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Topic: Archimedean spiral

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Logarithmic spiral

Spiral

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	Spiral - Wikipedia, the free encyclopedia
		In mathematics, a spiral is a curve which turns around some central point or axis, getting progressively closer to or farther from it, depending on which way one follows the curve.
		For example, a conic helix may be defined as a spiral on a conic surface, with the distance to the apex an exponential function of θ.
		A spherical spiral (rhumb line) is the curve on a sphere traced by a ship traveling from one pole to the other while keeping a fixed angle (but not a right angle) with respect to the meridians of longitude, i.e.
	en.wikipedia.org /wiki/Spiral (311 words)

	Archimedean spiral (Site not responding. Last check: 2007-11-07)
		This spiral is a generalization of Archimedes' spiral (a=1), named to the Greek Archimedes (225 BC).
		The inverse of the spiral with a constant a is an Archimedean spiral with a constant -a.
		An Archimedean spiral with parameter a has as polar inverse an Archimedean spiral with parameter -a: so the lituus and Fermat's spiral are inversely related, and also the hyperbolic and the Archimedes' spiral.
	www.2dcurves.com /spiral/spirala.html (101 words)

	Xah: Special Plane Curves: Archimedean Spiral
		The inverse curve of an Archimedean spiral with respect to the center is another Archimedean spiral scaled.
		The inverse curve of Archimedes' spiral with inversion circle of radius 1 at pole is the reciprocal spiral.
		The inverse curve of Fermat's spiral with inversion circle of radius 1 at pole is the lituus.
	xahlee.org /SpecialPlaneCurves_dir/ArchimedeanSpiral_dir/archimedeanSpiral.html (390 words)

	Logarithmic spiral: Definition and Links by Encyclopedian.com - All about Logarithmic spiral (Site not responding. Last check: 2007-11-07)
		The logarithmic spiral can be distinguished from the Archimedean spiral by the fact that the distance between the arms of a logarithmic spiral increase in geometric progression, while in an Archimedean spiral these distances are constant.
		Hawks approach their prey in the form of a logarithmic spiral: their sharpest view is at an angle to their flight direction; this angle is the same as the spiral's pitch.
		The arms of spiral galaxies are roughly logarithmic spirals.
	www.encyclopedian.com /go/Golden-spiral.html (628 words)

	Archimedean spiral
		A spiral, like that of the groove in a phonograph record, in which the distance between adjacent coils, measured radially out from the center, is constant.
		It was first studied by Archimedes and was the main subject of his treatise On Spirals.
		The Archimedean spiral is distinguished from the logarithmic spiral by the fact that successive arms have a fixed distance (equal to 2(pi)b if theta is measured in radians), whereas in a logarithmic spiral these distances form a geometric progression.
	www.daviddarling.info /encyclopedia/A/Archimedean_spiral.html (218 words)

	Multioctave microstrip antenna - US Patent 5313216 (Site not responding. Last check: 2007-11-07)
		That researcher concluded, however, that the achievement of a microstrip-type antenna with a wide bandwidth analogous to the conventional spiral (of a frequency-independent antenna) was not feasible because the radiation patterns of the contemplated low-profile antenna tend to exhibit a large axial ratio.
		To examine the effect of conformal mounting of the spiral microstrip antenna on a curved surface, we placed a 3-inch diameter spiral microstrip antenna on a half-cylinder shell with a radius of 6 inches and a length of 14 inches.
		The diameter of each spiral (the Archimedean and the equiangular) was 3.0 inches, with foam absorbing material (loading) extending from 1.25 to 1.75 inches from center.
	www.patentstorm.us /patents/5313216.html (5229 words)

	Archimedean spiral - Wikipedia, the free encyclopedia
		An Archimedean spiral (also arithmetic spiral) is a curve which in polar coordinates (r, θ) can be described by the equation
		Virtually all static spirals appearing in nature are logarithmic spirals, not Archimedean ones.
		Many dynamic spirals (such as the Parker spiral of the solar wind, or the pattern made by a St.
	www.wikipedia.org /wiki/Archimedean_spiral (224 words)

	Spirals
		The radius r(t) and the angle t are proportional for the simpliest spiral, the spiral of Archimedes.
		Spirals in their diverse art forms were intended as objects of expressing spirituality for contemplation and meditation.
		Spherical Spirals, Logarithmic Spiral, Logarithmic Spiral Evolute, Loxodrome, Curlicue Fractal, Cornu Spiral,...
	www.mathematische-basteleien.de /spiral.htm (1708 words)

	Phased array antenna including archimedean spiral element array and related methods - US Patent 6781560 (Site not responding. Last check: 2007-11-07)
		More particularly, the imaginary Archimedean spiral may include a plurality of levels, and a spacing between adjacent pairs of phased array antenna elements along the imaginary Archimedean spiral may be substantially equal to a radial spacing between adjacent levels.
		The Archimedean spiral may include a plurality of levels, and arranging may include setting a spacing between adjacent pairs of phased array antenna elements along the imaginary Archimedean spiral to be substantially equal to a radial spacing between adjacent levels.
		The Archimedean spiral may include a plurality of levels 14-17, and arranging may include setting a spacing x between adjacent pairs of phased array antenna elements 12 to be substantially equal to a radial spacing x between adjacent levels.
	www.patentstorm.us /patents/6781560.html (3754 words)

	Spiral article - Spiral Vangelis Spiral spaceplane Spiral (spaceplane) mathematics curve - What-Means.com (Site not responding. Last check: 2007-11-07)
		A two-dimensional spiral may be described using polar coordinates by saying that r is a continuous monotonic function of θ.
		The Archimedean spiral — r = a + bθ
		A spherical spiral is the curve on a sphere traced by a ship traveling from one pole to the other while keeping a fixed angle (but not a right angle) with respect to the meridians of longitude (cf.
	www.what-means.com /encyclopedia/Spiral (263 words)

	spiral.htm
		A spiral is plane curve that, in general, unwinds around a point while moving ever farther from the point.
		The Archimedean spiral is described in polar coordinates by
		The famous equiangular spiral was discovered by Rene Descartes, and its properties of self-reproduction by Jacob Bernoulli (1654-1705) who requested that the curve be engraved upon his tomb with the phrase "Eadem mutata resurgo" ("I shall arise the same, though changed.")
	www.math.tamu.edu /~dallen/digitalcam/spiral/spiral.htm (566 words)

	logarithmic spiral
		Hawks approach their prey in the form of a logarithmic spiral and their sharpest view is at an angle to their flight direction that is the same as the spiral's pitch.
		In polar coordinates (r, theta) the equation of the logarithmic spiral is
		It can be distinguished from the Archimedean spiral by the fact that the distance between the arms of a logarithmic spiral increase in a geometric sequence while in an Archimedean spiral this distance is constant.
	www.daviddarling.info /encyclopedia/L/logarithmic_spiral.html (432 words)

	Logarithmic spiral - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-07)
		A logarithmic spiral, equiangular spiral or growth spiral is a special kind of spiral curve which often appears in nature.
		The logarithmic spiral was first described by Descartes and later extensively investigated by Jakob Bernoulli, who called it Spiralis mirabilis and wanted one engraved on his headstone.
		Logarithmic spirals are self-similar in that they are self-congruent under all similarity transformations (enlarging it gives the same result as rotating it).
	xahlee.org /_p/wiki/Logarithmic_spiral.html (711 words)

	SPIRAL - LoveToKnow Article on SPIRAL (Site not responding. Last check: 2007-11-07)
		A group of spirals are included in the parabolic spirals given by the equation r=aO~ the more important are the Archimedean spiral, r =aO (fig.
		Its p r equation is p=rf/~ (a2+rf), and the angle between the radius vector and the tangent equals the vector angle.
		Another group of spiralstermed Cotess spirals appear as the path of a particle moving under the influence of a central force varying as the inverse cube of the distance (see MECHANICS).
	www.1911encyclopedia.org /S/SP/SPIRAL.htm (491 words)

	Spiral (Site not responding. Last check: 2007-11-07)
		In mathematics, a spiral is a curve which turns aroundsome central point or axis, getting progressively closer to or farther from it, depending on which way you follow the curve.
		A two-dimensional spiral may be described using polarcoordinates by saying that r is a continuous monotonic function of θ.
		A spherical spiral is the curve on a sphere traced by a ship traveling from one pole to the other while keeping afixed angle (but not a right angle) with respect to the meridians of longitude (cf.
	www.therfcc.org /spiral-17892.html (236 words)

	Rolling Ball Technology - The Scoop Wheel or Tympanum
		It is sometimes named a spiral pump, and was made to raise water for a dye house in the vicinity of that city.
		As a spiral it is arranged round the circumference of a cone or cylinder, and then resembles the worm of a still.
		An Archimedean spiral does have the interesting property that when rotated with uniform angular velocity the linear velocity of the spiral past, say, the y axis is constant.
	www.marcdatabase.com /~lemur/rbt-scoopwheel.html (1874 words)

	Archimedes' spiral
		The Archimedes' spiral (or spiral of Archimedes) is a kind of Archimedean spiral.
		Three-dimensionally the curve is the orthogonal projection (on a plane perpendicular to the axis) of the spiral cone of Pappus.
		This spiral can be seen on the desktop at startup of your computer, when your friend has been affected by the win32.hybris virus.
	www.2dcurves.com /spiral/spiralaa.html (446 words)

	A Lesson on Spirals (Site not responding. Last check: 2007-11-07)
		The Spiral of Theodorus approximates the Logarithmic Spiral.
		Ironically, the spiral on his tombstone appears to be an Archimedean spiral as opposed to a logarithmic spiral.
		Using an overhead of an Archimedean spiral and some bird seed, demonstrate that the area of one circuit is one third of the area of the circle on the larger radius.
	courses.wcupa.edu /jkerriga/Lessons/A%20Lesson%20on%20Spirals.html (2508 words)

	Spiral Notebook (Site not responding. Last check: 2007-11-07)
		In mathematics, a spiral is a curve which turns around some central point or axis, getting progressively closer to or farther from it, depending onwhich way you follow the curve.
		For compound 3-d spirals, such as the spherical spiral described below, h increases with θ on one side of apoint, and decreases with θ on the other side.
		A spherical spiral (rhumb line) is the curve on a sphere traced by aship traveling from one pole to the other while keeping a fixed angle (but not a right angle) with respect to the meridians of longitude, i.e.
	www.elusiveeye.com /side11320-spiral-notebook.html (341 words)

	Nurad Technologies, Inc. Spiral Antennas Page
		These Archimedean spirals employ very broadband balun feed networks and are available in right- and left-hand polarizations.
		Current spiral designs provide frequency coverage in discrete bands from 200 MHz to 40 GHz and diameters from greater than 30 inches to less than 1 inch.
		The cavity backed spiral antenna's rugged construction and lightweight, moisture sealed design make it well suited for the extreme conditions of airborne platforms, and typical applications include RWR and direction finding systems for both airborne and shipboard systems.
	www.nurad.com /products/antennas/spiral-antennas.asp (168 words)

	Some Pics
		At the transition, the superimposed spiral degenerates to a sector.
		The superpatterns consist of dark regions where the wavelength of the primary spiral is shorter, and bright regions of larger wavelength.
		The wavetrains emitted by the spiral wave have become unstable such that local variations in the wavenumber are amplified.
	www.math.umn.edu /~scheel/pics/spiral (541 words)

	Construct Arch Sprials (Site not responding. Last check: 2007-11-07)
		One kind of spiral is the Archimedean spiral (named after the 3rd Century Greek mathematician, Archimedes, who studied them extensively) where the spiral goes out from the center by adding equal steps of distance to the previous distance for every equal increase in the amount of angle as we go around the circle.
		The other main kind of spiral is logarithmic, where the amount of distance that is added with each step to the distance from the center of the previous step is not the same at each step.
		Because we want to run our psychological experiment on the psychophysics of the aesthetics of spirals for spirals with different numbers of turns within the same diameter (space), lets try to make some Archimedean spirals with two and three turns (720° 1080° respectively) about the circle within the 10 units of distance.
	www.blueberry-brain.org /syndyn/spirals/spm2.htm (451 words)

	Spiral (Grades K-4) (Site not responding. Last check: 2007-11-07)
		This spiral was studied by Archimedes in about 225 BC in a work On Spirals.
		Although it had already been considered by his friend Conon, it is often called the Spiral of Archimedes.
		Measure the rays radiating from the center of the spiral.
	www.math.nmsu.edu /breakingaway/Lessons/spiral_K_1/spiral_K.html (211 words)

	Archimedean Spiral (Site not responding. Last check: 2007-11-07)
		An Archimedean spiral is characterized by the radius
		For a typical solar wind speed between 300 and 400 km/s, the spiral field line is inclined at an angle of about 55° to 45° in the vicinity of the Earth at 1 AU.
		This is how the spiral magnetic field lines would appear to an observer (for example, on Ulysses) looking down on our solar system from the northern ecliptic pole.
	urap.gsfc.nasa.gov /www/reiner/archimedean.html (258 words)

	The Geometry Junkyard: Spirals
		Archimedean spiral extended into three dimensions, from the Mathematica graphics gallery.
		This shape, constructed by inscribing circular arcs in a spiral tiling of squares, resembles but is not quite the same as a logarithmic spiral.
		A similar spiral is used as the Sybase Inc. logo.
	www.ics.uci.edu /~eppstein/junkyard/spiral.html (508 words)

	default (Site not responding. Last check: 2007-11-07)
		Spiral was formed on July 5, 1963 as a result of that meeting.
		The group's name is based on the Archimedean spiral that "moves outward embracing all directions, yet constantly upward." Spiral brought together a dynamic group of artists divergent in terms of age, background, interests and style of work, which ranged from abstractionist to realist.
		Despite the success of the showing, Spiral ceased to exist after two years when the artists believed they had outgrown the aesthetic limitations and urgent concerns of the period.
	www.asrc.cornell.edu /blacknessincolor/galleries/galllery7left.html (785 words)

	Archimedean spiral -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		Note that the Archimedean spiral has two arms, one for θ > 0 and one for θ
		Other spirals falling into this group include the (Click link for more info and facts about hyperbolic spiral) hyperbolic spiral, (Click link for more info and facts about Fermat's spiral) Fermat's spiral, and the (Click link for more info and facts about lituus) lituus.
		Virtually all spirals appearing in nature are (Click link for more info and facts about logarithmic spiral) logarithmic spirals, not Archimedean ones.
	www.absoluteastronomy.com /encyclopedia/A/Ar/Archimedean_spiral.htm (194 words)

	Archimedes' Spiral History - Archimedes' Spiral Information (Site not responding. Last check: 2007-11-07)
		The groove in an old-style LP record is an example of such an Archimedean spiral.
		However, in ancient Greece either a physical measurement of the circumference of the circle had to be made or a critical factor in the still not widely known equation for determining the area had to be used.
		He started the drawing of the spiral at the center of a circle and rotated and opened the compass in such a way that the spiral reached the perimeter after one turn.
	www.bookrags.com /sciences/mathematics/archimedes-spiral-wom.html (545 words)

	NGA \| Bearden: A Leader in the Arts Community - The Spiral Group
		Initially the group was concerned with logistical issues, such as obtaining busses to travel to the March on Washington in the summer of 1963.
		Spiral member Norman Lewis framed the question: "Is there a Negro Image?" To which group member Felrath Hines responded, "There is no Negro Image in the twentieth century—in the 1960s.
		Woodruff suggested Spiral as a name for the group, alluding to the Archimedean Spiral, which moves outward and constantly upward.
	www.nga.gov /education/classroom/bearden/lead1.htm (388 words)

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