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  2. Beltrami–Klein model - Wikipedia

    en.wikipedia.org/wiki/Beltrami–Klein_model

    Many hyperbolic lines through point P not intersecting line a in the Beltrami Klein model A hyperbolic triheptagonal tiling in a Beltrami–Klein model projection. In geometry, the Beltrami–Klein model, also called the projective model, Klein disk model, and the Cayley–Klein model, is a model of hyperbolic geometry in which points are represented by the points in the interior of the unit ...

  3. Vertex (geometry) - Wikipedia

    en.wikipedia.org/wiki/Vertex_(geometry)

    In geometry, a vertex (pl.: vertices or vertexes) is a point where two or more curves, lines, or edges meet or intersect. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices. [1] [2] [3]

  4. Power of a point - Wikipedia

    en.wikipedia.org/wiki/Power_of_a_point

    Secant-, chord-theorem. For the intersecting secants theorem and chord theorem the power of a point plays the role of an invariant: . Intersecting secants theorem: For a point outside a circle and the intersection points , of a secant line with the following statement is true: | | | | = (), hence the product is independent of line .

  5. Intersection (geometry) - Wikipedia

    en.wikipedia.org/wiki/Intersection_(geometry)

    A transversal intersection of two curves touching intersection (left), touching (right) Two curves in R 2 {\displaystyle \mathbb {R} ^{2}} (two-dimensional space), which are continuously differentiable (i.e. there is no sharp bend), have an intersection point, if they have a point of the plane in common and have at this point (see diagram):

  6. Line-cylinder intersection - Wikipedia

    en.wikipedia.org/wiki/Line-cylinder_intersection

    Cyan line has a single point of intersection. Green line has two intersections. Yellow line lies tangent to the cylinder, so has infinitely many points of intersection. Line-cylinder intersection is the calculation of any points of intersection, given an analytic geometry description of a line and a cylinder in 3d space.

  7. Projective plane - Wikipedia

    en.wikipedia.org/wiki/Projective_plane

    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. Renaissance artists, in developing the techniques of drawing in perspective, laid the groundwork for this mathematical topic.

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