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geometry

  

reciprocation

  

find the reciprocation of a point or a line with respect to a circle

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

reciprocation(Q, P, c)

Parameters

Q

-

the name of the object to be created

P

-

point or line

c

-

circle

Description

• 

Let c=Or be a fixed circle and let P be any ordinary point other than the center O. Let P' be the inverse of P in circle Or. Then the line Q through P' and perpendicular to OPP' is called the polar of P for the circle c.  Note that when P is a line, then Q will be a point.

• 

Note that this routine in particular, and the geometry package in general, does not encompass the extended plane, i.e., the polar of center O does not exist (though in the extended plane, it is the line at infinity) and the polar of an ideal point P does not exist either (it is the line through the center O perpendicular to the direction OP in the extended plane).

• 

If line Q is the polar point P, then point P is called the pole of line Q.

• 

The pole-polar transformation set up by circle c=Or is called reciprocation in circle c

• 

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

• 

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

Examples

withgeometry:

circlec,pointOO,0,0,2,x,y:

pointP,1,0:

inversionPP,P,c:

reciprocationl,P,c

l

(1)

detaill

name of the objectlform of the objectline2dequation of the line4+x=0

(2)

drawc,dsegmentdsg,P,PP,l,printtext=true,view=3..5,3..3,axes=NONE

reciprocationA,l,c:

coordinatesA=coordinatesP

1,0=1,0

(3)

See Also

geometry[draw]

geometry[inversion]

geometry[objects]

geometry[transformation]

 


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