Jordanova miera
Miera (dĺžka) úsečky
Miera v Poincare Disku
Nech
sú ľubovoľné dva body patriace Poincare Disc. Hyperbolickú hPriamku
označíme
a "nevlastné" koncové body tejto priamky pomocou
.
Tieto body pomenujeme tak, aby platilo
.
![A, B A, B](https://lms.umb.sk/filter/tex/pix.php/72f3a84b55c4b9374aedd136d7fc7d3d.png)
![AB AB](https://lms.umb.sk/filter/tex/pix.php/adfda2c63a6b4f70f610eb963324646d.png)
![l l](https://lms.umb.sk/filter/tex/pix.php/5016ca32fd411451fb91fcbd157027e4.png)
![P,Q P,Q](https://lms.umb.sk/filter/tex/pix.php/243abdafc8064e8d50323d6df0b853d5.png)
Tieto body pomenujeme tak, aby platilo
![P ∗ B ∗ A ∗ Q P ∗ B ∗ A ∗ Q](https://lms.umb.sk/filter/tex/pix.php/3f9037c2c711f935b7da3e790400b060.png)
Nech A, B, P, Q sú navzájom rôzne kolineárne body také, že platí
.
Dvojpomer usporiadanej štvorice bodov
je podiel deliacich pomerov
a
; (dvojpomer takejto štvorice bodov
označujeme
).
![P ∗ B ∗ A ∗ Q P ∗ B ∗ A ∗ Q](https://lms.umb.sk/filter/tex/pix.php/3f9037c2c711f935b7da3e790400b060.png)
Dvojpomer usporiadanej štvorice bodov
![A, B, P, Q A, B, P, Q](https://lms.umb.sk/filter/tex/pix.php/0bc53c70143b3871ad9042088dfbefce.png)
![(ABP) (ABP)](https://lms.umb.sk/filter/tex/pix.php/250a93887e24f331541f28bb93c01aab.png)
![(ABQ) (ABQ)](https://lms.umb.sk/filter/tex/pix.php/7e0b3de4f2e9112722254157131fa28e.png)
![A, B, P, Q A, B, P, Q](https://lms.umb.sk/filter/tex/pix.php/0bc53c70143b3871ad9042088dfbefce.png)
![(ABPQ) (ABPQ)](https://lms.umb.sk/filter/tex/pix.php/d3dcb83c86981cd28665116217c331bd.png)
![(ABPQ) := \frac{(ABP)}{(BAQ)} (ABPQ) := \frac{(ABP)}{(BAQ)}](https://lms.umb.sk/filter/tex/pix.php/f0c1df5688d6d80e59e48efbbc892cbf.png)
Príklad
Otvorte applet Tu
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