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Curve traced by a point on a rolling circle
In geometry, a cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. A cycloid is a specific form of trochoid
Cycloid
Hard skeletal covering of fish
ancestors to all jawed fishes today. Most bony fishes are covered with the cycloid scales of salmon and carp, the ctenoid scales of perch, or the ganoid scales
Fish_scale
Japanese media franchise
Street Fighter is a Japanese media franchise centered on a series of fighting games developed and published by Capcom. The first game in the series was
Street_Fighter
Topics referred to by the same term
cycloid is a curve traced by a rolling circle. "Cycloid" can also refer to: Cyclida (formerly Cycloidea), an order of prehistoric crustaceans Cycloid
Cycloid_(disambiguation)
Fastest curve descent without friction
are cycloids. But the portion of the cycloid used for each varies. Specifically, the brachistochrone can use up to a complete rotation of the cycloid (at
Brachistochrone_curve
Abnormal condition of the mind
Myxedematous psychosis Stimulant psychosis Tardive psychosis Shared psychosis Cycloid psychosis is typically an acute, self-limiting form of psychosis with psychotic
Psychosis
Curve for which the time to roll to the end is equal for all starting points
curve. The curve is a cycloid, and the time is equal to π times the square root of the radius of the circle which generates the cycloid, divided by the square
Tautochrone_curve
Toothed gear based on epicycloids and hypocycloids
independent of the number of teeth. A Roots blower is one extreme, a form of cycloid gear where the ratio of the pitch diameter to the generating circle diameter
Cycloid_gear
Visual mathematical proofs
area of the cycloid is 3πr2: it is 3 times the area of the generating circle. The tangent cluster can be seen to be a circle because the cycloid is generated
Visual_calculus
Curve traced by a string as it is unwrapped from another curve
demonstrationes geometricae (1673), where he showed that the involute of a cycloid is still a cycloid, thus providing a method for constructing the cycloidal pendulum
Involute
Italian Jesuit mathematician (1648–1737)
"Cycloidum anomalarum". The principle involved is that of doubling angles. The cycloid of Ceva has the polar equation r = 1 + 2 cos ( 2 θ ) {\displaystyle r=1+2\cos(2\theta
Tommaso_Ceva
Eccentric gear reduction mechanism
to 119:1 and double stage up to 7,569:1. The cycloid disc is usually designed with a shortened cycloid in order to minimize the eccentricity of the disc
Cycloidal_drive
Psychosis beginning suddenly in the first two weeks after childbirth
psychiatry, manic and cycloid syndromes are regarded as distinct, but, studied long-term among childbearing women, the bipolar and cycloid variants are intermingled
Postpartum_psychosis
French polymath (1623–1662)
treatise on the arithmetical triangle. Between 1658 and 1659, he wrote on the cycloid and its use in calculating the volume of solids. Following several years
Blaise_Pascal
Geometrical concept relating area and volume
arcs of cycloids. By Cavalieri's principle, the circle therefore has the same area as that region. Consider the rectangle bounding a single cycloid arch
Cavalieri's_principle
Curve traced by a circle rolling along a line
point is on the circle, the trochoid is called common (also known as a cycloid); if the point is inside the circle, the trochoid is curtate; and if the
Trochoid
Centers of curvature of a curve
because the tautochrone curve is a cycloid, and the cycloid has the unique property that its evolute is also a cycloid. The theory of evolutes, in fact
Evolute
1673 book on pendular motion by Christiaan Huygens
keep perfect time can be achieved if the path of the pendulum bob is a cycloid. However, it was unclear what form to give the metal cheeks regulating
Horologium_Oscillatorium
Circle of immediate corresponding curvature of a curve at a point
{\textstyle {\frac {d^{2}\gamma }{ds^{2}}}} with respect to the arc length s. A cycloid with radius r can be parametrized as follows: γ ( t ) = [ r ( t − sin
Osculating_circle
Curve traced by a point on a circle rolling within another circle
the larger circle is increased, the hypocycloid becomes more like the cycloid created by rolling a circle on a line. The 2-cusped hypocycloid called
Hypocycloid
Mathematical curves generated by rolling other curves together
geometry of curves, a roulette is a kind of kinematic curve, generalizing cycloids, epicycloids, hypocycloids, trochoids, epitrochoids, hypotrochoids, and
Roulette_(curve)
Piano manufacturer
York; Herman is best known for patenting the firm's unusually shaped "Cycloid" square piano, and with his brother Ferdinand, and son George, he headed
William_Lindeman
Extinct order of crustaceans
Cyclida (formerly Cycloidea, and so sometimes known as cycloids) is an extinct order of crab-like fossil arthropods that lived from the Carboniferous to
Cyclida
Gear with teeth whose profile is an involute of a circle
gear profile is the most commonly used system for gearing today, with cycloid gearing still used for some specialties such as clocks. In an involute
Involute_gear
Family of fishes
and sprats. Many members of the family have a body protected with shiny cycloid (very smooth and uniform) scales, a single dorsal fin, and a fusiform body
Clupeidae
Study of the form or morphology of fishes
scales covering the outer body. Singular bowfin cycloid scale Cycloid scales covering rohu Bowfin cycloid scales There are four principal types of fish
Fish_anatomy
1996 video game
Bloody Hokuto, and two cyborgs named Cycloid-β and Cycloid-γ. Cycloid-β (サイクロイド-β, Saikuroido Bēta) and Cycloid-γ (サイクロイド-γ, Saikuroido Ganma), both appear
Street_Fighter_EX
Distance along a curve
with closed-form solutions for arc length include the catenary, circle, cycloid, logarithmic spiral, parabola, semicubical parabola and straight line.
Arc_length
Species of fish
ventral fins, one long, continuous dorsal fin, long pectoral fins, and tiny, cycloid scales. The tail fin is nearly as long as the dorsal fin and deeply forked
American_butterfish
Genus of fishes
a genus of flying fishes. It is a bony fish. The body is covered with cycloid scales. The mouth is wide, and the jaws bear teeth. It is a marine fish
Exocoetus
Wheel designed for railway tracks
rubber-tyred trams have guide wheels.[citation needed] Adhesive weight Cycloid and trochoid Wheelset (rail transport)#Conical wheel-tread Lewis, R.; Olofsson
Train_wheel
2011 video game
work with the Cycloid Emperor. The president was actually intending to have the aliens kill Duke so he could control the Earth with Cycloid Emperor. He
Duke_Nukem_Forever
Diverse clade of vertebrate animals
teleost scales. Teleost scales are then divided into two subgroups which are cycloid scales and ctenoid scales. All of these scales have a base of bone that
Osteichthyes
Brachistochrone Butterfly curve (transcendental) Catenary Clélies Cochleoid Cycloid Horopter Isochrone Pursuit curve Rhumb line Syntractrix Tractrix Trochoid
Gallery_of_curves
Species of fish
terminal mouth, as well as small eyes, and the body is covered in tough cycloid scales. The pinktail triggerfish is found throughout the Indian and Pacific
Pinktail_triggerfish
Animals that comply with Jewish regulations for consumption
placoid, cosmoid, ganoid, ctenoid and cycloid. The majority of kosher fish exhibit the latter two forms, ctenoid or cycloid, but the bowfin (Amia calva) is
Kosher_animals
Ancient paradox in geometry
Ps travel in a cycloid path as they roll together one revolution. While each travels 2πR horizontally from start to end, Ps's cycloid path is shorter
Aristotle's_wheel_paradox
Proposed momentum exchange tether
and the tether rotation rate are synchronized, the tether tip moves in a cycloid curve. At the lowest point it is momentarily stationary with respect to
Skyhook_(structure)
Home video game console
Nintendo of America; and the NES Max, a controller with grip handles and a "cycloid" sliding-disc D-pad in place of the traditional one. Both controllers have
Nintendo_Entertainment_System
Brachistochrone Butterfly curve (transcendental) Catenary Clélies Cochleoid Cycloid Horopter Isochrone Isochrone of Huygens (Tautochrone) Isochrone of Leibniz[1]
List_of_curves
Extinct genus of ray-finned fishes
completely made of bone. Another modern development in Leptolepis were its cycloid scales, which lacked the covering of ganoine present in more basal teleosts
Leptolepis
Curve traced by a vertex of a polygon as it rolls
as the number of sides increases to infinity, the cyclogon becomes a cycloid. The cyclogon has an interesting property regarding its area. Let A denote
Cyclogon
Season of television series
when the truly massive Gorem and Julie work together in the end they beat Cycloid and Billy. 11 "Grandpa's Got A Brand New Bakugan" Transliteration: "The
Bakugan Battle Brawlers season 1
Bakugan_Battle_Brawlers_season_1
Branch of mathematics
fluid, the oblateness of the earth, the motion of a weight sliding on a cycloid, and many other problems discussed in his Principia Mathematica (1687)
Calculus
French lineographer and mathematician (1584–1640)
mathematician and published works on geostatics. He is credited with naming the cycloid. He lived and worked in Paris as an artist until his death in 1640. D Diderot
Jean_de_Beaugrand
Genus of fishes
consists predominantly of ctenoid scales, whereas in Hemeraia it is mainly cycloid scales. In contrast to Hemeraia and Teleocichla, in Saxatilia the infraorbitals
Saxatilia
Art museum in Texas, US
using a cycloid curve for the gallery vaults would reduce the ceiling height and provide other benefits as well. The relatively flat cycloid curve would
Kimbell_Art_Museum
Subfamily of fishes
absent or incomplete, by having no scales or if scales are present they are cycloid. One species, Gymnapogon urospilotus, is notable for its larvae being rather
Pseudaminae
Species of fish
laterally compressed, with a distinctly humped back. The scales are large and cycloid in shape, with a complete lateral line. Serration is present on the last
Japanese_white_crucian_carp
first. Torricelli extended Cavalieri's work to other curves such as the cycloid, and then the formula was generalized to fractional and negative powers
History_of_calculus
Extinct family of ray-finned fishes
among the first fish to possess certain teleost synapomorphies, such as cycloid scales and fully ossified vertebrae. Arratia, G.; Hikuroa, D. C. H. (2010)
Leptolepidae
Small rigid plate that grows out of an animal's skin
Amblypterus striatus Placoid scales on a lemon shark (Negaprion brevirostris) Cycloid scales on a common roach (Rutilus rutilus) True cosmoid scales can only
Scale_(zoology)
Species of fish
cause a cross-hatched look along the body. The scales on these fish are cycloid scales, a type of leptoid scale. It is possible to find the age of a fish
Bluntnose_minnow
Suborder of ray-finned fish
6 lbs). Most loaches are small, narrow-bodied and elongate, with minute cycloid scales that are often embedded under the skin, patterns of brown-to-black
Loach
Extinct genus of ray-finned fishes
Steurbautichthys †Catervariolidae Catervariolus Kisanganichthys Songanella Cycloid clade †Antofagastaichthys †Araripichthys †Cavenderichthys †Koonwarria?
Archaeomaene
Extinct genus of fishes
Steurbautichthys †Catervariolidae Catervariolus Kisanganichthys Songanella Cycloid clade †Antofagastaichthys †Araripichthys †Cavenderichthys †Koonwarria?
Leedsichthys
Order of ray-finned fishes
are usually ctenoid (rough to the touch), although sometimes they are cycloid (smooth to the touch) or otherwise modified. "Perciform - Form and function"
Perciformes
Mental disorder that encompasses a range of similar conditions
schizophrenic) and for affective disorders (cyclothymic temperament – cycloid 'psychopathy' – manic-depressive disorder), as well as by Eugen Bleuler
Spectrum_disorder
Species of fish
considered an accurate reflection of its scale size; the scales themselves are cycloid. The original description gave it the common name "large-scaled chalceus"
Pinktail_chalceus
1996 first-person shooter video game
Los Angeles once again, and kills the leader of the alien menace: the Cycloid Emperor. The game ends as Duke promises that after some "R&R", he will
Duke_Nukem_3D
Genus of fishes
closely related close to that genus but is different in the possession of cycloid scales, non-uniform teeth, weak spines in the anal fin and a more cavernous
Larimichthys
{4A}{\pi }}{\frac {1}{4n^{2}-1}}\cos {\frac {2\pi nx}{p}}} non-continuous Cycloid p − p cos ( f ( − 1 ) ( 2 π x p ) ) 2 π {\displaystyle {\frac {p-p\cos
List_of_periodic_functions
Type of motion which combines translation and rotation with respect to a surface
axis is a line, while the trajectory of any point in the object rim is a cycloid. The velocity of any point in the rolling object is given by v = ω × r
Rolling
Family of ray-finned fishes
Anarrhichthys. There is a single pair of nostrils. The scales, if present, are cycloid, tiny and do not overlap. There are well developed movement sensitive sensory
Anarhichadidae
Species of fish
soft-rayed portion. The scales on the body of the butterfish are small, cycloid, and very deciduous (meaning that they are shed off easily). This species
Pacific_rudderfish
Special case of the Euler-Lagrange equations
{\displaystyle \phi } being a variable. These are the parametric equations for a cycloid. Consider a string with uniform density μ {\displaystyle \mu } of length
Beltrami_identity
Pendulum whose period is precisely two seconds
following a cycloid motion instead of a simple circle would be more accurate. After developing some clocks to correct the motion with "cycloid cheeks", Huygens
Seconds_pendulum
Kind of space tether
rotates like a wheel". The tip of the tether moves in approximately a cycloid, in which it is momentarily stationary with respect to the ground. In this
Momentum_exchange_tether
Bowditch curve Brachistochrone Butterfly curve Catenary Clélies Cochleoid Cycloid Horopter Isochrone Isochrone of Huygens (Tautochrone) Isochrone of Leibniz
List_of_mathematical_shapes
†Prolatcyclus kindzadza Mychko et al., 2019 Crustacean Kin-dza-dza! A fossil cycloid from the Carboniferous of Orenburg Oblast, Russia. Coptoborus brigman Smith
List of organisms named after works of fiction
List_of_organisms_named_after_works_of_fiction
Genus of fishes
belly with the anus sitting between these membranes. The tiny scales are cycloid and may be absent from the head region. If present on the head they are
Rabbitfish
Genus of fishes
out as well, ringed with golden yellow. The body is covered in minute cycloid scales and its silvery, iridescent guanine coating is easily abraded. The
Opah
Species of fish
gill arches that contain one or two rows of distinctive teeth. It has cycloid scales, but a scaleless head. There are 19 caudal rays, and the dorsal
Blacknose_shiner
Primitive way of calculating area
employed the method of exhaustion to discover the exact arc length of the cycloid. Archimedes computed the area of one turn of the spiral S {\textstyle S}
Method_of_exhaustion
Curve which could be used to trisect an angle with compass and straightedge
(the graph of the cube function) Hyperbola with eccentricity 2 Parabola Cycloid of Ceva A related concept is a sectrix, which is a curve which can be used
Trisectrix
Palestinian-American artist (born 1936)
artist books, drawings, and limited edition artist prints. Her Helixes and Cycloid series, as well as her Diagonal Flight series, are examples of her perceptual
Samia_Halaby
Species of ray-finned fish
rays, and 25 vertebrae. The body is elongated and compressed with large cycloid scales. The body is blackish-brown when young, though after maturing into
Synagrops_japonicus
Species of fish
of moderate depth and laterally compressed, and has a covering of small cycloid scales. The largest fish have been measured at 190 cm (75 in) in total
Greater_amberjack
All Latin and Greek roots beginning with G
(kuklikós) acyclic, anticyclone, anticyclonic, bicycle, cycle, cyclic, cyclide, cycloid, cyclone, cyclops, cyclosis, cyclotomic, dicyclic, eccyclema, epicycle
List of Greek and Latin roots in English/A–G
List_of_Greek_and_Latin_roots_in_English/A–G
Species of fish
edge, the largest being twice the size of the second largest. They have cycloid scales, a feature of Teleostei fishes, and are derived from ganoid scales
Mediterranean_rainbow_wrasse
Proprietary marine propulsion system
rotors for drone applications. Azipod – Electric drive azimuth thruster Cycloid – Curve traced by a point on a rolling circle Cyclorotor – Perpendicular-axis
Voith_Schneider_Propeller
Evolution of crustaceans into crab-like forms
Schweigert, Günter (2007). "Juracyclus posidoniae n. gen. and sp., the first cycloid arthropod from the Jurassic" (PDF). Journal of Paleontology. 81 (1): 213–215
Carcinisation
Ray-finned fish
sturgeon, as they have ganoid scales instead of the permitted ctenoid and cycloid scales. While all Orthodox groups forbid the consumption of sturgeon, some
Sturgeon
has the special property of being the minimal surface that contains a cycloid as a geodesic. It is also swept out by a family of parabolae. The surface
Catalan's_minimal_surface
epicycloid or hypocycloid variety. The classic Spirograph toy traces out these curves. Centered trochoid Cycloid Epicycloid Hypocycloid Spirograph [1]
Cyclocycloid
Plane curve traced by a point on a circle rolled around another circle
-r\sin \left({\frac {R+r}{r}}\theta \right)} List of periodic functions Cycloid Cyclogon Deferent and epicycle Epicyclic gearing Epitrochoid Hypocycloid
Epicycloid
Extinct genus of fishes
Steurbautichthys †Catervariolidae Catervariolus Kisanganichthys Songanella Cycloid clade †Antofagastaichthys †Araripichthys †Cavenderichthys †Koonwarria?
Pachycormus_(fish)
Species of freshwater fish
of the body are ctenoid, whereas the scales of the top of the head are cycloid. Kissing gourami reach a maximum of 30 cm (12 in) in total length. There
Kissing_gourami
Species of fish
species of the United States since 1994. The genus name translates as "true cycloid goby", referring to the scales, while the species epithet is in honor of
Northern_tidewater_goby
Subfamily of fishes
they lack barbels on the mouth and chin and they are covered in small cycloid scales arranged in horizontal or diagonal rows. Some species have a modified
Ophidiinae
Dutch mathematician and physicist (1629–1695)
showed it to be a cycloid, rather than the circular arc of a pendulum's bob, and therefore that pendulums needed to move on a cycloid path in order to
Christiaan_Huygens
Extinct genus of ray-finned fishes
Steurbautichthys †Catervariolidae Catervariolus Kisanganichthys Songanella Cycloid clade †Antofagastaichthys †Araripichthys †Cavenderichthys †Koonwarria?
Oreochima
Genus of fishes
smaller than in other pike cichlids. Instead, the regions covered with cycloid scales are more extensive. The edge of the preoperculum is smooth. The
Hemeraia
Curve traced by a point outside a circle rolling within another circle
support of the eigenvalues of some random matrices with cyclic correlations. Cycloid Cyclogon Epicycloid Rosetta (orbit) Apsidal precession Spirograph J. Dennis
Hypotrochoid
Mathematical term for squaring a plane figure
With its help, Galileo Galilei and Gilles de Roberval found the area of a cycloid arch, Grégoire de Saint-Vincent investigated the area under a hyperbola
Quadrature_(mathematics)
Extinct genus of fishes
Steurbautichthys †Catervariolidae Catervariolus Kisanganichthys Songanella Cycloid clade †Antofagastaichthys †Araripichthys †Cavenderichthys †Koonwarria?
Syntegmodus
Extinct genus of fishes
Steurbautichthys †Catervariolidae Catervariolus Kisanganichthys Songanella Cycloid clade †Antofagastaichthys †Araripichthys †Cavenderichthys †Koonwarria?
Pholidorhynchodon
Extinct genus of fishes
Steurbautichthys †Catervariolidae Catervariolus Kisanganichthys Songanella Cycloid clade †Antofagastaichthys †Araripichthys †Cavenderichthys †Koonwarria?
Pentanogmius
Family of fishes
referred to as the axillary pelvic process. The scales are typically smooth, cycloid, or slightly rough to the touch, and weakly ctenoid. The lateral line is
Sparidae
Species of fish
another. Inner gill slits are wide. The scales are small, rudimentary, cycloid, relatively well embedded below the epidermis and therefore often difficult
American_eel
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CYCLOID
n. pl.
An order of ganoid fishes, having cycloid scales. The bowfin (Amia calva) is a living example.
a. & n.
Same as 2d and 3d Cycloid.
n.
One of the Cycloidei.
n.
One of the small, thin, membranous, bony or horny pieces which form the covering of many fishes and reptiles, and some mammals, belonging to the dermal part of the skeleton, or dermoskeleton. See Cycloid, Ctenoid, and Ganoid.
a.
Of or pertaining to the Cycloidei.
n.
The curve described by any point in a wheel rolling on a line; a cycloid; a roulette; in general, the curve described by any point fixedly connected with a moving curve while the moving curve rolls without slipping on a second fixed curve, the curves all being in one plane. Cycloids, epicycloids, hypocycloids, cardioids, etc., are all trochoids.
a.
Pertaining to, or resembling, a cycloid; as, the cycloidal space is the space contained between a cycloid and its base.
n.
A curve generated by a point in the plane of a circle when the circle is rolled along a straight line, keeping always in the same plane.
n.
A curve, in which a body, starting from a given point, and descending solely by the force of gravity, will reach another given point in a shorter time than it could by any other path. This curve of quickest descent, as it is sometimes called, is, in a vacuum, the same as the cycloid.
n. pl.
One of the subclasses of fishes. They have an arterial cone and bulb, spiral intestinal valve, and the optic nerves united by a chiasma. Many of the species are covered with bony plates, or with ganoid scales; others have cycloid scales.
n.
the curve traced by any point in the plane of a given curve when the latter rolls, without sliding, over another fixed curve. See Cycloid, and Epycycloid.
n.
A curved line, such that a heavy body, descending along it by the action of gravity, will always arrive at the lowest point in the same time, wherever in the curve it may begin to fall; as, an inverted cycloid with its base horizontal is a tautochrone.
n. pl.
An order of fishes, formerly proposed by Agassiz, for those with thin, smooth scales, destitute of marginal spines, as the herring and salmon. The group is now regarded as artificial.