Kakeya tube ($|T_{\delta }|{\asymp }_n{\delta }^{n-1}$)

A Kakeya tube is a neighborhood of transverse radius $\delta$ of a line segment of fixed unit length. Round cross-sections and comparable rectangular cross-sections are interchangeable up to fixed constants. The tube has Lebesgue measure comparable to ${\delta }^{n-1}$ in ${\mathbb{R}}^n$.