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A transversal that cuts two parallel lines at right angles is called a perpendicular transversal. In this case, all 8 angles are right angles [1] When the lines are parallel, a case that is often considered, a transversal produces several congruent supplementary angles. Some of these angle pairs have specific names and are discussed below ...
In mathematics, transversality is a notion that describes how spaces can intersect; transversality can be seen as the "opposite" of tangency, and plays a role in general position. It formalizes the idea of a generic intersection in differential topology. It is defined by considering the linearizations of the intersecting spaces at the points of ...
An independent transversal (also called a rainbow-independent set or independent system of representatives) is a transversal which is also an independent set of a given graph. To explain the difference in figurative terms, consider a faculty with m departments, where the faculty dean wants to construct a committee of m members, one member per ...
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.
A transversal in a Latin square is a choice of n cells, where each row contains one cell, each column contains one cell, and there is one cell containing each symbol. One can consider a Latin square as a complete bipartite graph in which the rows are vertices of one part, the columns are vertices of the other part, each cell is an edge (between ...
The following example, due to Marshall Hall Jr., shows that the marriage condition will not guarantee the existence of a transversal in an infinite family in which infinite sets are allowed. Let F {\displaystyle {\mathcal {F}}} be the family, A 0 = N {\displaystyle A_{0}=\mathbb {N} } , A i = { i − 1 } {\displaystyle A_{i}=\{i-1\}} for i ≥ ...
The corresponding angles formed by a transversal property, used by W. D. Cooley in his 1860 text, The Elements of Geometry, simplified and explained requires a proof of the fact that if one transversal meets a pair of lines in congruent corresponding angles then all transversals must do so. Again, a new axiom is needed to justify this statement.
A transversal in a Latin square of order n is a set S of n cells such that every row and every column contains exactly one cell of S, and such that the symbols in S form {1, ..., n}. Let T(n) be the maximum number of transversals in a Latin square of order n. Estimate T(n). Proposed: by Ian Wanless at Loops '03, Prague 2003
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