论文标题
平行四边形与其他相互规则的偶数之间的Banach-Mazur距离
Banach-Mazur distances between parallelograms and other affinely regular even-gons
论文作者
论文摘要
我们表明，平行四边形和仿射期限六角形之间的Banach-Mazur距离为$ \ frac {3} {2} $，我们得出的结论是，中央对称平面凸形体的直径只是$ \ frac {3} {2} $。这一事实的证明似乎并未较早出版。阿斯普伦德（Asplund）在他的论文中没有证明这一点，证明了任何平面对称物体的Banach-Mazur距离最多是$ \ frac {3} {2} $。类似地，我们处理平行四边形和剩余元素规则均匀的偶数之间的Banach-Mazur距离。
We show that the Banach-Mazur distance between the parallelogram and the affine-regular hexagon is $\frac{3}{2}$ and we conclude that the diameter of the family of centrally-symmetric planar convex bodies is just $\frac{3}{2}$. A proof of this fact does not seem to be published earlier. Asplund announced this without a proof in his paper proving that the Banach-Mazur distance of any planar centrally-symmetric bodies is at most $\frac{3}{2}$. Analogously, we deal with the Banach-Mazur distances between the parallelogram and the remaining affine-regular even-gons.
