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2D CURVES

French version
See notations below.

 Curves beginning by...

A
B
C1
C2
D
E
F
G
H
I
JK
L
M
N
O
P
Q
R
S
T
U V W X Y Z

ABDANK-ABAKANOVICZ ( QUADRATRIX OF)

AGNESI  (WITCH OF)

ALAIN'S CURVE

ALGEBRAIC CURVE

ALYSOID

ANALLAGMATIC CURVE

ANAMORPHOSIS

ANGUINEA

ANTICAUSTIC

ANTI-CLOTHOID

ANTIHYPERBOLISM  OF A CURVE

APLANETIC  CURVE

APOLLONIUS  CUBIC

ARACHNEA

ARCHIMEDEAN SPIRAL

ASTROID

ATRIPHTHALOID

BARYCENTRIC CURVE

BASE CURVE

BEETLE CURVE

BERNOULLI  (LEMNISCATE OF/)

BERNOULLI  (SPIRAL OF/)

BESACE

BEZIER  CURVE

BEZIER CURVE (RATIONAL/)

BICIRCULA R  ALGEBRAIC CURVE

BIFOLIUM

BIFOLIUM (REGULAR/, RIGHT/))

BIQUARTIC

BLANCMANGE CURVE

BOOTH  (CURVE, LEMNISCATE, OVAL)

BOWDITCH CURVE

BRACHISTOCHRONE CURVE

BROWNIEN (CURVE OF the / MOVEMENT)

BULLET NOSE CURVE

BUS DOOR (CURVE OF THE)

CAMPYLE OF EUDOXUS

CAPPA

CARDIOID

CARTESIAN CURVE

CARTESIAN FOLIUM

CARTESIAN OVAL

CASSINIAN CURVE

CASSINIAN OVAL

CATACAUSTIC

CATALAN (TRISECTRIX  OF)

CATENARY

CATENARY OF EQUAL RESISTANCE

CATENARY (ELLIPTIC/, HYPERBOLIC /)

CAUSTIC

CAYLEY'S SEXTIC

CAYLEY'S OVAL

CENTRED TROCHOID

CIRCLE

CIRCULAR ALGEBRAIC CURVE

CISSOIDAL  CURVE

CISSOIDAL CURVE (ZAHRADNIK'S)

CISSOID

CISSOID (DIOKLES'/)

CISSOID (RIGHT/)

CLINOID

CLOTHOID

COCHLEOID

COCKED HAT

CONCHAL

CONCHOID

CONCHOID (DURER'S/)

CONCHOID OF NICOMEDES

CONCHOID OF ROSE

CONIC SECTION

CONSTANT WIDTH (CURVE OF)

CORNOID

CORNU SPIRAL

COTES'  SPIRAL

CURVE

CROSSCURVE

CUBIC

CUBICAL (PARABOLA)

CUBIC OF AGNESI

CUBIC (APOLLONIAN/)

CUBIC OF CHASLES

CUBIC (CIRCULAR/)

CUBIC (RATIONAL CIRCULAR/)

CUBIC (DUPLICATRIX/)

CUBIC (ELLIPTIC/)

CUBIC (ISOPTIC/)

CUBIC (LAME/)

CUBIC (MIXED/)

CUBIC (RATIONAL/)

CUBIC OF SLUZE

CUBIC OF TSCHIRNHAUSEN

CUBOCYCLOID

CUP OF COFFEE (CURVE OF THE)

CYCLIC CURVE

CYCLOID

CYCLOIDAL CURVE

CYCLOID (EXTENDED/, PORLATE/)

CYCLOID WITH CENTRE

DELAUNAY'S ROULETTE

DELTOID

DIACAUSTIC

DINOSTRATUS' QUADRATRIX

DIOKLES' CISSOID

DIVERGENT PARABOLA

DOG CURVE
    Running  towards his boss
    Firing at the leash
    Swimming in the current

DOUBLE HEART CURVE

DROPLET CURVE

DUPLICATRIX

DURER'S CONCHOID

DURER'S FOLIUM

EIGHT CURVE

ELASTIC CURVE

ELLIPSE

ELLIPTIC CURVE

ENVELOPE OF A FAMILY OF CURVES

EPISPIRAL

EPICYCLOID

EPICYCLOID (EXTENDED, PROLATE)

EPITROCHOID

EQUIANGULAR SPIRAL

EQUILATERAL  HYPERBOLA

EQUIPOTENTIAL  CURVE

EQUITANGENTIAL CURVE

EUDOXUS' KAMPYLE

EULERIAN SPIRAL

EVOLUTE OF A CURVE

EXTENDED (CYCLOID, EPICYCLOID, HYPOCYCLOID)

FERMAT'S CURVE

FERMAT'S SPIRAL

FIXED CURVE IN A RIGID MOTION

FLOWER (JASMINE/)

FOCAL OF QUETELET

FOCAL OF VAN  REES

FOLIUM

FOLIUM (CARTESIAN/)

FOLIUM (DOUBLE/)

FOLIUM OF DURER

FOLIUM (PARABOLIC/)

FOLIUM (RIGHT/)

FOLIUM (SIMPLE/)

FREETH'S NEPHROID

GALILEO'S SPIRAL

GAUSSIAN CURVE

GENUS  OF AN ALGEBRAIC CURVE

GERONO'S LEMNISCATE

GLISSETTE

GOLDEN SPIRAL

GUTSCHOVEN'S CURVE

HIPPIAS' SECTRIX

PROCLUS' HIPPOPED

LA HIRE'S LINE

HYPERBOLA

HYPERBOLA (CUBICAL/)

HYPERBOLISM OF A CURVE

HYPOCYCLOID

HYPOCYCLOID (EXTENDED/, PROLATE//)

STEINER'S HYPOCYCLOID

HYPOTROCHOID

INFLECTION (CURVE OF LONG/)

INTEGRAL CIRCLE

INVERSE OF A CURVE WITH RESPECT TO A POINT

INVOLUTE  OF A CURVE

INVOLUTE ( CIRCLE/)

ISOCHRONOUS CURVE

ISOPTIC CUBIC

JASMINE FLOWER CURVE

JERABEK'S  CURVE

JORDAN'S CURVE

KAMPYLE OF EUDOXUS

KAPPA CURVE

KEPLER'S EGG

KIEPERT'S CURVE

KISS CURVE

KLEIN'S QUARTIC

LA HIRE'S LINE

LAME'S CURVE

LEMNISCATE

LEMNISCATE (BERNOULLI'S/)

 LEMNISCATE (BOOTH'S/)

LEMNISCATE (GERONO'S/)

LEMNISCATE WITH n  POLES

L'HOSPITAL CUBIC

SNAIL (TRISECTOR/)

LISSAJOUS CURVE OR FIGURE

LITUUS

LOGARITHMIC CURVE

LOGARITHMIC SPIRAL

LOGOCYCLE

MACLAURIN'S TRISECTRIX

MAGNETIC FIELD LINE

MANNHEIM'S CURVE

MEDIAN CURVE

MULTICIRCULAR CURVE

MULTIFOLIUM

NEGATIVE PEDAL

NEILE'S PARABOLA

NEPHROID

NEPHROID OF FREETH

NEWTON'S STROPHOID

NEWTON'S TRIDENT

NICOMEDES' CONCHOID

NODAL CURVE

N-SECTRIX

OBLIQUE (CISSOID  OR STROPHOID/)

OPHIURID

ORTHOCAUSTIC

ORTHOPTIC CURVE

ORTHOTOMIC  CURVE

OVAL

PARABOLA

PARABOLA (CARTESIAN/)

PARABOLA (CUBICAL/)

PARABOLA (DIVERGENT/)

PARABOLA (NEILE'S /)

PARABOLA (SEMICUBICAL/)

PARABOLIC SPIRAL

PEANUT CURVE

PERICYCLOID

PERITROCHOID

PIRIFORM QUARTIC

PEDAL

POINSOT'S SPIRAL

FISH CURVE

POLAR  OF A CURVE WITH RESPECT TO A CONIC

POLYNOMIAL CURVE

POLYZOMAL CURVE

PROLATE (CYCLOID, EPICYCLOID, HYPOCYCLOID)

PURSUIT CURVE

PSEUDO-SQUARE

PTEROID

QUADRATRIX

QUADRATRIX OF ABDANK-ABAKANOVICZ'S

QUADRATRIX OF DINOSTRATUS

QUADRIFOLIUM

QUARTIC CURVE

QUARTIC (BICIRCULAR/)

QUARTIC (RATIONAL BICIRCULAR)

QUARTIC (PIRIFORM)

RATIONAL QUARTIC

QUINTIC

RADIAL CURVE OF A CURVE

RATIONAL CURVE

RECIPROCAL SPIRAL

REES  (FOCAL OF VAN/)

REFRACTION (CAUSTIC CURVE BY/)

RHODONNEA

RIBAUCOUR'S CURVE

RIGHT CISSOID,  STROPHOID

RIGID MOTION

ROSE

ROSE (TROYAN/)

ROULETTE

ROULETTE OF DELAUNAY

RUIZ CASTIZO CURVE

SEMI CUBICAL PARABOLA OR CURVE

SEMI TRIDENT

SEPTIC CURVE

SERPENTINE CUBIC

RIGHT SERPENTINE 1

RIGHT SERPENTINE 2

SEXTIC CURVE

SEXTIC OF CAYLEY

SEXTIC (RATIONAL/)

SICI  SPIRAL

SINUSOIDAL SPIRAL

SINUSOID

SKIPPING ROPE CURVE

SLUZE'S CUBIC

SNAIL OF PASCAL

SPIRAL

SPIRAL OF ARCHIMEDES

SPIRAL OF COTES

SPIRAL (HYPERBOLIC/)

SPIRAL (LOGARITHMIC/)

SPIRAL (GOLDEN/)

SPIRAL (SINUSOIDAL/)

SPIRAL (TRACTRIX/)

SPLINE CURVE

STEINER'S HYPOCYCLOID

STEREOGRAPHIC  PROJECTION OF A SPHERICAL CURVE

STRAIGHT LINE

STROPHOIDAL CURVE

STROPHOID

STROPHOID  (RIGHT/, or NEWTON'S/)

SUPERELLIPSE

SWASTIKA

SWIMMING DOG CURVE

TANGENTOID

TAUTOCHRONOUS CURVE

TEAR DROP CURVE

TETRACUSPID

TOROID

TORPEDO CURVE

TRACTOR CURVE

TRACTOR CURVE OF THE CIRCLE

TRACTRIX

TRANSCENDENT ( CURVE)

TREFOIL

TREFOIL (EQUILATERAL/)

TRICUSPID

TRIDENT (NEWTON'S)

TRIFOLIUM

TRIFOLIUM (REGULAR/)

TRISECTRIX

TRISECTRIX OF CEVA

TRISECTRIX OF DELANGES

TRISECTRIX OF MACLAURIN

TROCHOIDAL CURVE

TROCHOID

THREE-BAR CURVE

TSCHIRNHAUSEN'S CUBIC

UNICURSAL CURVE

VERSIERA

VISIERA

WATT'S CURVE

WINDMILL CURVE

ZAHRADNIK'S CISSOIDAL CURVE
 
 


NOTATIONS

: curve in the process of study.
M : running point of the curve .
(D) : straight line, (C) : circle.
( O) :  direct orthonormal frame, of axes Ox and Oy.
( x, y): Cartesian coordinates of M.
X and Y : projected points from M on Ox and Oy.
: affix of M.
: polar coordinates of M .
t : parameter (= time).
speed vector.
acceleration vector.
: tangent.
: normal.
s : curvilinear abscissa.
,)
: tangent vector.
: measure of the tangential Cartesian angle , defined by , i.e. , therefore  .

: Measure of the tangential polar angle , defined by, therefore  ; moreother .

angle of contingence.

: normal vector.
Coordfinates of in the basis  in the basis 

V : algebraic speed (  ).

AT : tangential acceleration, AN : normal acceleration (  ).


 
 


 
H : projected point from O on the tangent to the curve.

:  pedal radius ( ).
: radius of curvature (,).
: curvature.
: centre of curvature in M.
Cartesian equation, parametrization : characterization in x and y.

Polar equation, parametrization : characterization in r and q.

Bipolar equation : characterization in r = FM and r' = FM (F and F' are the poles).

Intrinsic equation 1 (or intrinsic equation of Cesaro): characterization in RC and s; one integrates it by using :  allowing to obtain the
Intrinsic equation 2 (or intrinsic equation of Whewell) : characterization in s and j ; one integrates it by using : .


 
T: intersection point of the tangent with the Ox axis and also value of = "tangent".
= "sub tangent".
N: Intersection point of the normal with the Ox axis and also value of  = "normal".
= "sub normal".
: Intersection point of the tangent with the perpendicular in O to (OM) and also value of  = "polar tangent".
= "sub polar tangente".
NP: Intersection point of the normal with the perpendicular in O to (OM) and also value of  = " polar normal".

= " sub polar normal".


 
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