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Topic: Winding number

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	Winding Number & Linking Number
		In mathematics, the winding number of closed curve in the plane around a given point is an integer representing the total number of times that curve travels counterclockwise around the point.
		Winding numbers are fundamental objects of study in algebraic topology, and they play an important role in vector calculus, complex analysis, geometric topology, differential geometry, and physics.
		In topology, the winding number is an alternate term for the degree of a continuous mapping.
	www.juliantrubin.com /encyclopedia/mathematics/winding_number.html (1841 words)

	Coil winding number variable type motor and coil winding number varying method for varying cooling and heating capacity ...
		The coil wound in the motor of the reciprocating compressor is divided into the main coil and the plurality of sub-coils and the winding number of the motor coil is varied by itself to control the stroke of the reciprocating compressor, thereby effectively coping with the change in the voltage or the load.
		The motor and controller of claim 1, wherein the motor coil comprises: a main coil wound in the motor and configured to occupy a majority of the winding number of the motor coil; and a plurality of sub-coils wound in the motor and configured to be connected to the main coil.
		Therefore, an object of the present invention is to provide a coil winding number variable type motor for varying a cooling and heating capacity of a reciprocating compressor that is capable of varying the number of winding, a capacity of a motor itself, by itself to cope with a load and a voltage change.
	www.freepatentsonline.com /6841967.html (2222 words)

	NetMotion Advisor on Stepping Motors
		With winding number 1 energised, the rotor teeth marked X are attracted to this winding's poles.
		In use, the center taps of the windings are typically wired to the positive supply, and the two ends of each winding are alternately grounded to reverse the direction of the field provided by that winding.
		Motor winding number 1 is distributed between the top and bottom stator pole, while motor winding number 2 is distributed between the left and right motor poles.
	www.netmotion.com /htm_files/advisory/advisor_types.htm (1831 words)

	Winding number - Wikipedia, the free encyclopedia
		The term winding number may also refer to the rotation number of an iterated map.
		In mathematics, the winding number is a topological invariant playing a leading role in complex analysis.
		The winding number is used in the residue theorem.
	en.wikipedia.org /wiki/Winding_number (464 words)

	Conversion from odd to non-zero winding number specification using an extended frame buffer - Patent 5319346
		Conversion from odd to non-zero winding number convention for representation of polygons in a graphics system comprises entry of a polygon in a frame buffer using distinguished states.
		A further object of the present invention is to provide conversion of the odd winding number convention to the non-zero winding number convention in an efficient manner.
		2, for the non-zero winding number definition of a polygon, the left and right boundaries are entered into the frame buffer using two states, one for downward drawn edges, and another for upward drawn edges.
	www.freepatentsonline.com /5319346.html (4336 words)

	Winding Number and Topological Explanations
		As they say in the trade, "winding number is invariant under continuous deformations." There are fancier definitions of winding number, with integrals and stuff, and related concepts for other sorts of shapes, which are also constant under continuous deformations.
		Winding number also shows up in pattern formation.
		Winding number will be conserved if spiral waves always emerge in pairs, rotating in opposite directions.
	cscs.umich.edu /~crshalizi/notebooks/winding-number.html (594 words)

	Implement multi-winding transformer with taps - Simulink
		The winding terminals are identified by the corresponding winding number.
		The first winding is the first one on the primary side (upper-left side) and the last winding is the last one on the secondary side (bottom-right side).
		The tap terminals are identified by their winding number followed by a dot character and the tap number.
	www.mathworks.com /access/helpdesk/help/toolbox/physmod/powersys/ref/multiwindingtransformer.html (1351 words)

	Exploring Winding Numbers and Homotopies
		The winding number of the curve only changes when the homotopy pushes the curve through the origin.
		When a2 = 1, and the others are zero, the winding number is 2, and similarly for a3.
		The standard curve with winding number 3 is indicated in fl.
	web.mit.edu /javalib/src/WebEQ/samples/winding/explore.html (186 words)

	Polygon Fill Teaching Tool (Site not responding. Last check: )
		The method of the non-zero winding number rule is to count the number of times edges wind around a point P in a counter-clockwise direction.
		Add 1 to the winding number for every edge that crosses the line from P in one direction (clockwise or counter-clockwise) and subtract 1 from the winding number for every crossing edge in the opposite direction.
		If the winding number is not equal to zero, the point P is within the polygon.
	www.cs.rit.edu /~icss571/filling/alt_parity.html (165 words)

	PlanetMath: winding number
		Winding numbers are a basic notion in algebraic topology, and play an important role in connection with analytic functions of a complex variable.
		is an integer and has the expected properties of a winding number around
		This is version 5 of winding number, born on 2002-08-14, modified 2003-06-13.
	planetmath.org /encyclopedia/Index2.html (250 words)

	Glossary of Motor Terms -"P"- B-9652-4
		A standard part winding start induction motor is arranged so that one-half of its primary winding can be energized initially and subsequently the remaining half can be energized, both halves then carrying the same current.
		The number of poles is a determinant of the motor's speed.
		This is due to the fact that the different windings are identical and, unlike the capacitor motor, the currents are balanced.
	www.reliance.com /prodserv/motgen/b9652_p.htm (886 words)

	Point in Polygon Strategies
		If a number of points are to be tested against a polygon, it may be worthwhile determining whether the polygon is convex at the start and so be able to use a faster test.
		Winding numbers also have a sign, which corresponds to the direction the edges wrap around the point.
		The bounding box surrounding the polygon is split into a number of horizontal bins and the parts of the edges in a bin are kept in a list, sorted by the minimum X component.
	www.acm.org /pubs/tog/editors/erich/ptinpoly (4418 words)

	What is Algebraic Topology?
		If we deform the curve, the winding number has to vary continuously but, since it is constrained to be an integer, it cannot change and must be a constant unless the curve is deformed through the origin.
		If not, the winding number is 0 which means that the polynomial must have degree 0, in other words, it is a constant.
		Second, when we deform the geometric object, the winding number does not change, hence, it is called an invariant of deformation or, synomynously, an invariant of homotopy.
	www.math.rochester.edu /people/faculty/jnei/algtop.html (1161 words)

	Point in Polygon Strategies
		If a number of points are to be tested against a polygon, it may be worthwhile determining whether the polygon is convex at the start and so be able to use a faster test.
		Winding numbers also have a sign, which corresponds to the direction the edges wrap around the point.
		The bounding box surrounding the polygon is split into a number of horizontal bins and the parts of the edges in a bin are kept in a list, sorted by the minimum X component.
	www.erichaines.com /ptinpoly (4418 words)

	Jones on Stepping Motor Types
		Bifilar windings on a stepping motor are applied to the same rotor and stator geometry as a bipolar motor, but instead of winding each coil in the stator with a single wire, two wires are wound in parallel with each other.
		Winding 2 in Figure 1.4 is shown with a parallel connection; this allows low voltage high-current operation.
		Winding 1 in Figure 1.4 is shown with a series connection; if the center tap is ignored, this allows operation at a higher voltage and lower current than would be used with the windings in parallel.
	www.cs.uiowa.edu /~jones/step/types.html (2453 words)

	Intuition behind Winding Numbers
		On intuitive way to think of the winding number is to imagine the curve made of a very slippery elastic cord, and to think of the point as being replaced by a post or spool cemented to the plane.
		The cord will be wrapped around the spool some number of times, and this is basically the winding number.
		along the curve, and presto-chango out comes the winding number, which is a global property of the curve and p, and which seemingly has nothing to do with the values of some obscure function along the curve.
	web.mit.edu /javalib/src/WebEQ/samples/winding/intuitive.html (409 words)

	EDN Access -- 04.13.95 Finding the keys to flyback power supplies produces efficient design
		The sum of the distance from primary winding (or lead exits) to the core, and the distance from the core to the secondary (or lead exits) must be equal to or greater than required creepage distance.
		C winding is easier to use and costs less-but at the expense of higher loss and lower efficiency.
		Note that, because the bias winding is a primary circuit, margin-wound transformers must have another layer of supplementary or reinforced insulation between the secondary and alternate bias winding.
	www.edn.com /archives/1995/041395/08df3.htm (3854 words)

	Harmony Theory
		The Ω (frequency ratio) or average shift of the angle theta or winding number is conjectured to be a lorentz contraction (alpha) or α=Ω.
		The winding number in the sine circle map is investigated experimentally by the Josephson junction in a microwave field.
		The winding number for the superconducting Josephson junction is the quantization.
	www.ispub.com /ostia/index.php?xmlFilePath=journals/ijwh/vol3n1/space.xml (2921 words)

	Body (Site not responding. Last check: )
		As the number of poles increases, the length of the path is reduced.
		The coils in this winding are uniformly distributed around the lamination stack and therefore, would, as a result of their interaction with the magnets, produce symmetrical torque around the air-gap.
		Whatever type of winding may be used in the design of the motor, it is important to divide up the available space for the stator in the most optimal way between steel and copper.
	www.consult-g2.com /course/chapter7/chapter.html (6235 words)

	MOSIS Technical Notes: Polygons and Winding Numbers
		A polygon encloses an area of the plane, thus dividing the plane into that area which is "inside" the polygon and that which is "outside." For a simple polygon, the two regions are the obvious ones.
		A winding number is an attribute of a point with respect to a polygon that tells us how many times the polygon encloses (or wraps around) the point.
		Regions of winding number 0 (unenclosed) are obviously outside the polygon, and regions of winding number 1 (simply enclosed) are obviously inside the polygon.
	www.mosis.org /Faqs/tech-polygon.html (167 words)

	The Cosmological Twin Paradox
		The winding number is the number of times the world-line is wrapped around the cylinder when the two encounter points are brought together and the "world-lines pulled taut".
		The twin with winding number zero is distinguished because his "surfaces of simultaneity" are closed curves.
		The topological system is the cylinder with the two world-lines, one straight (A) with a winding number of zero, and one wound round the cylinder (B) with a winding number of one.
	www.physicsforums.com /showthread.php?p=363681 (2942 words)

	Astronomical Glossary
		The number of such crests passing a fixed point in 1 second is known as the frequency (a crest per second = 1 Hertz); a short wavelength thus implies high frequency.
		It is the number of wave cycles in unit distance, and is often used in spectroscopy.
		R = k (10g + f) where k is a constant depending on observing conditions, g is the number of sunspot groups, and f is the number of individual spots visible on the Sun at a given time.
	nedwww.ipac.caltech.edu /level5/Glossary/Glossary_W.html (2488 words)

	GameDev.net - Point in a poly
		For non intersecting polygons if the winding number is non-zero then the test point is inside the polygon.
		A figure 8 will give a negitive winding number for a test point in one of the loops and a positive winding number for the other loop, with all points outside having a winding number of 0.
		Other advantages of the winding number calculation are that it does not suffer from the confusion of the infinite ray algorithm when the ray crosses a vertex or is colinear with an edge.
	www.gamedev.net /reference/articles/article421.asp (275 words)

	Point in Polygon Winding Number Inclusion
		However, the validity of the crossing number method is based on the "Jordan Curve Theorem" which says that a simple closed curve divides the 2D plane into exactly 2 connected components: a bounded "inside" one and an unbounded "outside" one.
		Thus, since it is more accurate in general, the winding number algorithm should be the preferred method to determine inclusion of a point in an arbitrary polygon.
		Here is a "C++" implementation of the winding number algorithm for the inclusion of a point in polygon.
	www.geometryalgorithms.com /Archive/algorithm_0103/algorithm_0103.htm (2662 words)

	Winding resistance reporter
		Each file can contain a virtually unlimited number of winding resistance measurements with tap and winding details of each, and several fields of information about the transformer, its location and the operator's name.
		Accurate measurement of transformer winding resistance can provide valuable information about the condition of transformer windings when applied as part of a preventive maintenance program or as a routine test in a manufacturing process.
		The winding resistance test is particularly valuable for transformers with on-load tapchangers because they have hundreds of bolted connections and moving contacts.
	www.adwel.com /winding.html (475 words)

	11011110: Formal knot theory, II: winding numbers and antimatroidality
		Ok, I think my idea from last time of using winding numbers is enough to patch Kaufmann's broken proof that his system of states of a knot diagram (equivalently, spanning trees of a plane-embedded graph, rooted at a vertex of the outer face) forms a lattice.
		The key property of these numbers is that the only rotations that can change the winding number of v are rotations at v itself.
		A rotation in which the parent of v was counterclockwise of r (as viewed from v) before the rotation, and is clockwise of r after the rotation, increases the winding number by one, and the reverse rotation decreases the winding number by one.
	11011110.livejournal.com /127074.html (767 words)

	Multi-winding motor patent invention
		Two kinds of discrete winding wirings A, B are wound together with the same winding number onto each of the magnetic pole sections 13A-13L of the divided cores 9.
		[0013] Preferably, the kind of the discrete winding wiring selected from the N kinds of discrete winding wirings (A, B) wound on the M magnetic pole sections, which are regularly arranged, may be different from that of the discrete winding wiring selected from the adjacent magnetic pole sections in the regular arrangement.
		Two three-phase exciting windings (Sa, Sb) are constructed in such a manner that corresponding two of the exciting windings for one phase (U1 and U2, V1 and V2, W1 and W2) form an identical phase of the two three-phase exciting windings.
	www.freshpatents.com /Multi-winding-motor-dt20061005ptan20060220486.php (1491 words)

	Skyrmions and disoriented domains in 2d-O(3) model
		The Skyrme-Witten conjecture identifies the (integer) winding number B with baryon number.
		The structure of the emerging defects is characterized by bag formation: large gradients in the angular variables (which imply large winding density) is preferably tied to small values of the modulus field (to reduce local energy) i.e.
		If their size is of the order of the lattice unit then the evolution leaves a large number of them embedded in the smooth background (even for B=0 configurations) and the size of aligned domains saturates at a finite value (inversely proportional to the sqrt of the defect density).
	int.phys.washington.edu /SEMINARS/Holzwarth/talk.html (1095 words)

	Argument Principle and Rouche's Theorem
		Theorem 8.8, known as the argument principle, is useful in determining the number of zeros and poles that a function has.
		The answer lies with a fascinating application known as the winding number.
		Thus winding number is indeed an appropriate term.
	math.fullerton.edu /mathews/c2003/RoucheTheoremMod.html (560 words)

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