Rotation and Dilation
combine rotation and dilation
In this example, a triangle (named 'poly1') is rotated and dilated with a specified angle t and factor r, about the center A. The two transformations can be combined as one in the command.
Dilate[Rotate[poly1, t, A], r, A]
repeat the action
We can continue with this action on each object formed, resulting in a series of triangles, which can be named as poly2, poly3, poly4, etc by repeating the command in the following way:
poly2=Dilate[Rotate[poly1, t, A], r, A]
poly3=Dilate[Rotate[poly2, t, A], r, A]
poly4=Dilate[Rotate[poly3, t, A], r, A]
poly5=Dilate[Rotate[poly4, t, A], r, A]
…...
figure 2
varying the parameters
Here is another way for creating each of these triangles by varying the angle and factor each time, but applying the transformation to the first figure only.
Dilate[Rotate[poly1, n*t, A], r^n, A]
We use the letter n to indicate suitable angle and factor if the action is repeated on the first triangle. Drag the slider for n to see the effect.