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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 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) $H\left(\mathrm{O},k\right)$ 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 $\mathrm{SensedMagnitude}\left(\mathrm{OQ}\right)=k\mathrm{SensedMagnitude}\left(\mathrm{OP}\right)$. 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);
 $\begin{array}{ll}{\text{name of the object}}& {B}\\ {\text{form of the object}}& {\mathrm{point2d}}\\ {\text{coordinates of the point}}& \left[{-3}{,}{-3}\right]\end{array}$ (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); 