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geometry

  

StretchRotation

  

find the stretch-rotation of a geometric object

  

homology

  

find the homology of a geometric object

  

SpiralRotation

  

find the spiral-rotation of a geometric object

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

StretchRotation(Q, P, O, theta, dir, k)

homology(Q, P, O, theta, dir, k)

SpiralRotation(Q, P, O, theta, dir, k)

Parameters

Q

-

the name of the object to be created

P

-

geometric object

O

-

point which is the center of the homology

theta

-

number which is the angle of the homology

dir

-

name which is either clockwise or counterclockwise

k

-

number which is the ratio of the homology

Description

• 

Let O be a fixed point in the plane, k a given nonzero real number, theta and dir denote a given sensed angle. By the homology ( or stretch-rotation, or spiral-rotation) HO,k,θ we mean the product RO,thetaHO,k where RO,θ,dir is the rotation with respect to O an angle theta in direction dir and HO,k is the dilatation with respect to the center O and ratio k.

• 

Point O is called the center of the homology, k the ratio of the homology, theta and dir the angle of the homology.

• 

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

• 

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

Examples

with(geometry):

point(OO,0,0):

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)]):

Equation(p1,[x,y]);

x24y2=0

(1)

homology(p2,p1,OO,Pi/2,'counterclockwise',2):

Equation(p2);

y216+x4=0

(2)

homology(p3,p1,OO,Pi,'counterclockwise',2):

Equation(p3);

x216+y4=0

(3)

homology(p4,p1,OO,Pi/2,'clockwise',2):

Equation(p4);

y216x4=0

(4)

homology(p5,p1,OO,0,'clockwise',2):

Equation(p5);

x216y4=0

(5)

draw({p1(color=green,style=LINE,thickness=2,numpoints=50),p2,p3,p4,p5},
   style=POINT,numpoints=200,color=brown,title=`homology of a parabola`);

See Also

geometry[dilatation]

geometry[draw]

geometry[objects]

geometry[reflection]

geometry[transformation]