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Projective plane

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In mathematics, a projective plane is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect at a single point, but there are some pairs of lines that do not intersect. A projective plane can be thought of as an ordinary plane equipped with additional "points at infinity" where parallel lines intersect. Thus any two distinct lines in a projective plane intersect at exactly one point.

These parallel lines appear to intersect in the vanishing point "at infinity". In a projective plane this is actually true.

Topology

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Topology is the part of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself.

Möbius strips, which have only one surface and one edge, are a kind of object studied in topology.

A continuous transformation can turn a coffee mug into a donut. Ceramic model by Keenan Crane and Henry Segerman.