On the Lassak Conjecture for a Convex Body
Abstract
In 1993 M. Lassak formulated (in the equivalent form) the following conjecture. If we can inscribe a translate of the cube $[0,1]^n$ into a convex body $C \subset R^n$, then $\sum_{i=1}^n \frac{1}{\omega_i} \geq 1$. Here $\omega_i$ denotes the width of $C$ in the direction of the ith coordinate axis. The paper contains a new proof of this statement for n = 2. Also we show that if a translate of $[0,1]^n$ can be inscribed into the n-dimensional simplex, then for this simplex holds $\sum_{i=1}^n \frac{1}{\omega_i} = 1$.
About the Author
M. V. Nevskii
Ярославский государственный университет им. П.Г. Демидова
Russian Federation
Russian Federation
References
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Review
For citations:
Nevskii M.V. On the Lassak Conjecture for a Convex Body. Modeling and Analysis of Information Systems. 2011;18(3):5-11. (In Russ.)
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