On the shortest distance between consecutive straight lines

Joseph Lipke
1907 Bulletin of the American Mathematical Society  
CERTAIN well-known geometric results concerning space curves and surfaces have been obtained by a discussion of the shortest distance between consecutive positions of a straight line moving continuously in space. These results have been gained by a discussion (recapitulated in §1) of the numerator of the expression for the shortest distance.* It is the purpose of this paper to complete the discussion by examining ( § § 2-3) the denominator of the distance expression, placing special emphasis
more » ... n the conditions that the distance be an infinitesimal of the second order, and upon a geometric interpretation of this case. § 1. Brief Discussion of the Numerator, The equations of the straight line are
doi:10.1090/s0002-9904-1907-01505-7 fatcat:zghr6hf2ubcqtdxucwi2kvoumi