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Addressing a question of De Bruijn and Erd\\H{o}s, we define a family of sequences for which the asymptotic least upper bound of this ratio, \\[ \\mu_r(\\boldsymbol{a}) \\;=\\; \\limsup_{n\\to\\infty}\\mu^r_n(\\boldsymbol{a}) , \\] can easily be calculated. 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The first $n$ of these points cuts the circle into $n$ pieces. For any given $r$, let $\\mu^r_n(\\boldsymbol{a})$ be the ratio between the maximum and minimum sizes of $r$ consecutive pieces. Addressing a question of De Bruijn and Erd\\H{o}s, we define a family of sequences for which the asymptotic least upper bound of this ratio, \\[ \\mu_r(\\boldsymbol{a}) \\;=\\; \\limsup_{n\\to\\infty}\\mu^r_n(\\boldsymbol{a}) , \\] can easily be calculated. 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