Introduction E9F5FC

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Correspondences

• Full line to circle. Infinity as distinguished point on the circle.
• Full line to infinite copies of a rolling circle. Periodic.

Transformations

• https://en.m.wikipedia.org/wiki/Linear_fractional_transformation
• https://en.m.wikipedia.org/wiki/Homography#Over_a_ring
• https://en.m.wikipedia.org/wiki/Gnomonic_projection

Geometries

• https://en.m.wikipedia.org/wiki/Real_projective_line
• https://en.m.wikipedia.org/wiki/Projective_space

Affine geometry

Rn

affine spaces are open subspaces of projective spaces, which are quotients of vector spaces.

Projective geometry

Rn + Rn-1 + ... + R0 difference is geometry

half sphere

vector space

zero

zero and infinity are balanced

lines in P2 or more generally hyperplanes in Pn always do intersect

Conformal geometry

Infinity is represented by the z axis which is perpendicular to the represented plane.