2d curves Index and notations

23.11.2018

2d curves : Index and notations

https://www.mathcurve.com/courbes2d.gb/courbes2d.shtml

1/11

2D CURVES

Translated from French by David Michel

Version française

See

notations

below.

Curves beginning by...

ABDANK-ABAKANOVICZ ( QUADRATRIX OF)

ANTIHYPERBOLISM OF A CURVE

BERNOULLI (LEMNISCATE OF/)

BERNOULLI (SPIRAL OF/)

BESACE

BEZIER CURVE

BEZIER CURVE (RATIONAL/)

BICIRCULA R ALGEBRAIC CURVE

BICORN

BIFOLIUM

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BIFOLIUM (REGULAR/, RIGHT/))

BIQUARTIC

BLANCMANGE CURVE

BOOTH (CURVE, LEMNISCATE, OVAL)

BOWDITCH CURVE

BRACHISTOCHRONE CURVE

BRACHISTOCHRONE OF GIVEN LENGTH

BROCARD TRANSFORMATION

BROWNIEN (CURVE OF the / MOVEMENT)

BULLET NOSE CURVE

BUS DOOR (CURVE OF THE)

CATALAN (TRISECTRIX OF)

CATENARY

CATENARY OF EQUAL STRENGTH

CATENARY (ELLIPTIC/, HYPERBOLIC /)

CIRCULAR ALGEBRAIC CURVE

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CONCHOID OF NICOMEDES

CONCHOID OF ROSE

CONIC SECTION

CONSTANT WIDTH (CURVE OF)

CUBIC (RATIONAL CIRCULAR/)

CUBIC OF TSCHIRNHAUSEN

CUBOCYCLOID

CUP OF COFFEE (CURVE OF THE)

CURTATE (

CYCLOID (PROLATE/, CURTATE)

DINOSTRATUS' QUADRATRIX

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DIOKLES' CISSOID

DIVERGENT PARABOLA

DOG CURVE

Running towards its master

Pulling on the leash

Swimming against the current

ENVELOPE OF A FAMILY OF CURVES

EPISPIRAL

EPICYCLOID

EPICYCLOID (PROLATE, CURTATE)

EPITROCHOID

EQUIANGULAR SPIRAL

EQUILATERAL HYPERBOLA

FIXED CURVE IN A RIGID MOTION

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GENUS OF AN ALGEBRAIC CURVE

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

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LEMNISCATE

LEMNISCATE (BERNOULLI'S/)

LEMNISCATE (BOOTH'S/)

LEMNISCATE (GERONO'S/)

LEMNISCATE WITH n POLES

L'HOSPITAL CUBIC

LISSAJOUS CURVE OR FIGURE

MACLAURIN'S TRISECTRIX

OBLIQUE (

CISSOID OR STROPHOID/)

PARABOLA (CARTESIAN/)

PARABOLA (CUBICAL/)

PARABOLA (DIVERGENT/)

PARABOLA (NEILE'S /)

PARABOLA (SEMICUBICAL/)

PARABOLIC SPIRAL

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POLAR OF A CURVE WITH RESPECT TO A CONIC

PROLATE (

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

REFRACTION (CAUSTIC CURVE BY/)

RIGHT

SEMI CUBICAL PARABOLA OR CURVE

SEMI TRIDENT

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SLUZE'S

SPIRAL (LOGARITHMIC/)

STEINER'S HYPOCYCLOID

STEREOGRAPHIC PROJECTION OF A SPHERICAL CURVE

STRAIGHT LINE

STROPHOIDAL CURVE

STROPHOID

STROPHOID (RIGHT/, or NEWTON'S/)

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TRACTOR CURVE

TRACTOR CURVE OF THE CIRCLE

TRACTRIX

TRANSCENDENTAL ( CURVE)

TREFOIL

TREFOIL (EQUILATERAL/)

TRISECTRIX OF DELANGES

TRISECTRIX OF MACLAURIN

TROCHOIDAL CURVE

TROCHOID

THREE-BAR CURVE

TSCHIRNHAUSEN'S CUBIC

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).

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speed vector.

acceleration vector.

: 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

angle of contingence.

: normal vector.

Coordinates of

in the basis

V : algebraic speed (

: tangential acceleration, A

: normal acceleration

(

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

: pedal radius (

radius of curvature (

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: curvature.

: centre of curvature in M.

Cartesian equation, parametrization :
characterization in x and y.

Polar equation, parametrization : characterization in

and

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 R

and s; one integrates it by

using :

allowing to obtain the

Intrinsic equation 2 (or intrinsic equation of
Whewell) : characterization in s and

; 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 at O to (OM) and also value of

= "polar tangent".

= "sub polar tangente".

: Intersection point of the normal with the

perpendicular at O to (OM) and also value of

= " polar normal".

= " sub polar normal".

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