Configurations of Multiple Skew Lines
A configuration of skew lines is a set of lines in which all pairs are skew. Two configurations are said to be isotopic if it is possible to continuously transform one configuration into the other, maintaining throughout the transformation the invariant that all pairs of lines remain skew. Any two configurations of two lines are easily seen to be isotopic, and configurations of the same number of lines in dimensions higher than three are always isotopic, but there exist multiple non-isotopic configurations of three or more lines in three dimensions (Viro & Viro 1990). The number of nonisotopic configurations of n lines in R3, starting at n = 1, is
- 1, 1, 2, 3, 7, 19, 74, ... (sequence A110887 in OEIS).
Read more about this topic: Skew Lines
Famous quotes containing the words multiple and/or lines:
“There is a continual exchange of ideas between all minds of a generation. Journalists, popular novelists, illustrators, and cartoonists adapt the truths discovered by the powerful intellects for the multitude. It is like a spiritual flood, like a gush that pours into multiple cascades until it forms the great moving sheet of water that stands for the mentality of a period.”
—Auguste Rodin (1849–1917)
“Child of Light! thy limbs are burning
Through the vest which seems to hide them;
As the radiant lines of morning
Through the clouds ere they divide them;
And this atmosphere divinest
Shrouds thee wheresoe’er thou shinest.”
—Percy Bysshe Shelley (1792–1822)