Lebesgue Minimal Problem
Find the plane Lamina of least Area 
which is capable of covering any plane figure of unit GeneralDiameter. A Unit Circle is too small, but a Hexagon circumscribed on the UnitCircle is too large. More specifically, the Area is bounded by
(Pal 1920).See also Area, Borsuk's Conjecture, Diameter (General), Kakeya Needle Problem
References
Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, p. 99, 1987. Coxeter, H. S. M. ``Lebesgue's Minimal Problem.'' Eureka 21, 13, 1958. Grünbaum, B. ``Borsuk's Problem and Related Questions.'' Proc. Sympos. Pure Math, Vol. 7. Providence, RI: Amer. Math. Soc., pp. 271-284, 1963. Kakeya, S. ``Some Problems on Maxima and Minima Regarding Ovals.'' Sci. Reports Tôhoku Imperial Univ., Ser. 1 (Math., Phys., Chem.) 6, 71-88, 1917. Ogilvy, C. S. Excursions in Geometry. New York: Dover, pp. 142-144, 1990. Pál, J. ``Ueber ein elementares Variationsproblem.'' Det Kgl. Danske videnkabernes selskab, Math.-fys. meddelelser 3, Nr. 2, 1-35, 1920. Yaglom, I. M. and Boltyanskii, V. G. Convex Figures. New York: Holt, Rinehart, & Winston, pp. 18 and 100, 1961.
- Reflexive Closure
- Reflexive Graph
- Reflexive Reduction
- Reflexive Relation
- Reflexivity
- Region
- Regression
- Regression Coefficient
- Regula Falsi
- Regular Function
- Regular Graph
- Regular Isotopy
- Regular Isotopy Invariant
- Regularity Theorem
- Regularized Beta Function
- Regularized Gamma Function
- Regular Local Ring
- Regular Number
- Regular Parameterization
- Regular Patch
- Regular Point
- Regular Polygon
- Regular Polyhedron
- Regular Prime
- Regular Ring