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Centers of curvature of a curve
shape will be the evolute of that curve. The evolute of a circle is therefore a single point at its center. Equivalently, an evolute is the envelope of
Evolute
Private organization in the Netherlands
The Evolute Institute is a private organization based in the Netherlands[where?] that offers programs combining legal psychedelic retreats (notably
Evolute_Institute
Plane curve; an epicycloid with radii differing by 1/2
\varphi +\cos 3\varphi ,3\sin \varphi +\sin 3\varphi )} (see above). The evolute of a curve is the locus of centers of curvature. In detail: For a curve
Nephroid
Curve traced by a string as it is unwrapped from another curve
as the string is either unwrapped from or wrapped around the curve. The evolute of an involute is the original curve. It is generalized by the roulette
Involute
Curve generated by rolling a circle inside another circle with 4x or (4/3)x the radius
used), cubocycloid, and paracycle. It is nearly identical in form to the evolute of an ellipse. If the radius of the fixed circle is a then the equation
Astroid
Type of plane curve
of the circle k {\displaystyle k} , one gets a limaçon of Pascal. The evolute of a curve is the locus of centers of curvature. In detail: For a curve
Cardioid
On points of extreme curvature in curves
correspond to the cusps of its evolute, the curve formed by the centers of curvature of the given curve. Thus, the evolute of any smooth closed curve has
Four_vertex_theorem
Extinct subclass of cephalopod molluscs
Anahoplites). Where it does not cover those preceding, the specimen is said to be evolute (e.g., Dactylioceras). A thin living tube called a siphuncle passed through
Ammonoidea
1673 book on pendular motion by Christiaan Huygens
pendulum. These and other results led Huygens to develop his theory of evolutes and provided the incentive to write a much larger work, which became the
Horologium_Oscillatorium
Surface able to be flattened without distortion
analogous to the concept of the evolute in plane curves, although note that in the plane, there is only one evolute per curve, but in space there in
Developable_surface
Extinct suborder of ammonites
loosely coiled, evolute and gyroconic shells in which the sutural element are said to have complex moss-like endings. Shells are generally evolute, with all
Lytoceratina
Concept in Hindu philosophy
mahat is a concept in the Samkhya philosophy of Hinduism. It is the first evolute of Prakriti, the causeless cause of the world, that is generated after
Mahat-tattva
Dutch mathematician and physicist (1629–1695)
amount of dispersion. As a mathematician, Huygens developed his theory of evolutes and wrote on games of chance and the problem of points in Van Rekeningh
Christiaan_Huygens
If a smooth plane curve has monotonic curvature, then its osculating circles are nested
of the evolute, the curve traced out by the centers of osculating circles. For curves with monotone curvature, the arc length along the evolute between
Tait–Kneser_theorem
Curve traced by a point on a rod as one end is dragged along a line
Mamikon's theorem. The envelope of the normals of the tractrix (that is, the evolute of the tractrix) is the catenary (or chain curve) given by y = a cosh x/a
Tractrix
Curve generated by the projections of a fixed point on the tangents of another curve
the curve and the envelope of such normals is its evolute. Therefore, YR is tangent to the evolute and the point Y is the foot of the perpendicular from
Pedal_curve
Genus of molluscs (fossil)
in the Middle Triassic of the Himalaya. The shell is thinly discoidal, evolute, and smooth; cross section highly compressed; venter narrowly rounded except
Ananorites
Subcompact sedan
Aeolus A60 EV (electric version) Aeolus E70 (facelift electric version) Evolute i-Pro (Russia) Production 2011–present Model years 2012–present Assembly
Aeolus_A60
Circle of immediate corresponding curvature of a curve at a point
curvature, form another curve, called the evolute of C. Vertices of C correspond to singular points on its evolute. Within any arc of a curve C within which
Osculating_circle
Genus of molluscs
Palembang shales of Sumatra. The eggcase of this species is considerably more evolute than that of Argonauta, possessing an open umbilical region, and seems
Kapal
Radius of the circle which best approximates a curve at a given point
An ellipse (red) and its evolute (blue). The dots are the vertices of the ellipse, at the points of greatest and least curvature.
Radius_of_curvature
Point of extreme curvature on a curve
typically only have 3-point contact with their osculating circle. The evolute of a curve will generically have a cusp when the curve has a vertex; other
Vertex_(curve)
Cubic plane curve
between the origin and point (4,8), one gets the arc length 9.073. The evolute of the parabola ( t 2 , t ) {\displaystyle (t^{2},t)} is a semicubical
Semicubical_parabola
Genus of molluscs (fossil)
restricted to the Triassic period. As common to the family, the shell is evolute with lateral tubercles. The suture is not elaborate. Arkel et al., Mesozoic
Balkanites
Spiral with constant distance from itself
contribution from Mikhail Gaichenkov). As the Archimedean spiral grows, its evolute asymptotically approaches a circle with radius |v|/ω. Sometimes the term
Archimedean_spiral
Center of the circle which best approximates a curve at a given point
locus of centers of curvature for each point on the curve comprise the evolute of the curve. This term is generally used in physics regarding the study
Center_of_curvature
Extinct order of molluscs
overwhelmingly produced planospirally coiled discoidal shells that may be evolute with inner whorls exposed or involute with only the outer whorl showing
Ceratitida
1999 film by George Lucas
light forces are locked in an eternal battle while being two sides (or evolutes) of the same "Force", the force of time itself (Zurvan)—the prime mover
Star Wars: Episode I – The Phantom Menace
Star_Wars:_Episode_I_–_The_Phantom_Menace
Genus of molluscs (fossil)
genus of the Lower Triassic with a strongly ribbed, commonly tuberculate, evolute shell. included in the Xenoceltitidae (Tozer, 1994). Both genera are included
Abichites
Benacoceras is a strongly ribbed, evolute ammonite from the Late Jurassic, coiled so that all whorls are exposed. Ribbing is biplicate, with very short
Benacoceras
Genus of molluscs (fossil)
which Austroceratites is placed, is a mid Triassic family that has left evolute to involute, stoutly ribbed, discoidal shells with ceratitic sutures. Austroceratites
Austroceratites
the subfamily Xipherceratinae. Whorls are strongly depressed, but still evolute in coiling. The early growth state is prolonged, and smooth, followed by
Bifericeras
Genus of molluscs (fossil)
Kosmoceras is a moderately evolute ammonite genus from the upper Callovian (Middle Jurassic) of Europe with a simple aperture and irregular ribbing interrupted
Kosmoceras
Extinct genus of molluscs
Ptychitidae and, Isculitidae. Nannites is very small, subglobose, generally evolute and smooth, with a rounded venter, and simple goniatitic sutures. Treatise
Nannites
Genus of molluscs (fossil)
and parts of Europe. The shell of Gastrohoplites is variably involute to evolute. Sides and venter are flat, shoulders sharp. Ribs more or less prominent
Gastrohoplites
Genus of molluscs (fossil)
inside of the whorls, unusual for ammonoids. Clymenia has a closely coiled evolute shell that may be faintly ribbed. The dorsum, on the inside of the whorl
Clymenia_(ammonite)
Type of plane curve
(red) and its evolute (blue), the locus of its centers of curvature. The four marked vertices of the ellipse correspond to the four cusps of the evolute.
Convex_curve
Genus of molluscs (fossil)
from the Lower Jurassic with coarsely ribbed rounded whorls. The shell is evolute, early whorls a barrel-shaped cadicone, later become serpenticonic. Jurassic
Aegoceras_(Beaniceras)
Compact crossover SUV
Lamari Eama (Iran) Cirelli 5 (Italy) Cirelli 5zero5 (Italy) EVO 6 (Italy) Evolute i‑SKY (Russia) Production 2020–present Assembly China: Liuzhou (Dongfeng
Forthing_T5_Evo
Lower Jurassic ammonite
Rasenoides is a flat sided, evolute, radially ribbed Lower Jurassic ammonite belonging to the ammonitida. Russian and Switzerland Notes Sepkoski, Jack
Rasenoides
Extinct genus of molluscs
Mississippian of North America (Michigan) and Europe. The shell of Maccoyocerasis evolute, volutions only slightly impressed, whorl section hexagonal. Venter flattened
Maccoyoceras
Genus of molluscs (fossil)
family Hildoceratidae. The shells are characterized by a narrow discoidal evolute shape, keeled venter, concave ribs along the outer flanks, and a shallow
Hildoceras
Perisphinctidae and superfamily Perisphinctaceae, is small, compressed, evolute, with long secondary ribs and very large asymmetric spatulate lappets that
Cleistosphinctes
Battery electric compact crossover SUV
Manufacturer Dongfeng Nammi Also called Dongfeng Vigo (other overseas markets) Evolute i-JOY (Russia, second generation) Production 2025–present Assembly China:
Nammi_06
Suborder of cephalopods
includes the living Nautilus. The Nautilidae are involute or slightly evolute and generally smooth with straight to sinuous sutures. The Cymatoceratidae
Nautilina
Extinct genus of molluscs
the arietitid subfamily Asteroceratinae. The shell of Aegasteroceras is evolute with curve forward and meet at a broad low ventral keel. Aegasteroceras
Aegasteroceras
Genus of molluscs (fossil)
Berriasella is a discoidal evolute perisphinctacean ammonite, and type genus for the neocomitid subfamily Berriasellinae. Its ribbing is distinct, consisting
Berriasella
Curve traced by a point on a rolling circle
epicycloids, and hypocycloids have the property that each is similar to its evolute. If q is the product of that curvature with the circle's radius, signed
Cycloid
Extinct genus of molluscs
sometimes split into at least three subgenera. Cheiloceras (Cheiloceras) has evolute juvenile stages, the umbilicus closing later, while C. (Compactoceras)
Cheiloceras
Term for space or æther
category encompassing the Samkhya-Yoga and Vedanta, views Akasha as an evolute of something else. The third category regards Akasha as a mental concept
Akasha
Compact crossover SUV
3 DFSK Seres 3 Cirelli 2 (Italy) Ruichi S513 DFSK 500 Landian E3 (EV) Evolute i-Joy (Russia, until 2025) Al Damani DMV 300 (UAE) Lamaco Flo (Iran) Production
Fengon_500
Extinct order of molluscs
Campbelloceras, Tarphyceras, and Trocholites, are tightly coiled, but evolute with all whorls showing. The body chamber of tarphycerids is typically
Tarphycerida
Extinct suborder of ammonites
and symmetrical from side to side. They come in various forms, including evolute shells where all whorls are exposed, and strongly involute shells with
Ammonitina
Genus of molluscs (fossil)
Jurassic included in the Hammatoceratidae and lacking a keel. The shell is evolute, inner whorls exposed; whorls compressed and slightly overlapping. Bears
Zurcheria
Genus of molluscs
order Ceratitida, included in the family Megaphyllitidae that produced evolute compressed planispiral shells with rounded venters, inner whorls ornamented
Dobrogeites
Points with more than one closest boundary point
An ellipse (red), its evolute (blue), and its medial axis (green). The symmetry set, a super-set of the medial axis, is the green and yellow curves. One
Medial_axis
Genus of molluscs (fossil)
The shell, which grew to be rather large, is evolute, strongly and sharply ribbed. Ribbing is both simple and biplicate, with primary ribs bifurcating
Glottoptychinites
Genus of molluscs (fossil)
superfamily Xenodiscaceae. Doulingo""ceras produced a narrowly discoidal evolute shell with concave sides, a narrowly rounded rim (venter) that bears several
Doulingoceras
Plane curve traced by a point on a circle rolled around another circle
one cusp is a cardioid, two cusps is a nephroid. An epicycloid and its evolute are similar. Assuming that the position of p {\displaystyle p} is what
Epicycloid
Genus of molluscs (fossil)
during the Late Cretaceous in the late Campanian has a strongly ribbed evolute shell, all whorls exposed, ribs crossing the rounded outer rim, or venter
Karapadites
Extinct genus of molluscs
the living Nautilus. Stroboceras is characterized by a loosely coiled evolute shell bearing prominent longitudinal ridges and grooves; with a variable
Stroboceras
Family of single-celled organisms
included genera are characterized by asymmetrical, semi-involute to partially evolute, aragonitic tests consisting of an undivided planispiral or trochospiral
Planispirillinidae
Genus of molluscs (fossil)
Flemingites is an extinct genus of evolute, ceratitic ammonoid from the Smithian portion of the Olenekian age (Lower Triassic Period) with spiral ridges
Flemingites
incomplete, crushed specimen from the Permian of China. Its shell is very evolute, with an hexagonal whorl section, and six rows of tubercles, in pairs on
Hexagonites
Genus of molluscs (fossil)
cephalopods were fast-moving nektonic carnivores. Shells of Lytoceras are evolute, round or quadrate in section, covered with crinkled growth lines or riblets
Lytoceras
Genus of molluscs (fossil)
Calycoceras as the subgenus Calycoceras (Conlinocras), is a strongly ribbed, evolute ammonite, belonging to the acanthoceratid subfamily Acanthoceratinae, known
Conlinoceras
Genus of molluscs (fossil)
Yakounia is a genus of evolutely coiled, planispiral ammonite, coiled so all whorls are exposed, with close transverse ribbing. This genus lived during
Yakounia
Bevahites is a Cretaceous ammonite with an evolute, ribbed, tuberculate, and keeled shell with a squarish to compressed whorl section. Bevahites is a
Bevahites
Self-similar growth curve
other curves: Logarithmic spirals are congruent to their own involutes, evolutes, and the pedal curves based on their centers. Complex exponential function:
Logarithmic_spiral
Genus of molluscs (fossil)
Danubitoidea. The Badiotitidae is included in the Ceratitoidea. Badiotites is evolute, compressed, and discoidal, with sigmoidal ribs, an acutely rounded venter
Badiotites
Genus of molluscs (fossil)
ammonoid cephalopod from the Jurassic, named by Spath in 1920. The shell is evolute, coiled such that all whorls are exposed. The whorl section is compressed
Dayiceras
Family of molluscs
varied genus that makes up the Jurassic Cenoceras complex. Cenoceras is evolute to involute, and globular to lentincular; with a suture that generally
Nautilus
Genus of molluscs (fossil)
the Valanginian,(Lower Cretaceous), of Argentina. Frenguelliceras has an evolute, flat sided shell with coarse, simple or widely splayed ribs dividing from
Frenguelliceras
Swiss mathematician (1655–1705)
y'=p(x)y+q(x)y^{n}.} Jacob Bernoulli also discovered a general method to determine evolutes of a curve as the envelope of its circles of curvature. He also investigated
Jacob_Bernoulli
Genus of molluscs (fossil)
Dipoloceras is a rather evolute, strongly ribbed and well keeled acanthocerataean ammonite from the Albian stage of the Lower Cretaceous included in the
Dipoloceras
Liza (28 September 2022). "В России запустили производство электромобилей Evolute". motor.ru (in Russian). Retrieved 15 October 2022. Ananyev, Ivan (26 May
Plug-in electric vehicles in Russia
Plug-in_electric_vehicles_in_Russia
Plane curve
locus of all the centers of curvature is called an evolute. In the case of an ellipse, the evolute is an astroid. Ellipses appear in triangle geometry
Ellipse
Extinct family of molluscs
Middle and Upper Permian genera characterized by compressed, discoidal, evolute shells with rounded to acute venters and commonly with lateral ribs. Sutures
Xenodiscidae
Extinct genus of nautiloids
lobes and with shallow ventral lobes. The earlier, related Domatoceras is evolute, with a more quadrate whorl section. Gryponautilus, from the Upper Triassic
Grypoceras
Viviani's curve Caustic including Catacaustic and Diacaustic Cissoid Conchoid Evolute Glissette Inverse curve Involute Isoptic including Orthoptic Negative pedal
List_of_curves
Extinct superfamily of ammonites
lobes are smooth and undivided. Shells are variable in form, both ribbed, evolute forms and smooth, involute forms are included. Families regarded as part
Hoplitoidea
Genus of molluscs (fossil)
of genera like Monophyllites and Ussurites. The shell of Eophyllites is evolute, discoidal; whorls compressed, deeply embracing; flanks gently convex,
Eophyllites
Genus of molluscs (fossil)
California in the United States, and Indonesia. The shell is in general evolute, but deeply impressed along the inner, or dorsal, margin. The whorl section
Anatropites
Genus of molluscs (fossil)
between about 295 and 290 million years ago. The shell of Atsabites is evolute, discoidal; whorls slightly impressed dorsally, with numerous prominent
Atsabites
Extinct family of ammonites
ammonites from Europe, North Africa, and Asia characterized by narrow, evolutely coiled shells, usually with coarse ventral ribbing on the body chamber
Juraphyllitidae
Extinct superfamily of nautiloids
Trigonoceratidae, type family, named by Hyatt, 1884, are loosely coiled to evolute, with oval to subquadrate, compressed to depressed whorl sections, and
Trigonoceratoidea
Genus of molluscs (fossil)
been found in the Alps, Sicily, and possibly in California. The shell is evolute and ribbed, with the outer whorls becoming smooth. Arnioceltities is included
Arnioceltites
Extinct genus of ammonites
Hungary and probably also in Austria. Ammonites belonging to this genus have evolute shells of small size. Inner whorls are cadicone, while outer whorls are
Septimaniceras
Genus of molluscs (fossil)
Neocardioceras is a genus of evolute acanthoceratid ammonites from the uppermost Cenomanian, Upper Cretaceous, of Europe, western U.S. and Brazil. As
Neocardioceras
Genus of molluscs (fossil)
thought of as a subgenus of Ammonoceratites. Argonauticeras produced an evolute shell with a trapezoidal whorl section, slightly impressed inner rim (or
Argonauticeras
Genus of molluscs (fossil)
Aulacostephanidae. Aulacostephanus produced a discoidal, strongly ribbed, evolute shell of moderate size, reaching diameters of 16 cm (~6.5in.), or so. Ribs
Aulacostephanus
Family of molluscs (fossil)
of the superfamily Hoplitoidea. Members of the Hoplitidae are typically evolute, with inner whorls exposed, although some are more involute, and are commonly
Hoplitidae
Genus of molluscs (fossil)
Collignociceras is a strongly ribbed and tuberculate, evolute ammonite from the Turonian of the western U.S. and Europe belonging to the ammonitid family
Collignoniceras
Genus of molluscs (fossil)
Cretaceous period, from the Hauterivian age to the Barremian age. It is evolute, compressed. The Whorl section is rectangular. The ribs are simple or branching
Hemihoplites
Extinct subfamily of molluscs
the Acanthoceratidae (Ammonoidea) characterized by moderately to very evolute shells with rectangular to squarish whorl sections along with blunt umbilical
Mammitinae
Extinct genus of molluscs
nektonic carnivores are variable in form, depending on species; ranges from evolute to involute, compressed lenticular to globose with rounded to flattened
Cenoceras
a surface in three dimension the focal surface, surface of centers or evolute is formed by taking the centers of the curvature spheres, which are the
Focal_surface
Pascal (1623–1662) – projective geometry Christiaan Huygens (1629–1695) – evolute Giordano Vitale (1633–1711) Philippe de La Hire (1640–1718) – projective
List_of_geometers
Extinct superfamily of ammonites
Jurassic (Bajocian) to Lower Cretaceous (Barremian) ammonites, commonly with evolute shells with strong ribbing that typically divides about mid flank before
Perisphinctoidea
Method for representing the local symmetries of a curve
corresponding to vertices of the curve. Such points will lie at cusp of the evolute. At such points the curve will have 4-point contact with the circle. For
Symmetry_set
EVOLUTE
EVOLUTE
EVOLUTE
EVOLUTE
Boy/Male
Biblical
An eminence or high place.
Boy/Male
Indian
Grape
Boy/Male
Indian
The first God
Boy/Male
Gaelic
Christ bearer.
Girl/Female
Indian, Sanskrit
Evolving
Boy/Male
Indian, Tamil
God Ganesh
Girl/Female
Australian, Gaelic, German, Irish
Fair Lady
Girl/Female
Anglo Saxon
Joyous.
Girl/Female
Arabic, Muslim
Of Beautiful Eyes
Girl/Female
American, Australian, Christian, German
Free; Form of Cheryl
EVOLUTE
EVOLUTE
EVOLUTE
EVOLUTE
EVOLUTE
n.
The formation of an involute by unwrapping a thread from a curve as an evolute.
n.
The involute of a curve. See Involute, and Evolute.
n.
A curve traced by the end of a string wound upon another curve, or unwound from it; -- called also evolvent. See Evolute.
n.
A curve from which another curve, called the involute or evolvent, is described by the end of a thread gradually wound upon the former, or unwound from it. See Involute. It is the locus of the centers of all the circles which are osculatory to the given curve or evolvent.