论文标题
平面中重复角度的角度，具有代数切线的角度
Repeated Angles in the Plane for Angles with Algebraic Tangents
论文作者
论文摘要
我们用$ω（n^2 \ log n）构建一组点，每当$ \ tan（θ）$都在$ \ mathbb {q} $上，确定一个角度$θ$，与Pach和Sharir的上限匹配。这在原始结构上有所改善，仅适用于$ \ tan（θ）= a \ sqrt {m}/b $，带有$ a，b，m $阳性整数。
We construct a set of points with $Ω(n^2\log n)$ triples determining an angle $θ$ whenever $\tan(θ)$ is algebraic over $\mathbb{Q}$, matching the upper bound of Pach and Sharir. This improves upon the original construction, which was optimal only for $\tan(θ)=a\sqrt{m}/b$ with $a,b,m$ positive integers.
