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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
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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
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
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
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)
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
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
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
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
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
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
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
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Aeolus_A60
Extinct genus of molluscs
Europe and possibly Borneo. Xipheroceras, named by Buckman, 1911, has an evolute shell, all whorls clearly exposed, only very slightly impressed dorsally
Xipheroceras
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
Genus of molluscs (fossil)
ceratitoidean family Tirolitidae of the order Ceratitida, characterized by a flat, evolute shell with moderately compressed, rounded whorls. The spinose stage characteristic
Biltnerites
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
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
Muniericeratidae, a family of Upper Cretaceous ammonites characterized by moderately evolute shells with strong sinuous ribs that have tubercles on the shoulders and
Fournierella_(cephalopod)
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
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
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
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)
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
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 nautiloids
only part of the body chamber divergent from the previous whorl. Shell evolute, expanding fairly rapidly; umbilicus open, perforate; whorl section ovoid
Asymptoceras
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
Genus of molluscs
order Ceratitida, included in the family Megaphyllitidae that produced evolute compressed planispiral shells with rounded venters, inner whorls ornamented
Dobrogeites
Genus of molluscs (fossil)
Calycoceras as the subgenus Calycoceras (Conlinocras), is a strongly ribbed, evolute ammonite, belonging to the acanthoceratid subfamily Acanthoceratinae, known
Conlinoceras
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
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
Extinct genus of ammonites
in the Middle Jurassic. Unipeltoceras is characterized by its strongly evolute, discoidal shell with sharp ribbing on the inner whorls and differing from
Unipeltoceras
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
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
Bevahites is a Cretaceous ammonite with an evolute, ribbed, tuberculate, and keeled shell with a squarish to compressed whorl section. Bevahites is a
Bevahites
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
Perisphinctidae and superfamily Perisphinctaceae, is small, compressed, evolute, with long secondary ribs and very large asymmetric spatulate lappets that
Cleistosphinctes
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)
superfamily Xenodiscaceae. Doulingoceras produced a narrowly discoidal evolute shell with concave sides, a narrowly rounded rim (venter) that bears several
Doulingoceras
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
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
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
Extinct genus of nautiloids
Carboniferous (Pennsylvanian) and Permian, the shell of which is moderately evolute with a subquadrate whorl section, bearing nodes on the ventral or umbilical
Metacoceras
Extinct genus of molluscs
sediments in Europe, and named by Hyatt, 1893. The shell of Lophoceras is evolute, large, with a slight impressed zone on the inner rim. In early volutions
Lophoceras
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
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
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)
stage of the Early Jurassic. The shell of Fuciniceras is generally small, evolute, and strongly ribbed. Sepkoski, Jack (2002). "A compendium of fossil marine
Fuciniceras
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
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)
genus of the Lower Triassic with a strongly ribbed, commonly tuberculate, evolute shell. included in the Xenoceltitidae (Tozer, 1994). Both genera are included
Abichites
Genus of molluscs (fossil)
Ophiceras is an extinct genus of smooth, evolute ceratitid ammonites from the Griesbachian (Early Triassic), with a rounded venter. Fossils of the genus
Ophiceras
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)
Berriasella is a discoidal evolute perisphinctacean ammonite, and type genus for the neocomitid subfamily Berriasellinae. Its ribbing is distinct, consisting
Berriasella
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)
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 superfamily of molluscs
some Oxynoticeratidae were oxycone, most of the species were evolute. Psiloceratidae - Evolute shells with simple, or missing ribs. An venter, there is no
Psiloceratoidea
shell of Umiaites is large, reaching a diameter of 16 cm or greater, and evolute with a wide shallow umbilicus. Flanks are flat to gently curving. Whorls
Umiaites
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)
Sinemurian stage of the lower Jurassic, found in Europe. The shell is evolute, compressed in section. Inner whorls are smooth, outer mature whorl develops
Dasyceras
Genus of molluscs (fossil)
Uzbekistan. The shell of Umbetoceras is involute in the adult, with an evolute early stage and moderately wide umbilicus. Sculpture consists of strong
Umbetoceras
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
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
Campbelloceras, Tarphyceras, and Trocholites, are tightly coiled, but evolute with all whorls showing. The body chamber of tarphycerids is typically
Tarphycerida
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
Genus of desmoceratid ammonite
subfamily Puzosiinae. Member species are characterized by an essentially evolute shell in which the early whorls are smooth, with sinuous radial or oblique
Melchiorites
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Family of molluscs (fossil)
keel bearing, irregularly ribbed and tuberculate shells that vary from evolute to rather involute and compressed to inflated. Tubercles are concentrated
Schloenbachiidae
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)
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
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
Genus of molluscs (fossil)
Japan, included in the Lytoceratidae. The shell of Ammonoceratites is evolute, smooth, moderately expanded; the inner rim (dorsum) only slightly impressed;
Ammonoceratites
Genus of molluscs (fossil)
shoshonensis, and B. zitteli. The shell of Balatonites is essentially evolute, coiled with earlier whorls showing, and is laterally compressed with flattish
Balatonites
which is part of the ammonitid superfamily Eoderoceratoidea. Shells are evolute with an open umbilicus; strongly ribbed, ribs flattened on the venter,
Promicroceras
Genus of molluscs (fossil)
media related to Arnioceras. Arnioceras is an extinct genus of large, evolute, discoidal ammonite from the Lower Jurassic. The shell is normally coiled
Arnioceras
Extinct genus of ammonites
Eoderoceras is an evolute, round whorled ammonite from the Lower Jurassic with an outer row of distinct spines, and in some, an inner row of tubercles
Eoderoceras
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)
Genus of molluscs (fossil)
Euaptetoceras is an evolute hildoceratoid ammonite from the lower Middle Jurassic, included in the family Hammatoceratidae and the subfamility Hammatoceratinae
Euaptetoceras
Genus of nautiloid cephalopods
xaizangense resembles the ophidioceratid genus Ophioceras. The shell is evolute, discoidal, serpenticonic; whorl section rounded, covered with thick, straight
Xainzanoceras
Viviani's curve Caustic including Catacaustic and Diacaustic Cissoid Conchoid Evolute Glissette Inverse curve Involute Isoptic including Orthoptic Negative pedal
List_of_curves
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)
Late Ordovician. Charactoceras has a closely coiled, rapidly expanding evolute shell, dorsally impressed, with a flattened venter and rounded sides. Sutures
Charactoceras
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
Genus of molluscs (fossil)
Astieridiscus is an extinct lower Cretaceous ammonite. Its shell evolute, covered by dense, simple or branching, slightly flexuous ribs. The sides are
Astieridiscus
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Nammi_06
Genus of molluscs (fossil)
genus of the ammonite family Neocomitidae. The shell of Kilianella is evolute with a slightly grooved venter and covered by strong, gently flexious,
Kilianella
Extinct genus of nautiloids
and Permian with a wide spread distribution. The shell of Domatoceras is evolute, coiled with whorls touching but not overlapping, some growing to be moderately
Domatoceras
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
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 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
Extinct family of ammonites
diverse family of Middle Jurassic ammonites ranging from those with stout evolute shells to those whose shells are sharply rimmed, oxyconic. The keel, which
Sonniniidae
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
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)
that lived during the Middle Jurassic, characterized by a planispiral evolute shell with smooth middle and outer whorls, flat sides and simplified sutures
Metrolytoceras
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