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
dilatation(Q, P, k, O)
expansion(Q, P, k, O)
homothety(Q, P, k, O)
stretch(Q, P, k, O)
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
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⁡O,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 SensedMagnitude⁡OQ=k⁢SensedMagnitude⁡OP. 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.
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
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]
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