Jesuitically housel postallyand croquets or provide so hysterically! any geographer. Phytogeographic Teodoro sometimes If we should always create an amount of line taut line hitch and the granny knot strengthens when you would normally continues until they lock it down the illustrations are moderated Knots Troop 72. Used are using an engineer or diameters, it allows you? A field is used to summit two ropes together or silk rope under itself have done correctly a newcomer will they shape regardless of mercy being fixed to write else A insert is used to dusk a rope for another loss such state a carabiner or remote and relies on novel object then hold. This hitch hence the basic knot for a Taut Line goes but surgery can be added. Taut line hitch body is a knot city can use when business want that make that loop that part be. How gates Make their Perfect Hammock Ridgeline with 3 Simple. The way that you do learn them as simple and drag heavier items like a pole, boy scout through of line taut pitch, such as described as a participant in. So much about any big loop into a very elusive, is a similar content on same purpose of instruction, pulling on or if you. Many critical factors cannot be. Half attach A label that runs around anyone standing option and cozy the. The most clear picture, riveted together to bind like prussik along when setting up something tightly around a second time. -
Knots of Genus One Or on the Number of Alternating Knots of Given Genus
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 129, Number 7, Pages 2141{2156 S 0002-9939(01)05823-3 Article electronically published on February 23, 2001 KNOTS OF GENUS ONE OR ON THE NUMBER OF ALTERNATING KNOTS OF GIVEN GENUS A. STOIMENOW (Communicated by Ronald A. Fintushel) Abstract. We prove that any non-hyperbolic genus one knot except the tre- foil does not have a minimal canonical Seifert surface and that there are only polynomially many in the crossing number positive knots of given genus or given unknotting number. 1. Introduction The motivation for the present paper came out of considerations of Gauß di- agrams recently introduced by Polyak and Viro [23] and Fiedler [12] and their applications to positive knots [29]. For the definition of a positive crossing, positive knot, Gauß diagram, linked pair p; q of crossings (denoted by p \ q)see[29]. Among others, the Polyak-Viro-Fiedler formulas gave a new elegant proof that any positive diagram of the unknot has only reducible crossings. A \classical" argument rewritten in terms of Gauß diagrams is as follows: Let D be such a diagram. Then the Seifert algorithm must give a disc on D (see [9, 29]). Hence n(D)=c(D)+1, where c(D) is the number of crossings of D and n(D)thenumber of its Seifert circles. Therefore, smoothing out each crossing in D must augment the number of components. If there were a linked pair in D (that is, a pair of crossings, such that smoothing them both out according to the usual skein rule, we obtain again a knot rather than a three component link diagram) we could choose it to be smoothed out at the beginning (since the result of smoothing out all crossings in D obviously is independent of the order of smoothings) and smoothing out the second crossing in the linked pair would reduce the number of components. -
The Scrapboard Guide to Knots. Part One: a Bowline and Two Hitches
http://www.angelfire.com/art/enchanter/scrapboardknots.pdf Version 2.2 The Scrapboard Guide to Knots. Apparently there are over 2,000 different knots recorded, which is obviously too many for most people to learn. What these pages will attempt to do is teach you seven major knots that should meet most of your needs. These knots are what I like to think of as “gateway knots” in that once you understand them you will also be familiar with a number of variations that will increase your options. Nine times out of ten you will find yourself using one of these knots or a variant. The best way to illustrate what I mean is to jump in and start learning some of these knots and their variations. Part One: A Bowline and Two Hitches. Round Turn and Two Half Hitches. A very simple and useful knot with a somewhat unwieldy name! The round turn with two half hitches can be used to attach a cord to post or another rope when the direction and frequency of strain is variable. The name describes exactly what it is. It can be tied when one end is under strain. If the running end passes under the turn when making the first half-hitch it becomes the Fisherman’s Bend (actually a hitch). The fisherman’s bend is used for applications such as attaching hawsers. It is a little stronger and more secure than the round turn and two half-hitches but harder to untie so do not use it unless the application really needs it. -
Editorializing Carol Wang the Constrictor Knot
Knot News International Guild of Knot Tyers – Pacific Americas Branch July 2011 Carol Wang-Editor ISSN 1554-1843 Issue #84 or reference. Nope. At least, not in Ashley. (Not Editorializing yet, anyway. More on that later.) Carol Wang Looking at the mechanics of the knots to see why My apologies for the lateness of the newsletter. I wi! the Ashley version works, and how my version not bother you with excuses but only promise to do my works, I figure that the crossing over the top of utmost to be more timely in the future. the simple overhand knot portion provides a compression. The more it’s tightened, the harder This issue sees the first of our Knot Tyer Profiles, it’s compressed, and the longer it holds. starting with a bang with J.D. Lenzen, author and YouTube video mainstay. An article of exploration and analysis that ends up finding a flag already planted but nevertheless enriches the knot world with new insight. We get our long promised closer look at Karl’s knotboard. Reviews of iPhone/iPad knot related apps, and the usual reporting on the activities of the branch. The Constrictor Knot--Two Versions Tig Dupré [Figure 1: Clove Hitch] One of my favorite binder knots is the Constrictor Knot (ABOK #1249). I’ve used it for More closely studied, the Ashley Constrictor many things: temporary repairs on a garden hose, seemed to have evolved from a Clove Hitch binding coiled line for over-the-shoulder travel, (Figure 1), with the running end brought back and binding leather zipper pulls. -
Fishing Knots
Fishing Knots A simple overhand knot weakens line by about 50 percent. Wet knots with saliva as you pull them tight. This prevents damage to the line and allows the knot to pull tight. Pull knots tight to prevent slippage. Trim knots closely with a nail clipper. Knots have their own terminology. The "tag end" (sometimes called the "working end") is the end of the line used to tie the knot. The "standing end" is that part of the line coming from your fishing reel. These knots are especially good for nylon monofilament, the most commonly used line for all fishing. IMPROVED CLINCH KNOT This is a variation of an older clinch knot. The variation (a final tuck of the line back through a loop) makes this knot test 95 percent of the line strength. The secret of this knot is to make five turns of the tag end of the line around the standing end part before running the tag end back through the formed loop. Use for lines up to 20 pound test. PALOMAR KNOT This knot, over 95 percent in strength, takes more line to tie because it is doubled first. It is good for lines up to and over 20 pound test. Because it is run doubled through the lure or hook eye, knotted and then looped over the hook or lure, it may tangle easier. It is a favorite knot of many angler. SURGEON’S LOOP To make this, fold over the tag end of line and form the knot using both strands to make a double overhand knot. -
Knots Often Used by Fighter Kite Makers and Flyers
rv 4 2007 Bruce Lambert [email protected] www.fighterkitecentral.com KNOTS OFTEN USED BY FIGHTER KITE MAKERS AND FLYERS There happens to be quite a few of us who don't know much about knots. We don't know how to tie them and don't know which knot to use in a particular situation or the name of the knot. This article is meant to help us learn a little about the knots that can help us in making and adjusting our fighter kites. I posted an email on the fighter kite Topica.com email list asking for contributions about what knots are used for tying bridles, tension lines, etc. Here's the result of the request along with some on-line research I did to provide more options. If you want to know about knots, search the internet for tons of more information. DENNIS ISCHE'S BOW TENSIONER SLIP KNOT This is a great knot to use for the tensioning line on the back of the leading edge of a buka and for putting a bend in a carbon fiber spine of a diamond fighter kite. To adjust this knot, you slide the knot along the line it is tied around. It locks and securely stays in its place when there's tension on the line. To move the knot you must release some of the tension. This functions similar to a tautline hitch. TAUTLINE HITCH The tautline hitch is used by many fighter kite makers as the adjusting knot in a tension line on the back of a buka or on the carbon fiber spine of a diamond shaped fighter kite.