The study of the probabilities involved in geometric problems, e.g., the distributions of length, area, volume, etc. for geometric objects under stated conditions.
The following table summarized known results for picking geometric objects from points in or on the boundary of other geometric objects, where is the Robbins constant.
type of selection | quantity | mean | distribution known? | point probability known? |
line line picking | length | yes | - | |
isosceles triangle line picking | length | - | ||
equilateral triangle line picking | length | - | ||
square line picking | length | yes | - | |
circle line picking | length | yes | - | |
disk line picking | length | yes | - | |
tetrahedron line picking | length | ? | - | |
cube line picking | length | yes | - | |
triangle triangle picking | area | |||
square triangle picking | area | yes | yes | |
pentagon triangle picking | area | |||
hexagon triangle picking | area | |||
circle triangle picking | area | |||
disk triangle picking | area | |||
tetrahedron triangle picking | area | ? | - | |
cube triangle picking | area | ? | - | |
ball triangle picking | area | - | ||
sphere triangle picking | area | ? | - | |
tetrahedron tetrahedron picking | volume | |||
cube tetrahedron picking | volume | |||
ball tetrahedron picking | volume | |||
sphere tetrahedron picking | volume | |||
octahedron tetrahedron picking | volume | ? |