  The writhe of a space curve fragment is considered for various boundary
conditions. An expression for the writhe as a function of arclength for an
arbitrary space curve is obtained. The formula is built on the base of closing
the tangent indicatrix with a geodesic. The corresponding closure of a curve in
3-space is explicitly constructed. The addition rule for writhe is formulated.
A relationship connecting the writhe with the Gauss integral over the open
curve is presented. The single and double regular helical shapes are examined
as examples.
