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In Euclidean 3-space, a regulus is a set of skew lines, R, such that through each point on each line of R, there passes a transversal of R and through each point of a transversal of R there passes a line of R. The set of transversals of a regulus R is also a regulus, called the opposite regulus, R o. In this space, three mutually skew lines can ...
Menelaus's theorem, case 1: line DEF passes inside triangle ABC. In Euclidean geometry, Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle ABC, and a transversal line that crosses BC, AC, AB at points D, E, F respectively, with D, E, F distinct from A, B, C. A ...
Vertex cover in hypergraphs (also known as: transversal); Line graph of a hypergraph ; Hypergraph grammar - created by augmenting a class of hypergraphs with a set of replacement rules;
Transversal plane theorem for planes: Planes intersected by a transversal plane are parallel if and only if their alternate interior dihedral angles are congruent. Transversal line containment theorem: If a transversal line is contained in any plane other than the plane containing all the lines, then the plane is a transversal plane.
An intersection point between two arcs is transverse if and only if it is not a tangency, i.e., their tangent lines inside the tangent plane to the surface are distinct. In a three-dimensional space, two curves can be transverse only when they have empty intersection, since their tangent spaces could generate at most a two-dimensional space.
a) different tangent lines (transversal intersection, after transversality), or b) the tangent line in common and they are crossing each other ( touching intersection , after tangency ). If both the curves have a point S and the tangent line there in common but do not cross each other, they are just touching at point S .
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