Verse and Dimensions Wikia
Verse and Dimensions Wikia

A Riemann sphere or complex projective line is a complex 1-dimensional (1D) manifold that consists of the complex line plus a point at ∞. Points on its surface represent extended complex numbers, the points near ∞ are numbers with larger absolute values, the points near ∞'s antipode 0 are numbers with smaller absolute values, and points on the equator are numbers with an absolute value of 1, numbers that satisfy where is a real number.

The extended complex line projected on the sphere is very useful to complex analysis because they allow division by zero to be well-behaved.

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Real dimensionality 0 1 2 3 ...
Real space

Point

Real line

Real plane

Real realm

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Real projective space

Point pair

Real projective line

Real projective plane

Real projective realm

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Complex space

Point

Complex line

Complex plane

Complex realm

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Complex projective space

Point pair

Complex projective line

Complex projective plane

Complex projective realm

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Quaternionic space

Point

Quaternionic line

Quaternionic plane

Quaternionic realm

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Quaternionic projective space

Point pair

Quaternionic projective line

Quaternionic projective plane

Quaternionic projective realm

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Octonionic space

Point

Octonionic line

Octonionic plane

Octonionic realm

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Octonionic projective space

Point pair

Octonionic projective line

Octonionic projective plane

Octonionic projective realm

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