geometry - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Geometry : 2-D Euclidean : Transformations : geometry/inversion

geometry

  

inversion

  

find the inversion of a point, line, or circle with respect to a given circle

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

inversion(Q, P, c)

Parameters

Q

-

the name of the object to be created

P

-

point, line, or circle

c

-

circle

Description

• 

If P is a point that is not the same as the center O of circle cr, the inverse of P in, or with respect to, circle cr is the point Q lying on the line OP such that SensedMagnitudeOPSensedMagnitudeOQ=r2.

• 

If P is a line passing through center O of circle cr, the inverse of P is P itself. In case P is a line not passing through center O of circle cr, the inverse of P is a circle Q passing though O perpendicular to P

• 

If P is a circle passing through the center O of circle cr, the inverse of P is a straight line Q not passing through O and perpendicular to the diameter of cr through O. In case P is a line not passing through the center O of circle cr, the inverse of P is a circle Q not passing through O and homothetic to circle cr with O as center of homothety.

• 

For a detailed description of Q the object created, use the routine detail (i.e., detail(Q);)

• 

The command with(geometry,inversion) allows the use of the abbreviated form of this command.

Examples

withgeometry:

Inversion of a point with respect to a circle

pointA,2,0:circlec1,x2+y2=16,x,y:

inversionB,A,c1:inversionC,B,c1:

coordinatesA=coordinatesC

2,0=2,0

(1)

Inversion of a line with respect to a circle

linel1,y=x,x,y:

IsOnLinecenterc1,l1

true

(2)

inversionl2,l1,c1:

Equationl1=Equationl2

yx=0=yx=0

(3)

linek,x=2,x,y:

inversionk1,k,c1:inversionkk1,k1,c1:

formk1

circle2d

(4)

Equationk,Equationkk1

x2=0,16+8x=0

(5)

inversion of a circle with respect to a circle

circlec2,pointA,4,0,1,x,y:

IsOnCirclecenterc2,c1

true

(6)

inversionc3,c2,c1:

formc3

circle2d

(7)

circlec2,x32+y2=36,x,y:

inversionc3,c1,c2:inversionc4,c3,c2:

Equationc1=Equationc4

x2+y216=0=x2+y216=0

(8)

detailc1,c2,c3

name of the objectc1form of the objectcircle2dname of the centercenter_c1coordinates of the center0,0radius of the circle16equation of the circlex2+y216=0,name of the objectc2form of the objectcircle2dname of the centercenter_c2coordinates of the center3,0radius of the circle36equation of the circlex2+y26x27=0,name of the objectc3form of the objectcircle2dname of the centercenter_c3coordinates of the center1297,0radius of the circle36167equation of the circle491296x2301216x455144+491296y2=0

(9)

See Also

geometry[homothety]

geometry[objects]

geometry[SensedMagnitude]

geometry[transformation]

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam