Minkowski plane

In mathematics, a Minkowski plane (named after Hermann Minkowski) is one of the Benz planes: Möbius plane, Laguerre plane and Minkowski plane.

Applying the pseudo-euclidean distance ${\displaystyle d(P_{1},P_{2})=(x'_{1}-x'_{2})^{2}-(y'_{1}-y'_{2})^{2}}$ on two points ${\displaystyle P_{i}=(x'_{i},y'_{i})}$ (instead of the euclidean distance) we get the geometry of hyperbolas, because a pseudo-euclidean circle ${\displaystyle \{P\in \mathbb {R} ^{2}\ |\ d(P,M)=r\}}$ is a hyperbola with midpoint ${\displaystyle M}$.

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