The mean line segment length 
is the average length of a line
segment in line segment picking within
some given shape. As summarized in the following table (where 
denotes the Robbins
constant and 
its generalization to dimension 
), it is possible to compute the mean line segment length in
closed form for line segment picking for some
simple shapes.
| shape |  | normalization | reference |
| (3,4,5) triangle line picking |  | edge lengths 3, 4, 5 | E. Weisstein (Aug. 6-9, 2010), A. G. Murray (Apr. 4, 2020) |
| 30-60-90 triangle line picking |  | unit hypotenuse | E. Weisstein, M. Trott, A. Strzebonski (Aug. 25, 2010), A. G. Murray (Apr. 4, 2020) |
| ball line picking |  | unit radius | |
| circle line picking |  | unit radius | |
| cube line picking |  (Robbins constant) | unit volume (= unit edge length) | Robbins (1978), Bailey et al. (2007) |
| disk line picking |  | unit radius | |
| equilateral triangle line picking |  | unit edge length | E. Weisstein (Mar. 16, 2004), A. G. Murray (Apr. 4, 2020) |
| hypercube line picking |  | unit edge length | Bailey et al. (2007) |
| isosceles right triangle line picking |  | edges lengths 1, 1,  | M. Trott (Mar. 10, 2004), A. G. Murray (Apr. 4, 2020) |
| line line picking |  | unit segment length | |
| sphere line picking |  | unit radius | Solomon (1978, p. 163) |
| square line picking |  | unit edge length | |
| tetrahedron line picking |  | unit edge length | Beck (2023) |
In some cases, a closed form can also be obtained for the probability density function of line segment lengths.
Beck (2023) found closed forms for the mean line segment lengths for all five Platonic solids.
