Search results
Results From The WOW.Com Content Network
The Euler characteristic can be defined for connected plane graphs by the same + formula as for polyhedral surfaces, where F is the number of faces in the graph, including the exterior face. The Euler characteristic of any plane connected graph G is 2.
It has Euler characteristic 1, hence a demigenus (non-orientable genus, Euler genus) of 1. The topological real projective plane can be constructed by taking the (single) edge of a Möbius strip and gluing it to itself in the correct direction, or by gluing the edge to a disk. Alternately, the real projective plane can be constructed by ...
Formally, a complex projective space is the space of complex lines through the origin of an (n+1)-dimensional complex vector space. The space is denoted variously as P(C n+1), P n (C) or CP n. When n = 1, the complex projective space CP 1 is the Riemann sphere, and when n = 2, CP 2 is the complex projective plane (see there for a more ...
Euler's formula states that if a finite, connected, planar graph is drawn in the plane without any edge intersections, and v is the number of vertices, e is the number of edges and f is the number of faces (regions bounded by edges, including the outer, infinitely large region), then
Alternatively, it can be defined for a closed surface in terms of the Euler characteristic χ, via the relationship χ = 2 − k, where k is the non-orientable genus. For instance: A real projective plane has a non-orientable genus 1. A Klein bottle has non-orientable genus 2.
The Euler characteristic of the real projective plane is 1, and in general the Euler characteristic of the connected sum of k of them is 2 − k. It follows that a closed surface is determined, up to homeomorphism, by two pieces of information: its Euler characteristic, and whether it is orientable or not.
The Euler characteristic of the real projective plane is 1, and in general the Euler characteristic of the connected sum of k of them is 2 − k. Teichmüller space
The projective plane over K, denoted PG(2, K) or KP 2, has a set of points consisting of all the 1-dimensional subspaces in K 3. A subset L of the points of PG(2, K) is a line in PG(2, K) if there exists a 2-dimensional subspace of K 3 whose set of 1-dimensional subspaces is exactly L.