Conversely, any set of non-orthogonal equiangular lines in a euclidean space can give rise to a two-graph ( see equiangular lines for the construction ).
32.
In contrast, the regular pentagon is unique up to similarity, because it is equilateral and, moreover, it is equiangular ( its five angles are equal ).
33.
Indeed, intersecting such a system of equiangular lines with a Euclidean sphere centered at their common intersection yields the twelve vertices of a regular icosahedron as can easily be checked.
34.
Computing the maximum number of equiangular lines in " n "-dimensional Euclidean space is a difficult problem, and unsolved in general, though bounds are known.
35.
In contrast, the regular pentagon is unique, because it is equilateral and moreover it is equiangular ( its five angles are equal; the measure is 108 degrees ).
36.
A rectangle ( equiangular quadrilateral ) with integer side lengths may be tiled by unit squares, and an equiangular hexagon with integer side lengths may be tiled by unit equilateral triangles.
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A rectangle ( equiangular quadrilateral ) with integer side lengths may be tiled by unit squares, and an equiangular hexagon with integer side lengths may be tiled by unit equilateral triangles.
38.
The algorithm is similar to forward stepwise regression, but instead of including variables at each step, the estimated parameters are increased in a direction equiangular to each one's correlations with the residual.
39.
So this Welch bound is met with equality if and only if the set of vectors \ { x _ i \ } is an equiangular tight frame in \ mathbb { C } ^ n.
40.
The maximal number of equiangular lines in 2-dimensional Euclidean space is 3 : we can take the lines through opposite vertices of a regular hexagon, each at an angle 120 degrees from the other two.
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