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:
“Creativity seems to emerge from multiple experiences, coupled with a well-supported development of personal resources, including a sense of freedom to venture beyond the known.”
—Loris Malaguzzi (20th century)
“... when I awake in the middle of the night, since I knew not where I was, I did not even know at first who I was; I only had in the first simplicity the feeling of existing as it must quiver in an animal.... I spent one second above the centuries of civilization, and the confused glimpse of the gas lamps, then of the shirts with turned-down collars, recomposed, little by little, the original lines of my self.”
—Marcel Proust (1871–1922)