otheruses File Cycloid f.gif right frame A cycloid generated by a rolling circle A cycloid is the curve ... of a roulette curve roulette , a curve generated by a curve rolling on another curve. The cycloid ... 2010 The cycloid was first studied by Nicholas of Cusa and later by Marin Mersenne Mersenne . It was named by Galileo Galilei Galileo in 1599. In 1634 G.P. de Roberval showed that the area under a cycloid ... of a cycloid is four times the diameter of its generating circle. The cycloid has been called ... 400px A cycloid generated by a circle of radius r 2 The cycloid through the origin, generated by a circle ... frac y r right sqrt y 2r y math The first arch of the cycloid consists of points such that math 0 le t le 2 pi. , math The cycloid is differentiable everywhere except at the Cusp singularity cusps where ... C sup sup and the singularity where the derivative is 0 is an ordinary cusp. The cycloid satisfies ... . math Area One arch of a cycloid generated by a circle of radius r can be parameterized by math x r ... Cycloidal pendulum Expand section date December 2009 If its length is equal to that of half the cycloid, the bob of a pendulum suspended from the cusp of an inverted cycloid, such that the string is constrained between the adjacent arcs of the cycloid Clarify date October 2009 , also traces a cycloid ... from a supple rope or chain a cycloid is its own involute curve, and the cusp of an inverted cycloid ... Huygens Clocks Christiaan Huygens discovered this property of the cycloid and applied it to the design of more accurate clocks for use in navigation. Related curves Several curves are related to the cycloid. Curtate cycloid Here the point tracing out the curve is inside the circle, which rolls on a line. Prolate cycloid Here the point tracing out the curve is outside the circle, which rolls on a line. Trochoid refers to any of the cycloid, the curtate cycloid and the prolate cycloid. Hypocycloid ... are roulette curve roulettes with a circle rolled along a uniform curvature . The cycloid, epicycloids ... more details
A cycloid is a curve traced by a rolling circle. Cycloid can also refer to Cyclida formerly Cycloidea , an order of prehistoric crustaceans List of Street Fighter characters Cycloid and CycloidCycloid and Cycloid , characters in the Street Fighter games disambig ... more details
Deleted image removed Image cycloid3cogs.gif thumb Engaged cycloid gears with 3 cogs. The red parts of the curve on the left gear correspond to epicycloid fragments and the blue parts to hypocycloid fragments. Unreferenced date April 2009 The cycloidal gear profile is a form of toothed gear used in mechanical clock s. The gear tooth profile is based on the epicycloid and hypocycloid curves, which are the curves generated by a circle rolling around the outside and inside of another circle, respectively. When two toothed gears mesh, an imaginary circle, the pitch circle , can be drawn around the centre of either gear through the point at which their teeth make contact. The curves of the teeth outside the pitch circle are known as the addenda , and the curves of the tooth spaces inside the pitch circle are known as the dedenda . An addendum of one gear rests inside a dedendum of the other gear. In cycloidal gears, the addenda of the wheel teeth are convex epi cycloidal and the dedenda of the pinion are concave hypocycloidal curves generated by the same generating circle. This ensures that the motion of one gear is transferred to the other at locally constant angular velocity . Usually the pinion radius is made equal to twice the generating circle diameter since this gives radial dedenda which are convenient to manufacture on a hobbing machine . Citation needed date February 2007 There is some dispute over the invention of cycloidal gears those involved include G rard Desargues , Philippe de La Hire , Ole R mer , and Charles tienne Louis Camus . External links http www.csparks.com watchmaking CycloidalGears index.jhtml Designing cycloidal gears http kmoddl.library.cornell.edu index.php Kinematic Models for Design Digital Library KMODDL br Movies and photos of hundreds of working mechanical systems models at Cornell University. Also includes an http kmoddl.library.cornell.edu e books.php e book library of classic texts on mechanical design and engineering. http switzernet.com ... more details
Summary Original diagram by btarski. Tracing a point on a rolling circle using The Geometer s Sketchpad, version 4. Licensing GFDL self no disclaimers migration relicense ... more details
Summary This illustrates how Cavalieri s principle can be applied to finding an area bounded by a cycloid. Licensing PD self date March 2009 date March 2009 ... more details
unreferenced date July 2009 File NES Max Controller.jpg right thumb 250px The NES Max controller The NES Max is a gamepad that was released by Nintendo for the Nintendo Entertainment System in 1988. Like many later controllers such as those for the PlayStation and Nintendo 64 N64 , it has wings handles that extend from the edges of the pad. Design The controller is smaller in width than a standard NES controller and is slightly thinner. Unlike the standard controller, the Max has a small button shaped item called a cycloid, which can be moved in directions to control on screen movement. The cycloid can be moved by the player s thumb to function similar to a joystick , though it lacks analog response. For more traditional control, the cycloid area is surrounded by an 8 way control pad ring. The Max also features turbo button turbo A and B buttons in addition to the standard action buttons. Although there is no adjustment for the turbo rate as there is on the more famous NES Advantage , the NES Max was known to exceed the NES Advantage s maximum turbo setting. The Max s official Nintendo part number is NES 027. External links http www.axess.com twilight console detail nes max.html General information on the Max Nintendo hardware NES Category Nintendo Entertainment System accessories Category Nintendo hardware Category Game controllers videogame hardware stub nintendo stub sv NES Max ... more details
problems An introduction by Tom Apostol ref In it he shows that the problems of finding the area of a cycloid ... site. Area of a cycloid File Mamikon Cycloid.svg thumb right 300px Finding the area of a cycloid using Mamikon s theorem. The area of a cycloid can be calculated by considering the area between it an an enclosing ... the cycloid has radius r then this circle also has radius r and area r sup 2 sup . The area of the rectangle is 2 r .2 r 4 r sup 2 sup . Therefore the area of the cycloid is 3 r ... because the cyclod is generated by a circle and the tangent to the cycloid will be at right ... to finding the area under a cycloid, see Cavalieri s principle Cycloids . See also Cavalieri s principle ... more details
This is a list of variational topics in from mathematics and physics . See calculus of variations for a general introduction. Action physics Brachistochrone curve Calculus of variations Catenoid Cycloid Dirichlet principle Euler Lagrange equation cf. Action physics Fermat s principle Functional mathematics Functional derivative Functional integral Geodesic Isoperimetry Lagrangian Lagrangian mechanics Legendre transformation Luke s variational principle Minimal surface Morse theory Noether s theorem Path integral formulation Plateau s problem Prime geodesic Principle of least action Soap bubble Soap film Tautochrone curve Category Mathematics related lists Variations Category Calculus of variations ... more details
for the joint Pivot joint image CycloidAnim04.gif thumb 290px right A cycloid a common trochoid generated by a rolling circle Trochoid is the word created by Gilles de Roberval for the curve described by a fixed point as a circle rolls along a straight line. As a circle of radius a rolls without slipping along a line L, the center C moves parallel to L, and every other point P in the rotating plane rigidly attached to the circle traces the curve called the trochoid. Let CP b . If P lies inside the circle b < a , on its circumference b a , or outside b > a , the trochoid is described as being curtate, common, or prolate, respectively. Parametric equations of the trochoid, which assume L is the x axis, are math x a theta b sin theta , math math y a b cos theta , math where &theta is the variable angle through which the circle rolls. A curtate trochoid is traced by a pedal when a bicycle is pedaled along a straight line. A prolate , or extended trochoid is traced by the tip of a paddle when a boat is driven with constant velocity by paddle wheels this curve contains loops. A common trochoid, also called a cycloid , has cusp singularity cusp s at the points where P touches the L . A hypotrochoid is formed by a wheel rolling around the inside of a fixed circle. See also Epitrochoid Hypotrochoid Cycloid Epicycloid Hypocycloid Spirograph External links http www.xahlee.org SpecialPlaneCurves dir Trochoid dir trochoid.html MathWorld urlname Trochoid title Trochoid http jsxgraph.uni bayreuth.de wiki index.php Trochoid Online experiments with the Trochoid using JSXGraph Category Curves es Trocoide fr Trocho de ko nl Trocho de ja ru th geometry stub ... more details
Unreferenced date December 2009 Year nav topic 1634 science The year 1634 in science and technology involved some significant events. Botany Thomas Johnson botanist Thomas Johnson begins publishing Mercurius Botanicus , including a list of indigenous British plants. Mathematics Gilles de Roberval shows that the area under a cycloid is three times the area of its generating circle . Zoology Publication of Insectorum sive Minimorum Animalium Theatrum in London . Births Deaths November 7 Cornelius Drebbel , Netherlands Dutch inventor b. 1572 in science 1572 Martin Llewellyn , British Cartography cartographer b. 1565? Category 1634 in science fr 1634 en science hu 1634 a tudom nyban ... more details
Antoine de Laloub re 1600 1664 , a Jesuit , born in Languedoc , is chiefly known for an incorrect solution of Pascal s problems on the cycloid, which he gave in 1660, but he has a better claim to distinction in having been the first mathematician to study the properties of the helix . De Laloub re died at Toulouse . See also List of Jesuit scientists List of Roman Catholic scientist clerics This article is based on a public domain article from Wikipedia Rouse History of Mathematics Rouse History of Mathematics . Persondata Metadata see Wikipedia Persondata . NAME Laloubere, Antoine De ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 1600 PLACE OF BIRTH DATE OF DEATH 1664 PLACE OF DEATH DEFAULTSORT Laloubere, Antoine De Category 1600 births Category 1664 deaths Category French mathematicians Category French Jesuits Category Roman Catholic cleric scientists France mathematician stub ht Antoine de Laloub re sl Antoine de Laloub re ... more details
to the first will balance the input shaft and reduce vibration. See also Epicyclic gearing Cycloid gear A gear tooth shape based on the cycloid References references External links commons http kmoddl.library.cornell.edu .... http www.darali.com page17.html Darali Cycloid Reducers Gears Category Gears de Zykloidgetriebe ... more details
otheruses Fish scale disambiguation Image Scale Common Roach.JPG thumb upright 1.5 The cycloid scales of a common roach Rutilus rutilus . The row of lateral line scales is visible in the lower half of the image. The skin of most Osteichthyes bony and cartilaginous fish es are covered by scale zoology scale s . Scales vary enormously in size, shape, structure, and extent, ranging from rigid armor plates in fishes such as shrimpfish es and boxfish es, to microscopic or absent in fishes such as eel s and anglerfish es. The morphology biology morphology of a scale can be used to identify the species of fish they came from. Fish scales are produced from the mesoderm layer of the dermis , which distinguishes them from reptile scale s. The same gene s involved in tooth and hair development in mammal s are also involved in scale development. ref cite doi 10.1016 S0960 9822 01 00438 9 ref Types Placoid scales Also called dermal denticles , placoid scales are found on the cartilaginous fishes shark s, Batoidea rays , and chimaera s. They are structurally homology biology homologous with vertebrate tooth animal teeth denticle translates to small tooth , having a central pulp tooth pulp cavity supplied with blood vessel s, surrounded by a conical layer of dentine , all of which sits on top of a rectangular basal plate that rests on the dermis . The outermost layer is composed of vitrodentine, a largely inorganic Vitreous enamel enamel like substance. Placoid scales cannot grow in size, but rather more scales are added as the fish increases in size. Sharks are entirely covered by placoid ... reduced in thickness to resemble cycloid scales see below . Cycloid and ctenoid scales Cycloid and ctenoid scales are found in the teleost s, the more derived clade of ray finned fishes. Cycloid ... and cycloid scales on the blind side, while other species have ctenoid scales in males and cycloid scales ... structures. Cycloid and ctenoid scales are overlapping, making them more flexible than cosmoid and ganoid ... more details
math which is the differential equation of an inverted cycloid generated by a circle of diameter D ... a cycloid. ref name Struik Citation title A Source Book in Mathematics, 1200 1800 last Struik first ... is a cycloid. ref name Struik In an attempt to outdo his brother, Jakob Bernoulli created a harder version ... Galileo reviews his own work. The actual solution to Galileo s problem is half a cycloid. Galileo studied the cycloid and gave it its name, but the connection between it and his problem had to wait for advances in mathematics. See also Calculus of variations Beltrami identity Cycloid Tautochrone curve ... more details
A prolate trochoidal mass spectrometer is an chemical analysis instrument in which the ions of different mass to charge ratio are separated by means of mutually perpendicular electric field electric and magnetic field s so that the ions follow a prolate trochoid trochoidal path. ref name PhysRev.53.521 cite journal title A New Mass Spectrometer with Improved Focusing Properties journal Phys. Rev. date 1938 first Walker last Bleakney coauthors John A. Hipple, Jr. volume 53 issue 7 pages 521 529 doi 10.1103 PhysRev.53.521 url http link.aps.org abstract PR v53 p521 format accessdate 2007 10 02 ref ref GoldBookRef title Prolate trochoidal mass spectrometer file P04874 ref These devices are sometimes called cycloidal mass spectrometers, although the path is not a cycloid the prolate trochoid path has loops, the cycloid has cusps . Applications The instruments are used for the analysis of gases ref name pmid3149538 cite journal author Adamczyk B, Bederski K, W jcik L title Mass spectrometric investigation of dissociative ionization of toxic gases by electrons at 20 1000 eV journal Biomed. Environ. Mass Spectrom. volume 16 issue 1 12 pages 415 7 year 1988 pmid 3149538 doi 10.1002 bms.1200160181 ref and in gas chromatography mass spectrometry . ref name pmid8154592 cite journal author Laram e JA, Deinzer ML title Capillary gas chromatographic introduction of environmental compounds into a trochoidal electron monochromator mass spectrometer journal Anal. Chem. volume 66 issue 5 pages 719 24 year 1994 pmid 8154592 doi 10.1021 ac00077a022 ref The trochoidal configuration can also be used as the basis of an electron monochromator . ref name pmid12964744 cite journal author Voinov VG, Vasil ev YV, Morr J, Barofsky DF, Deinzer ML, Gonin M, Egan TF, F hrer K title A resonant electron capture time of flight MS with trochoidal electron monochromator journal Anal. Chem. volume 75 issue 13 pages 3001 9 year 2003 pmid 12964744 doi 10.1021 ac030019v ref References Reflist External link ... more details
pinpointed the nosological autonomy of cycloid psychoses, unsystematic and systematic schizophrenias ... of birth seasonality is confined to an excess of winter and spring births in cycloid psychoses ... and febrile affections in the first trimester of maternal gestation with the later occurrence of cycloid ... of the cycloid psychoses was substantiated by neurophysiological and morphometric studies. In a systematic twin study, he provided evidence that in cycloid psychosis monozygotic pairs had ... by a controlled family study, where first degree relatives of patients with cycloid psychoses ... more details
Image Tautochrone curve.gif 300px right thumb Four points run over a cycloid from different positions, but they arrive at the bottom at the same time. The blue arrows show the points acceleration along the curve. On the top is the time position diagram. A tautochrone or isochrone curve from Greek prefices wiktionary wiki tauto tauto meaning same or wiktionary wiki iso iso equal , and wiktionary wiki chrono chrono time is the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point. The curve is a cycloid , and the time is equal to Pi &pi times the square root of the radius over the acceleration of gravity. The tautochrone problem The tautochrone problem, the attempt to identify this curve, was solved by Christiaan Huygens in 1659. He proved geometrically in his Horologium oscillatorium , originally published in 1673, that the curve was a cycloid . On a cycloid whose axis is erected on the perpendicular and whose vertex is located at the bottom, the times of descent, in which a body arrives at the lowest point at the vertex after having departed from any point on the cycloid, are equal to each other... ref cite book last Blackwell first Richard J. title Christiaan Huygens The Pendulum Clock publisher Iowa State University Press date 1986 location Ames, Iowa isbn 0 8138 0933 9 Part II, Proposition XXV, p. 69 ref This solution was later used to attack the problem of the brachistochrone curve . Jakob Bernoulli solved the problem using calculus in a paper Acta Eruditorum , 1690 that saw the first ... parametrized cycloid , change variables to disentangle the transcendental and algebraic ... math are those of a circle rolling along a horizontal line &mdash a cycloid math begin align x & r ... math frac ds dy T 0 frac sqrt 2g pi frac 1 sqrt y math It can be shown that the cycloid obeys ... 9 A Treatise on The Cycloid and all forms of Cycloidal Curves 1878 , posted by http historical.library.cornell.edu ... more details
rm sech 1 y sqrt 1 y 2 ,y math . Involute of a cycloid One involute of a cycloid is a congruence geometry congruent cycloid. In cartesian coordinates the curve follows br math x r t sin t , math math ... more details
cycloid arthropod from the Jurassic journal Journal of Paleontology volume 81 issue 1 pages 213 215 ... cycloid crustaceans journal Journal of Morphology volume 269 issue 12 pages 1501 1519 ... not resemble those of other crustaceans. ref name Dzik Cycloid taxa differ in the number of walking ... 229 254.pdf format Portable Document Format PDF ref The first description of a cycloid was in the 1836 ... cycloid journal Journal of Paleontology volume 77 issue 2 pages 386 388 jstor 4094744 doi 10.1666 ... than a cycloid. ref name Bakel cite journal author Barry W. M. van Bakel, John W. M. Jagt, Ren H. B ... more details
Unreferenced date December 2009 Taxobox name Labrisomids image labrisomid.png image width 200px image caption Auchenionchus microcirrhis regnum Animal ia phylum Chordate Chordata classis Actinopterygii ordo Perciform es subordo Blennioidei familia Labrisomidae subdivision ranks Genus Genera subdivision See text. Labrisomids are small blenny blennioids , perciform marine fish belonging to the family Labrisomidae . Found mostly in the tropical Atlantic Ocean Atlantic and Pacific Ocean , the family contains approximately 98 species in 14 genera. Stockier than the average blenny, labrisomids are Ichthyology terms E elongate nonetheless their dorsal fin Ichthyology terms S spines outnumber soft Ichthyology terms R rays which may be absent altogether , and the pelvic fin s are long and slender. Like many other blennies, labrisomids have whisker like structures called Ichthyology terms C cirri on the head and Ichthyology terms N nape . Scales may be Ichthyology terms C cycloid or absent in labrisomids many species are brightly coloured. The hairy blenny Labrisomus nuchipinnis is the largest species at 23 centimeres in length most are far smaller. Generally staying within shallow coastal regions to depths of c. 10 metres, labrisomids are benthic fish spending most of their time on or near the bottom. Both sandy and rocky substrates are frequented, sometimes at reef s or amongst beds of seagrass . Labrisomids are shy fish and will retreat into crevices if threatened. Crustacean s, gastropod s, brittle star s and sea urchin s make up much of the labrisomid diet. Two genera of labrisomid are noted for their ovoviviparity Xenomeda and Starksia both retain eggs within the oviduct where they develop in safety. However, only Starksia species possess a Ichthyology terms G gonopodium a modified anal fin used as a copulatory organ . Genera Alloclinus Auchenionchus Calliclinus Cryptotrema Dialommus Exerpes Haptoclinus Labrisomus Malacoctenus Mnierpes Nemaclinus Paraclinus Starksia Xen ... more details
In mathematics , a transcendental curve is a curve that is not an algebraic curve . ref name newman Newman, JA, The Universal Encyclopedia of Mathematics , Pan Reference Books, 1976, ISBN 0330243969, Transcendental curves . ref Here for a curve C what matters is the point set typically in the plane mathematics plane underlying C , not a given parametrisation. For example, the unit circle is an algebraic curve pedantically, the real points of such a curve the usual parametrisation by trigonometric function s may involve those transcendental function s, but certainly the unit circle is defined by a polynomial equation. The same remark applies to elliptic curve s and elliptic function s and in fact to curves of genus mathematics genus 1 and automorphic function s. The properties of algebraic curves, such as B zout s theorem , give rise to criteria for showing curves actually are transcendental. For example an algebraic curve C either meets a given line L in a finite number of points, or possibly contains all of L . Thus a curve intersecting any line in an infinite number of points, while not containing it, must be transcendental. This applies not just to sinusoidal curves, therefore but to large classes of curves showing oscillations. The term is originally attributed to Gottfried Wilhelm von Leibniz Leibniz . Further examples Cycloid Trigonometric function s Logarithm ic and exponential function exponential functions Archimedes spiral Logarithmic spiral Catenary References reflist Category Curves ca Corba transcendental es Curva trascendente pt Curva transcendental ru uk ... more details
Ion cyclotron resonance is a phenomenon related to the movement of ions in a magnetic field . It is used for accelerating ions in a cyclotron , and for measuring the masses of an ionized analyte in mass spectrometry , particularly with Fourier transform ion cyclotron resonance mass spectrometers. It can also be used to follow the chemical kinetics kinetics of chemical reactions in a dilute gas mixture, provided these involve charged species. Definition of the resonant frequency An ion in a static and uniform magnetic field will move in a circle due to the Lorentz force . The circular motion may be superimposed with a uniform axial motion, resulting in a helix , or with a uniform motion perpendicular to the field, e.g., in the presence of an electrical or gravitational field, resulting in a cycloid . The angular frequency 2 Frequency f of this cyclotron motion for a given magnetic field strength B is given in SI units ref In SI units, the elementary charge e has the value 1.602 10 sup 19 sup Coulomb C , the mass of the ion m is often given in atomic mass unit or dalton 1 u 1 Da 1.660538782 83 10 sup 27 sup kilogram kg , the magnetic field B is measured in tesla unit teslas , and the angular frequency is measured in radian s per second . ref by math omega frac zeB m math . where z is the algebraic number of positive or negative charges of the ion, e is the elementary charge and m is the mass of the ion. The formula above means that an electric excitation signal having a frequency f will resonate with ions having a mass to charge ratio m z given by math frac m z frac eB 2 pi f math . References references See also Electron cyclotron resonance Cyclotron Fourier transform ion cyclotron resonance Category Condensed matter physics Category Electric and magnetic fields in matter Category Ion source Category Scientific techniques Category Plasma physics ... more details
cycloid reach the lowest point of the cycloid in the same time and thereby experimentally shows that the cycloid is the isochrone 1668 John Wallis suggests the law of conservation of momentum 1676 ... Bernoulli shows that the cycloid is the solution to the isochrone problem 1691 Johann Bernoulli shows ... have 1696 Johann Bernoulli shows that the cycloid is the solution to the brachistochrone problem 1714 ... more details
Drag physics drag . Citation needed date January 2010 They come in two forms Cycloid scales have ... fish bass and crappie . Reptilian scales main Reptile scales Reptile scale types include cycloid ... more details
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