Shephard's Problem
Measurements of a centered convex body in Euclidean 
-space (for 
) show that its brightness function (thevolume of each projection) is smaller than that of another such body. Is it true that its Volume is also smaller? C. M. Petty and R. Schneider showed in 1967 that the answer is yes if the body with the larger brightness function is aprojection body, but no in general for every .
References
Gardner, R. J. ``Geometric Tomography.'' Not. Amer. Math. Soc. 42, 422-429, 1995.
- Janko Groups
- Japanese Triangulation Theorem
- Jarnick's Inequality
- j-Conductor
- Jeep Problem
- Jenkins-Traub Method
- Jensen Polynomial
- Jensen's Formula
- Jensen's Inequality
- Jerabek's Hyperbola
- Jerk
- j-Function
- Jinc Function
- j-Invariant
- Jitter
- Joachimsthal's Equation
- Johnson Circle
- Johnson's Equation
- Johnson Solid
- Johnson's Theorem
- Join (Graph)
- Join (Spaces)
- Joint Distribution Function
- Joint Probability Density Function
- Joint Theorem