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.
- Improper Integral
- Improper Node
- Improper Rotation
- Impulse Pair
- Impulse Symbol
- Inaccessible Cardinal
- Inaccessible Cardinals Axiom
- Inadmissible
- In-and-Out Curve
- Incenter
- Incenter-Excenter Circle
- Incidence Axioms
- Incidence Matrix
- Incident
- Incircle
- Inclusion-Exclusion Principle
- Inclusion Map
- Incommensurate
- Incomplete Gamma Function
- Incompleteness
- Increasing Function
- Increasing Sequence
- Indefinite Integral
- Indefinite Quadratic Form
- Indegree