Minkowski plane

In mathematics, a Minkowski plane (named after Hermann Minkowski) is one of the Benz planes (the others being Möbius plane and Laguerre plane). == Classical real Minkowski plane == Applying the pseudo-euclidean distance d ( P 1 , P 2 ) = ( x 1 ′ − x 2 ′ ) 2 − ( y 1 ′ − y 2 ′ ) 2 {\displaystyle d(P_{1},P_{2})=(x'_{1}-x'_{2})^{2}-(y'_{1}-y'_{2})^{2}} on two points P i = ( x i ′ , y i ′ ) {\displaystyle P_{i}=(x'_{i},y'_{i})} (instead of the euclidean distance) we get the geometry of hyperbolas, because a pseudo-euclidean circle { P ∈ R 2 ∣ d ( P , M ) = r } {\displaystyle \{P\in \mathbb {R} ^{2}\mid d(P,M)=r\}} is a hyperbola with midpoint ⁠ M {\displaystyle M} ⁠.

Source: Wikipedia — Minkowski plane (CC BY-SA 4.0)

Minkowski plane

In mathematics, a Minkowski plane (named after Hermann Minkowski) is one of the Benz planes (the others being Möbius plane and Laguerre plane). == Classical real Minkowski plane == Applying the pseudo-euclidean distance d ( P 1 , P 2 ) = ( x 1 ′ − x 2 ′ ) 2 − ( y 1 ′ − y 2 ′ ) 2 {\displaystyle d(P_{1},P_{2})=(x'_{1}-x'_{2})^{2}-(y'_{1}-y'_{2})^{2}} on two points P i = ( x i ′ , y i ′ ) {\displaystyle P_{i}=(x'_{i},y'_{i})} (instead of the euclidean distance) we get the geometry of hyperbolas, because a pseudo-euclidean circle { P ∈ R 2 ∣ d ( P , M ) = r } {\displaystyle \{P\in \mathbb {R} ^{2}\mid d(P,M)=r\}} is a hyperbola with midpoint ⁠ M {\displaystyle M} ⁠.

Source: Wikipedia "Minkowski plane" · CC BY-SA 4.0

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