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Skew Lines: Solid Geometry, Parallel (Geometry), Coplanar, Degeneracy (Mathematics), Dimension, Regular Tetrahedron -

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2026-03-17
109,28 € 182,14 €

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High Quality Content by WIKIPEDIA articles! If each line in a pair of skew lines is defined by two points, then these four points must not be coplanar, so they must be the vertices of a tetrahedron of nonzero volume; conversely, any two pairs of points defining a tetrahedron of nonzero volume also define a pair of skew lines. Therefore, a test of whether two pairs of points (a,b) and (c,d) define skew lines ... Täielik kirjeldus

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High Quality Content by WIKIPEDIA articles! If each line in a pair of skew lines is defined by two points, then these four points must not be coplanar, so they must be the vertices of a tetrahedron of nonzero volume; conversely, any two pairs of points defining a tetrahedron of nonzero volume also define a pair of skew lines. Therefore, a test of whether two pairs of points (a,b) and (c,d) define skew lines is to apply the formula for the volume of a tetrahedron, V = (1/6)·|det(a¿b, b¿c, c¿d)|, and testing whether the result is nonzero. If four points are chosen at random within a unit cube, they will almost surely define a pair of skew lines, because (after the first three points have been chosen) the fourth point will define a non-skew line if, and only if, it is coplanar with the first three points, and the plane through the first three points forms a subset of measure zero of the cube.

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Kirjastaja OmniScriptum
Väljalaskeaasta 2026
Kaanetüüp Pehme kaanega
EAN 9786131165283
Kirjuta oma arvustus
Te vaatate: Skew Lines: Solid Geometry, Parallel (Geometry), Coplanar, Degeneracy (Mathematics), Dimension, Regular Tetrahedron
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109,28 € 182,14 €