Category:Definitions/Poincaré Plane
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This category contains definitions related to Poincaré Plane.
Related results can be found in Category:Poincaré Plane.
Let:
- $\H = \set {\tuple {x, y} \in \R^2: y > 0}$
Let $a \in \R$ be a real number.
Let:
- ${}_a L := \set {\tuple {x, y} \in \H: x = a}$
Define:
- ${}_A L := \set{ {}_a L: a \in \R}$
Let $c \in \R$ be a real number and $r \in \R_{>0}$ be a strictly positive real number.
Let:
- ${}_c L_r := \set {\tuple {x, y} \in \H: \paren {x - c}^2 + y^2 = r^2}$
Define:
- ${}_C L_R := \set { {}_c L_r: c \in \R \land r \in \R_{>0} }$
Finally let:
- $L_H = {}_A L \cup {}_C L_R$
The abstract geometry $\struct {\H, L_H}$ is called the Poincaré plane.
Pages in category "Definitions/Poincaré Plane"
The following 3 pages are in this category, out of 3 total.