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geometry

  

dilatation

  

find the dilatation of a geometric object

  

expansion

  

find the expansion of a geometric object

  

homothety

  

find the homothety of a geometric object

  

stretch

  

find the stretch of a geometric object

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

dilatation(Q, P, k, O)

expansion(Q, P, k, O)

homothety(Q, P, k, O)

stretch(Q, P, k, O)

Parameters

Q

-

the name of the object to be created

P

-

geometric object

k

-

number which is the ratio of the dilatation

O

-

point which is the center of the dilatation

Description

• 

Let O be a fixed point of the plane and k a given nonzero real number. By the dilatation (or expansion, or homothety, or stretch) HO,k we mean the transformation of S onto itself which carries each point P of the plane into the point Q of the plane such that SensedMagnitudeOQ=kSensedMagnitudeOP. The point O is called the center of the dilatation, and k is called the ratio of the dilatation.

• 

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

• 

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

Examples

withgeometry:

pointA,1,1:dilatationB,A,3,pointOO,3,3:

detailB

name of the objectBform of the objectpoint2dcoordinates of the point−3,−3

(1)

define the circle with center at (0,0) and radius 1

circlec,pointOO,0,0,1:

homothetyc1,c,3,OO:

drawccolor=red,style=POINT,symbol=DIAMOND,c1color=blue,style=POINT,symbol=CROSS,numpoints=100,title=`dilatation of a circle`

define the parabola with vertex at (0,0) and focus at (0,1/2)

parabolap1,'vertex'=point'ver',0,0,'focus'=point'fo',0,12:

expansionp2,p1,2,OO:

expansionp3,p1,12,OO:

expansionp4,p1,14,OO:

drawp1color=green,style=LINE,thickness=2,p2,p3,p4,style=POINT,color=brown,view=12..12,0.0..25,numpoints=400,title=`dilatation of a hyperbola`

See Also

geometry[draw]

geometry[objects]

geometry[transformation]

 


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