In geometry, Plücker coordinates, introduced by Julius Plücker in the 19th century, are a way to assign six homogeneous coordinates to each line in projective 3-space, P 3 {\displaystyle \mathbb {P} ^{3}} . Because they satisfy a quadratic constraint, they establish a one-to-one correspondence between the 4-dimensional space of lines in P 3 {\displaystyle \mathbb {P} ^{3}} and points on a quadric in P 5 {\displaystyle \mathbb {P} ^{5}} (projective 5-space).
In geometry, Plücker coordinates, introduced by Julius Plücker in the 19th century, are a way to assign six homogeneous coordinates to each line in projective 3-space, P 3 {\displaystyle \mathbb {P} ^{3}} . Because they satisfy a quadratic constraint, they establish a one-to-one correspondence between the 4-dimensional space of lines in P 3 {\displaystyle \mathbb {P} ^{3}} and points on a quadric in P 5 {\displaystyle \mathbb {P} ^{5}} (projective 5-space).
Source: Wikipedia "Plücker coordinates" · CC BY-SA 4.0
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