Klein model in a circle (and cross ratio)
You need plugins for Cabri2/Cabri3D to see
files embedded in htmls below, even if you
have those softwares. To download plugins,please
check these: cabri2 , cabri3D ．Once you install the plugins, you can
manuplate figures on the files with mouse
． To move the whole figure, please drag with
Ctrl key down . For reconstraction, please click the red
inverted triangle. At the bottom, there are also original
cabri files which you can directly manipulate
with Cabri/Cabri3D SOFTWARE (not plugins)．
If you can read Japanese , you can get detailed explanations of these
files and mathematical proves from the PDF
section below. There are one-to-one
links to Cabri/Geogebra files. Note that , however, you should use 'back
button' of your browser when you come back
from these links, if you close the brouser,
it also closes original PDFs.
- Cabri files (embedded in htmls)
-Cabri2&3D plugins are necessary-
- Basics of Klein model
- Relations with upper sphere model;
line&circle, horicircle&equi distant line
- Relations with Poincare disk;
part1, part2
- construction of circle, equi distant line
& horicircle
- construction of inversion
- construction of circle,equi distant line
& horicircle
- distance and angle（analytic)
- angle of 'sphere model' & 'Klein model'
- distance is direction dependant
- cross ratio(double ratio) of 4 points in
space (R3)
- cross ratio and inversion (with respect to
a sphere)
- cross rario & distance (geometric)
- Poincare upper planeH+: cross ratio&distance
- upper sphere: cross ratio &distance,
inversion which transforms H+
onto upper
sphere
- Poincare Disk: cross ratio&distance,
relations among 3 models
- Klein model: cross ratio&distance,
relations with upper sphere model
- cross ratio&angle
- Poincare upper planeH+
- upper sphere
- Poincare Disk
- Klein model
- cross ratios of various kinds
- cross ratio of 4 points on a line
- cross ratio of pencil (a set of lines which
meet together)
- cross ratio of 4 points on a circle:
when points move on a circle, when a pole moves
- 'distance & angle' of Klein model in
a conic
- Klein model in a circle: angle&cross ratio of a pencil
- Klein model in a conic: distance, angle
- PDF files (in Japanese)
-Please use 'back button', when you come back
from links!-
- Basics of Klein model
- construction of circle, equi distant line
& horicircle
- distance and angle（analytic)
- cross ratio(double ratio) of 4 points in
space (R3)
- cross rario & distance (geometric) （H+,Poincare Disk, sphere model)
- cross ratio&angle (same as above)
- cross ratios of various kinds
- 'distance & angle' of Klein model in
a conic
- Original Cabri files
- Macros of Cabri2
|
ogose shigeki (
), all rights reserved
Non Euclidian Geometry