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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

with(geometry):

point(A,1,1): dilatation(B,A,3,point(OO,3,3)):

detail(B);

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

(1)

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

circle(c,[point(OO,0,0),1]):

homothety(c1,c,3,OO):

draw({c(color=red,style=POINT,symbol=DIAMOND),
      c1(color=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)

parabola(p1,['vertex'=point('ver',0,0),'focus'=point('fo',0,1/2)]):

expansion(p2,p1,2,OO):

expansion(p3,p1,1/2,OO):

expansion(p4,p1,1/4,OO):

draw([p1(color=green,style=LINE,thickness=2),p2,p3,p4],
      style=POINT,color=brown,view=[-1/2..1/2,.0..2/5],
      numpoints = 400, title = `dilatation of a hyperbola`);

See Also

geometry[draw]

geometry[objects]

geometry[transformation]