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Click HERE for help on the viewer.
You may drag the magenta colored points.
The five points z1,...,z5 on the central
circle are constrained to lie on the unit
circle. z6 is computed from z1,...,z5 by
the condition multi-ratio(z1,z2,z3,z4,z5,z6)
= -1. You see that for any initinal (you
can drag the center of one petal circle)
radius There is a flower of six circles touching
at the zi. But only for one choice of this
radius the green "s-circles" are
all intersecting in one point "p".
Click HERE for help on the viewer.
The three sliders are the three initial parameters
of the conformally symmetric circle packings.
"evolve" and "shrink"
increase and decrease the number of circles
shown. "reset params" resets the
sliders.
Click HERE for help on the viewer.
The two sliders change the radii of the euqally
labeled circles. "evolve" and "shrink"
increase and decrease the number of circles
shown. "reset params" resets the
sliders.
How to use the Viewer
Pressing the right mouse button (or holding
down the <META> key while pressing
on one-button-mice systems) over the viewers
main window will bring up a pop up menu with
the following items
- translate:
- After selecting this you may drag the whole
viewed configuration
- scale:
- After selecting this, dragging the mouse
up or down will zoom in or out
- rotate:
- After selecting this dragging the mouse up
or down will rotate the configuration
- moebiustransform:
- this option allows to move "0",
"1", and "infinity" freely
and thus apply an arbitrary Möbius transformation.
These three points are shown with label (two
in blue and one in red). Mouse dragging will
drag the red one and a single click will
step through the three points selecting the
next one. You may also directly pick and
drag any of them. If one holds down <CONTROL>
key while dragging instead of the selected
point its inverse is moved. This way one
can get the point "infinity" away
from infinity in the beginning: Initially
only "0" and "1" are
visible. Click until both are blue. Then
<CONTROL>-drag until the red "inf"
labeled point moves into the visible area.
Then you can release <CONTROL> and
drag "inf" directly.
- invert on circle:
- lets you invert the whole configuration on
an arbitrary circle. Click dragging will
open a yellow circle. Releasing the mouse
button will do the inversion.
- save view:
- lets you store teh current view on the configuration
for later return.
- restore view:
- lets you successively restore any previously
saved views.
- reset view:
- resets the view to the initial settings.
- move points:
- In applets where points may be moved around
this option makes the points draggable again
when one has switched to other options inbetween.
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