Only the arc lengths of transcendental curves such as the cycloid and the logarithmic spiral had been calculated before this. |
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For hardwoods, such as flooring, siding and rafters, use spiral threaded nails that turn as they are driven into the wood. |
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So points on the spiral are 1.618 times as far from the centre after a quarter-turn. |
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Less than 30 seconds later, Maready was treading water as she watched the red beacon light of her tail rudder spiral deeper into the dark abyss. |
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The male reproductive system contains four pairs of accessory glands, the most prominent of which are the tightly coiled spiral accessory glands. |
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Much grandiose painting business is imposed on top of a large blue spiral enclosing washy green transparencies. |
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No guides accompanied us as we descended down a spiral staircase and into the past of Dubai. |
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A spiral staircase gives access to the attic room, while outside, the paved back garden has a water feature and patio area. |
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But her young life was cut short after she became caught in a spiral of drug addiction. |
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They produce quantities of small adornments of hammered sheet gold, including spiral ear and twisted nose ornaments. |
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The finished apartments will have exposed original timber beams, oak flooring, glazed balconies and spiral staircases. |
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Are we simply caught in a spiral here that will be destructive of our interests while, obviously, significantly advantaging theirs? |
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The water level has receded to expose the entire site, leaving the work as a low white spiral mound embedded in blindingly white salt flats. |
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Kids will love the medieval keep, with its spiral staircases, and dim lighting. |
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I could see how Andy was on a downward spiral and I think the rejection from us helped kick-start his career. |
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Paul eventually dragged me away from the dark spiral of regret and recollection plying me with heavy doses of bourbon. |
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What transpires is a downward spiral of shame and recriminations culminating in Veena being shunned by her family and turned out of the house. |
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Melinda, a mother-of-three, knows first-hand how emotions can spiral out of control after giving birth. |
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Butternut-squash soup, a bistro staple, benefits from freshly ground nutmeg and allspice and a spiral of pumpkinseed oil. |
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The galaxy's hallmark is a brilliant white, bulbous core encircled by the thick dust lanes comprising the spiral structure of the galaxy. |
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Pupils soon latch on to this, and the spiral of decline suddenly becomes much steeper. |
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Two models that have been proposed for this higher-order structure include a regular spiral and an irregular zigzag. |
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Displaced spiral fractures generally display shortening or rotation, whereas displaced transverse fractures may display angulation. |
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Mid-whorl gently convex bearing three coarse spiral cords, the uppermost of which forms an angulation, the base is not preserved. |
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Imports outweighed exports, and resultant trade deficits weakened states already in a downward economic spiral. |
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He gets into social life, the few extra lempiras a week, the booze, the downward spiral. |
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Laying the well-worn black spiral onto my lap, I stroked the cover reverently. |
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Then, I saw the smoke of the incense rise in a spiral, just like the coils of a snake, you know. |
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The atoms of natural sugars are all laid out in an asymmetrical manner, having a right-handed spiral twist. |
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Though you know what they say, that a cyclotron is just a linac coiled into a spiral. |
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The ritual humiliation and abuse begin immediately and rapidly threaten to spiral out of control. |
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The linker DNA follows a continuous spiral path between nucleosomes with a correspondingly large bend. |
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Both sculptures involve single plaster-walled cubes with open tops, out of which spiral successively smaller cubes made from metal rods. |
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Beyond mere survival are the severe long-term problems of a once major club in a spiral of decline. |
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The deflationary spiral under the long-wave Kondratiev cycle is far from over, in spite of appearances. |
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Soft lighting, copper tones, a spiral chandelier and an Art Deco bar create the ambience to make this a lounge lizard's paradise. |
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All other loxodromes, e.g. the direction NW, trace spiral paths that converge on either the north or south pole. |
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The trees are tapped for latex by cutting spiral grooves in the bark and inserting a spout with a cup for collection of the latex. |
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When we were first married, I would tape them to the fridge door on scraps torn out of a spiral bound notebook. |
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That might cause big mailers to move to alternatives even faster, triggering a spiral of falling revenues, rising debt, and declining service. |
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Black skies boiled and seethed above, clouds dark as pitch surging in an ominous spiral. |
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The further the excavation goes, the more events seem to spiral maliciously out of control, growing continuously more sinister. |
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We cannot condone terrorism, but the way to end it is not through a vicious spiral of violence. |
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The result is an escalating spiral of suspicion, greed and betrayal, in which family and friendships are put to the test. |
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Or get a spiral notebook and a ballpoint, plant yourself under a tree, and pen a few lines of prose. |
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Twist 14-gauge wire into spiral formations to bang out copper bangle bracelets assembly-line style. |
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He performed a tactical approach to the airfield, banking the plane 45 degrees in a tight downward spiral to the left. |
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A relevant example is that of spiral sculpture in the gastropod Nucella emarginata, which ranges from strongly sculptured to smooth. |
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These were generally straight but also included forms that were curved or spiral or had lateral arms. |
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The air around them was thick with dust and age as they descended a narrow set of spiral stone stairs. |
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Each floor has an oblong chamber with a small room and spiral stair in the wall thickness at the seaward end. |
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The enemy pilot had throttled back, reducing airspeed and flattening the spiral dive. |
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John gazes longingly at her but never dreams of making a move, despite his wife's spiral into self-absorbed hostility. |
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As a result, you can grow herbs, greens, medicinals, bulbs, and flowers on one spiral. |
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We need self-control in situations where anger or addictions cause us to spiral out of control. |
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They say that detention is creating a spiral of depression, psychotic symptoms and self-mutilation. |
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We are getting a small room built in the loft for Philipp, complete with a spiral staircase and two loft windows. |
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Also, hallucinogenic drugs, such as mescaline and LSD, are known to produce visions of striped tunnels and spiral chambers. |
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The costs spiral because each part of the construction has to be sequenced. |
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Heavier objects can be supported with a molly style hollow wall fastener, a spiral threaded fastener, or a toggle bolt. |
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Mr White believes this triggered a downward spiral fuelled by heavy drinking sessions. |
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When the bank moves in to foreclose, she decides to double-cross the duo, setting in motion a series of events which spiral out of control. |
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It measures 9x7m and houses two mezzanine floors once connected by a spiral staircase. |
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He carries a tote bag containing his playbook and a spiral notebook and takes a seat in the second row. |
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Spending levels are expected to spiral above even those in 1999, when major companies splurged out of fear of the millennium bug. |
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If the team applied just a few volts across the heart muscle for a few tens of milliseconds, a second, smaller spiral appeared. |
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The bird rises almost perpendicularly in the air with fluttering wingbeats before turning rapidly and making a slow spiral descent with wings and tail outspread. |
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This is the big enchilada, and the culmination of the alleged death spiral. |
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Once I was passing along the side of a deep abyss that seemed to spiral down forever and a strong wind started to blow, as if it were trying to push me in. |
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The shoes are the telling detail, proof that the song's protagonist has slipped from stability into a downward spiral of apathy and self-abnegation. |
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The spiral design is a metaphor of change and transition, a celebration of the coexistence of past and future. |
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In a 1990 piece, roses with long, spindly stems are placed to form a sunburst, their blossoms defining a central spiral and their stems radiating outward. |
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When Archimedes defines a spiral, he gives fundamental properties connecting the length of the radius vector with the angles through which it has revolved. |
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The spiral decorations, individually and in pairs joined by a loop, and the schematic lizard on the opposite side of the bell, suggest a Cross River origin. |
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Leung, however, has criticized Occupy Central for allowing the protests to spiral out of control. |
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Sometimes if parents set too many boundaries and discipline too much, they will then also rebel and spiral out of control. |
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Walking through the spiral hallway into the almost pitch black, circular room, the senses become immediately disoriented. |
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A secret trap door in the kiosk below the clock leads to a spiral staircase down to the lower level info booth. |
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The path was endless, constantly winding downward in a spiral. |
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I did have one solitary experience with Ms. Reynolds before our relationship started to grow and my life got a huge kick-start in its already progressing downward spiral. |
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One look at today's health exchange prices suggests that the death spiral is already beginning. |
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If Mitt Romney did the same, it might send the Iowa system into the death spiral it so richly deserves. |
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In June, she will take over a publication that has appeared in recent years to be in a death spiral. |
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To his fellow survivors and to the audience, this delusion indicates another slip on a downward spiral. |
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If you are bothered by deer, rabbits or even cats, protect the bark with either some wire mesh fencing or a spiral tree guard that wraps around the trunk. |
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Next, I added a row of cowrie shells around the base of the birdhouse and then topped it off with a spiral worm shell like a little birdie weathervane on the top. |
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The spiral worm shell is also considered to be a horn shell. |
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When exactly did this downward cultural spiral begin, this loss of tact and refinement and understanding that some things should not be said or directly represented? |
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The sense of an old hacienda is back, with arched hallways, massive ceiling beams, a spiral staircase with wrought-iron railing and a sunken garden. |
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They began to whisper, and one man scribbled on a spiral notepad. |
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Again and again Oney grabs the reader by the scruff of the neck, both through his dexterity with details and through the horror of the downward spiral of the case itself. |
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This downward spiral involving local power politics was obvious to the Americans in the valley. |
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The shopkeeper unlocked a door for us and we went down a narrow spiral staircase to a communal hole in the wall. |
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Even a modest hit from sanctions or pullback by foreign investors will only add to that downward spiral. |
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This fuels a vicious downward spiral of self-hatred and hatred of anomalous others from which it is difficult for the political discriminator to escape. |
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I entered this gigantic granite jewel, which is as light in its effect as a bit of lace and is covered with towers, with slender belfries to which spiral staircases ascend. |
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There was a large spiral staircase leading into the hallway in the front. |
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The tour in 1995, in which ticketless groups physically crashed down gates, was the bottom of a spiral that had been winding its way down for some time. |
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For many seniors, driving represents the difference between isolation and the frailty spiral. |
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Led by a Connecticut dentist, a research team says it has unraveled some of the mysteries surrounding the spiral horn grown by the small Arctic whale known as the narwhal. |
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A thin line of smoke started to spiral up from the ruptured engine as Ian scrambled round the back of the car, catching his trouser leg on the crumpled rear bumper. |
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The spokesman said an upward spiral in defence spending accelerated the arms race in the region, symmetrically or asymmetrically, voluntarily or involuntarily. |
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The now-convicted felons will hear their sentences in January, but their story continues to spiral downward. |
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The herb spiral has two diverse microclimates, ranging from a sunny, dry area on the upper southern half to a shaded, moist area on the north and around the base. |
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Wallace pointed to the spiral shaped thingamabob in her left pocket. |
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He will take them into the lighthouse and up the spiral staircase to the top, which affords a spectacular view of the Arabian Sea. |
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Besides Cartesian coordinates, polar coordinates may also be used to describe the spiral. |
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Their distance established spiral nebulae well beyond the edge of the Milky Way. |
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Still, he continued to spiral downward, at times sitting at home for hours without saying a word. |
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In these wind driven currents, the Ekman spiral effect results in the currents flowing at an angle to the driving winds. |
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Inside the tomb another stone has a small spiral pattern chipped into it, although its authenticity has been questioned. |
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A conveying device, as claimed in claim 1, further including a coaxial spiral body carried by and offstanding from the core. |
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The story perfectly traces an increasingly fast paced spiral of frantic activity generated by Wally when he is told he needs to nap. |
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Students can collect textures by pressing the foam onto shoe soles, watchbands, spiral notebooks, and objects close at hand. |
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Bally on August 16, 2006, alleging that he negligently removed Donald's spiral accessory nerve during the 2002 surgical procedure. |
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Anaesthetists are being urged to check procedures amid fears the problem will spiral as Brits get fatter. |
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The spiral disk of the Andromeda galaxy, the Milky Way's neighbor, is just a tiny part of a much larger entity. |
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From scrumptious karanjis to ghee-laden anarsas and spiral chaklis, making sweets and savouries during Diwali has been a long-standing tradition. |
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He and his German colleague did it by simulating what happens when dense neutron stars spiral together and collide in deep space. |
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The concept of modiolar hugging electrodes places the contacts of the electrodes closer to the eighth nerve and spiral ganglia. |
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Furthermore, I will exploit my role as lead for the Radio Galaxy Zoo project on spiral DRAGNs to find more of these sources. |
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The spiral growth of branches, needles, and cone scales are arranged in Fibonacci number ratios. |
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Anthers may be few, but often many are arranged in a spiral, are yellow or sometimes white, and with yellow pollen. |
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To accomplish this goal, most current electrode arrays are molded in a spiral shape designed to match the shape of the modiolar wall. |
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The Ekman layer, with its distinguishing feature the Ekman spiral, is rarely observed in the ocean. |
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Ekman himself developed a current meter to observe the spiral that bears his name, but was not successful. |
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These spiral around field lines, bouncing back and forth between the poles several times per second. |
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The Archimedean spiral looks like a coiled rope or the grooves on a vinyl record. |
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This approximates a pattern of Archimedean spiral in which the force of the solar wind is in the direction that all of the planets orbit. |
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Controlled trajectory curves of helical segment are structured by applying the Logarithmic spiral and Archimedean spiral equations. |
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For the studied case, the trajectory generated by the Wp-T contact point is a conical helix, a cylindrical helix, or an Archimedean spiral. |
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The surface shows strong, elevated, radiating wrinkles or lamellae, but no spiral markings when adult. |
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The ingenious packaging, with a hidden spiral binding, includes 3-D glasses, art paper and two markers. |
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The interior wooden floors have been lost, but the spiral staircase and the stone, vaulted roof remain intact and accessible. |
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Moreover, the centre of Rome hosts also Trajan's and Antonine Column, two ancient Roman columns with spiral relief. |
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To try to arrest the spiral of violence, I contacted Chief Buthelezi to arrange a meeting. |
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Then, while the hen runs a circle around him with lowered wings, he will wind his head in a spiral motion. |
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Further south-east, on the border with the constellation Antlia, the spiral galaxy NGC 3393 contains a pair of super-massive black holes. |
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Its two main strengths, strapwork and spiral turning had found favour here because of their relative cheapness of manufacture. |
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Irregular galaxies are chaotic in appearance, and are neither spiral nor elliptical. |
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Our solar system orbits within the Milky Way, a barred spiral galaxy that is a prominent member of the Local Group of galaxies. |
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The safety gate at the top of the spiral staircase had been left open for a second, and Jack, in baby-walker, toppled over the edge. |
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Both the Milky Way and one of our nearest galaxy neighbors, the Andromeda Galaxy, are spiral galaxies. |
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Domestic sheep are relatively small ruminants, usually with a crimped hair called wool and often with horns forming a lateral spiral. |
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This, in turn, began a downward spiral in the relationship between Britain and the Province of Massachusetts. |
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Now, however, it is firmly categorised as a barred spiral galaxy, with loosely wound arms and a relatively small central bulge. |
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A lathe equipped with indexing plates, profile cutters, spiral or helical guides, etc. |
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This allows the table feed to be synchronized to a rotary fixture, enabling the milling of spiral features such as hypoid gears. |
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The spiral starts at the center of the pocket to be machined and the tool gradually moves towards the pocket boundary. |
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In it I spoke of our country being in decline, of being in an ever downward, ever steepening, ever accelerating spiral. |
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Mackenzie can use a spiral staircase or stainless steel slide to leave her tree house. |
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He will rise high up in the sky, to turn and plummet downward, in a spiral, twisting and turning as he comes down. |
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The long-standing theory has been that spiral galaxies merge with each other forming most of the elliptical galaxies in the Universe. |
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The problem is that spiral galaxies are not supposed to have such large jets. |
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While other spiral galaxies are much neater, with their extended arms clearly visible. |
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On average stars in spiral galaxies tend to be much younger than those in ellipticals. |
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Like our own spiral galaxy, these two galaxies also have relatively large and nearby companions. |
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The surgeon tended the compound spiral fracture and bound the bone with kangaroo tendon. |
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Long Meg is marked with examples of megalithic art including a cup and ring mark, a spiral and rings of concentric circles. |
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Stoney showed that the chemical elements could be plotted in a logarithmic spiral with a sesquiple ratio. |
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He discovered that the gas clouds lined up along spiral arms, indicating that we live in a spiral galaxy. |
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I mean, what's the fun of seeing your friends' lives spiral out of control if you can't get in a snarkastic comment or two along the way? |
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During the oral relay, team members each answered five questions on astronomy topics such as black holes, spiral nebulae and red giants. |
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We detected a clear sign of non-linear interaction between wakelets, which make global spiral arms by connecting two adjacent wakelets. |
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Only He who made them can tell the number of the stars, and mark the place of each in the order of the one great dominant spiral. |
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The vain man grew his remaining hair long and twirled it in a spiral to try to cover his growing bald patch. |
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A bubble rising rapidly in water describes a spiral closely resembling a corkscrew. |
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This equation is descriptive of a Cornu spiral, a spiral whose curvative increases linearly with arclength. |
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But what followed for Lozano, his grieving family claims, was a death spiral into infantilism and madness. |
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The FLOWMASTER has a completely embedded spiral so that the metal cannot be attacked by the flowant. |
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The spiral stair is a type of stairway which, due to its complex helical structure, was introduced relatively late into architecture. |
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In 2013, Bogdan repeated that no more money was available, but that he hoped to avoid the death spiral. |
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The technique, which results in a spiral effect in the arch masonry, provides extra strength in the arch to compensate for the angled abutments. |
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An orbiting charge should steadily lose energy and spiral toward the nucleus, colliding with it in a small fraction of a second. |
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Landscaping in the 17th century added spiral paths to the castle motte during Fulke Greville's programme of restoration. |
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Lines are already inclined to spiral and metamorphose, as in the example shown. |
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Colours are very bright and the decoration has tremendous energy, with spiral forms predominating. |
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Curtis argued for the idea that spiral nebulae were star systems in their own right as island universes. |
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The Torah does not require any particular foods to be eaten on Rosh Hashanah, but challah is one of the basics, shaped in a spiral round, she notes. |
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They are commonly divided into spiral, elliptical and Irregular galaxies. |
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In particular, many consider the significance of Vesto Melvin Slipher's 1912 astrometric research at the Lowell Observatory on Doppler shift in a spiral nebula. |
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A spiral galaxy is organized into a flat, rotating disk, usually with a prominent bulge or bar at the center, and trailing bright arms that spiral outward. |
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Prior to the discovery of V1 many astronomers, including Harlow Shapley, thought spiral nebulae, such as Andromeda, were part of our Milky Way Galaxy. |
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It is possible to climb the 150 steps of its spiral staircase. |
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This is surrounded by four primary arms that spiral from the core. |
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The function of the spiral thread is uncertain, but it may absorb stress when prey tries to escape, and thus prevent the collobast from being torn apart. |
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There are also bosses and lenses with pelta and spiral designs. |
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A downwards spiral towards social disorder and chaos has begun. |
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Very simple looms use a spiral warp, in which the warp is made up of a single, very long yarn wound in a spiral pattern around a pair of sticks or beams. |
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This contract will allow SES to continue its efforts in driving knowledge management by supporting the ongoing spiral development of the Knowledge System Prototype. |
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Recurrence rate did not correlate with fixation technique, whether transfascial sutures combined with 1 row of spiral tacks or tacks placed in a double-crown pattern was used. |
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In this approach, the tool travels along a gradually evolving spiral path. |
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Depending on their separation distance and strength, the two vortices may simply orbit around one another or else may spiral into the center point and merge. |
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They typically have spiral threads that grip the side of the hole. |
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Money, which allows wealth to be conceived as pure quantity instead of quality, is an example of megatechnics, one which can spiral out of control. |
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Previous surveys had compared the motions of the local group of galaxies, including the one in which we live, to farily large reference groups of spiral galaxies. |
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The barley-sugar columns, carved in spiral channels with alternating bands of vine ornament, exist to this day though moved from their original site. |
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By that stage Sevilla were down to 10 men and Jorge Sampaoli, their manager, had been sent to the stands as a breathless encounter started to spiral out of control. |
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He was still prepared to go on collecting all that life could offer, like a chambered nautilus patiently adding new cells to its slowly expanding spiral. |
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Unlike grand design spiral galaxies, which contain perfectly distinct spiral arms, a flocculent spiral galaxy is not as well-defined and whose spiral arms appear disjointed. |
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Take parchment, tightly rolling up Yule log to form spiral shape. |
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The young nematocyst decreases in size and becomes coarsely granular, the granules arranging themselves in a spiral line close under the external membrane. |
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The mold used in this work has an Archimedean spiral shaped cavity that is 20 mm wide and having a maximum flow length of 850 mm and thickness of 3 mm. |
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A new study shows that the two spiral galaxies evolved in a highly similar fashion over the first 3 billion to 4 billion years of their histories. |
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The usual depiction of the spiral unicorn horn in art, derives from these. |
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The stone spiral staircase which once led to the beacon was demolished. |
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It was long thought to have four main bands of stars spinning from its center, but a new model shows that two of these arms dominate the spiral galaxy. |
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A credit crunch lowers investment and consumption and results in declining aggregate demand which additionally contributes to the deflationary spiral. |
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Investigation of aortocoronary artery bypass grafts by multislice spiral computed tomography with electrocardiographic-gated image reconstruction. |
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A standard needle scalp electrode was modified by placing a semirigid wire at the base of the attachment where the spiral electrode attached to the needle head. |
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Astronomers, using a new type of telescope made by stitching together telephoto lenses, recently discovered seven celestial surprises while probing a nearby spiral galaxy. |
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Snakes of the family Pareidae have more teeth on the right side of their mouths than on the left, as the shells of their prey usually spiral clockwise. |
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