2D CURVES
Translated from French by David Michel
See notations below.
Curves beginning by...
ABDANK-ABAKANOVICZ ( QUADRATRIX OF)
AGNESI (WITCH OF)
ALAIN'S CURVE
ALGEBRAIC CURVE
ALYSOID
ANALLAGMATIC CURVE
ANAMORPHOSIS
ANGUINEA
ANTICAUSTIC
ANTIPARALLELOGRAM
CURVE (ARTICULED/)
ANTICLOTHOID
ANTIHYPERBOLISM OF
A CURVE
APLANETIC CURVE
APOLLONIUS
CUBIC
ARACHNEA
ARCHIMEDEAN SPIRAL
ASTROID
ATRIPHTHALOID
BARYCENTRIC CURVE
BASE CURVE
BEETLE CURVE
BERNOULLIAN QUARTIC
BERNOULLI (LEMNISCATE
OF/)
BERNOULLI (SPIRAL OF/)
BESACE
BEZIER CURVE
BEZIER CURVE
(RATIONAL/)
BICIRCULA R ALGEBRAIC
CURVE
BICORN
BIFOLIUM
BIFOLIUM (REGULAR/,
RIGHT/))
BIQUARTIC
BLANCMANGE CURVE
BOOTH (CURVE, LEMNISCATE, OVAL)
BOWDITCH CURVE
BRACHISTOCHRONE CURVE
BRACHISTOCHRONE
OF GIVEN LENGTH
BROCARD TRANSFORMATION
BULLET NOSE CURVE
BUS DOOR (CURVE OF THE)
BUCKET CURVE
CAMPYLE OF EUDOXUS
CAPPA
CARDIOID
CARTESIAN CURVE
CARTESIAN FOLIUM
CARTESIAN OVAL
CASSINIAN CURVE
CASSINIAN OVAL
CATACAUSTIC
CATALAN CURVE
CATALAN (TRISECTRIX
OF)
CATENARY
CATENARY
OF EQUAL STRENGTH
CATENARY (ELLIPTIC/, HYPERBOLIC
/)
CATOPTRIX
CAUSTIC
CAYLEY SEXTIC
CAYLEY OVAL
CENTRED TROCHOID
CIRCLE
CIRCLE CAUSTIC
CIRCULAR ALGEBRAIC CURVE
CISSOIDAL CURVE
CISSOID
CISSOID (DIOKLES/)
CISSOID (RIGHT/)
CISSOID
(ZAHRADNIK/)
CLINOID
CLOTHOID
COCHLEOID
COCKED HAT
CONCHAL
CONCHOID
CONCHOID (DURER'S/)
CONCHOID OF
NICOMEDES
CONCHOID OF ROSE
CONIC SECTION
CONSTANT ANGULAR ACCELERATION
CURVE
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)
CURTATE (CYCLOID, EPICYCLOID,
HYPOCYCLOID)
CYCLIC CURVE
CYCLOID
CYCLOIDAL CURVE
CYCLOID (PROLATE/, CURTATE)
CYCLOID WITH CENTRE
DELAUNAY'S ROULETTE
DELTOID
DIACAUSTIC
DINOSTRATUS' QUADRATRIX
DIOKLES' CISSOID
DIVERGENT PARABOLA
DOG CURVE
Running
towards its master
Pulling on
the leash
Swimming against
the current
DOUBLE HEART CURVE
DROPLET CURVE
DUPLICATRIX
DURER'S CONCHOID
DURER'S FOLIUM
EIGHT CURVE
ELASTIC CATENARY
ELASTIC CURVE
ELLIPSE
ELLIPTIC CURVE
ENVELOPE OF A FAMILY OF CURVES
EPISPIRAL
EPICYCLOID
EPICYCLOID (PROLATE, CURTATE)
EPITROCHOID
EQUIANGULAR SPIRAL
EQUILATERAL HYPERBOLA
EQUIPOTENTIAL CURVE
EQUITANGENTIAL CURVE
EUDOXUS' KAMPYLE
EULERIAN SPIRAL
EVOLUTE OF A CURVE
EXPONENTIAL CURVE
FERMAT'S CURVE
FERMAT'S SPIRAL
FISH CURVE
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
GALILEAN 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
HOLDITCH CURVE
HUMBERT CUBIC
HYPERBOLA
HYPERBOLA (CUBICAL/)
HYPERBOLISM OF A CURVE
HYPOCYCLOID
HYPOCYCLOID (PROLATE/,
CURTATE/)
STEINER'S HYPOCYCLOID
HYPOTROCHOID
INFLECTION (CURVE OF LONG/)
INTEGRAL CIRCLE
INVERSE
CAUSTIC
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
JOUKOWSKI 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
LISSAJOUS CURVE OR FIGURE
LITUUS
LOGARITHMIC CURVE
LOGARITHMIC SPIRAL
LOGOCYCLE
MALTESE CROSS
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
POLAR OF A CURVE WITH RESPECT
TO A CONIC
POLYNOMIAL CURVE
POLYZOMAL CURVE
PROLATE (TROCHOID, EPITROCHOID,
HYPOTROCHOID)
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
RADIOID
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/)
SHADOWING CURVE
SICI SPIRAL
SINUSOIDAL
SPIRAL
SINUSOID
SKIPPING ROPE CURVE
SLUZE'S CUBIC
SNAIL OF PASCAL
SNAIL (TRISECTRIX)
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/)
STURM ROULETTE
SUPERELLIPSE
SWASTIKA
SWIMMING DOG CURVE
TANGENTOID
TAUTOCHRONOUS CURVE
TEAR DROP CURVE
TETRACUSPID
TIGHTROPE WALKER CURVE
TOROID
TORPEDO CURVE
TRACTOR CURVE
TRACTOR CURVE OF THE
CIRCLE
TRACTRIX
TRANSCENDENTAL ( 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
WITCH OF AGNESI
ZAHRADNIK'S
CISSOID
NOTATIONS
 :
curve being studied.
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.
For an implicit curve ,
notations of Monge :
 .
 : tangent.
 :
normal.
s : curvilinear abscissa.
(  , )
 :
tangent vector.
 :
measure of the Cartesian tangential angle  ,
defined by  ,
i.e.  ,
therefore 
.
 :
Measure of the polar tangential angle  ,
defined by ,
therefore
; moreother  .
: normal vector.
| Coordinates of |
in the basis  |
in the basis  |
|
|
|
|
|
|
V : algebraic speed ( 
).
AT :
tangential acceleration, AN :
normal acceleration ( 
). |
|
: pedal
radius ( 
).
.
: radius of curvature (
,
).
: curvature.
:
centre of curvature in M.
allowing to obtain the
.
=
"tangent".
=
"sub tangent".
= "normal".
= "sub normal".
: Intersection
point of the tangent with the perpendicular at O to (OM)
and also value of 
= "polar tangent".
=
"sub polar tangente".
= " polar normal".
=
" sub polar normal".