|
geometry[dilatation] - find the dilatation of a geometric object
geometry[expansion] - find the expansion of a geometric object
geometry[homothety] - find the homothety of a geometric object
geometry[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)  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  . 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
|
|
|
>
|
|
|
>
|
 
|
|
>
|
|
|
| (1) |
define the circle with center at (0,0) and radius 1
|
>
|
![circle(c, [point(OO, 0, 0), 1])](/support/helpjp/helpview.aspx?si=5896/file04106/math164.png)
|
|
>
|
|
|
>
|
|
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)])](/support/helpjp/helpview.aspx?si=5896/file04106/math178.png)
|
|
>
|
|
|
>
|
|
|
>
|
|
|
>
|
![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`)](/support/helpjp/helpview.aspx?si=5896/file04106/math194.png)
|
|
|
Download Help Document
Was this information helpful?
