We show an upper bound of $\frac{ \sin\left(\frac{3\pi}{10}\right) }{ \sin\left(\frac{2\pi}{5}\right)-\sin\left(\frac{3\pi}{10}\right) } <5.70$ on the spanning ratio of $\Theta_5$-graphs, improving on the previous best known upper bound of $9.96$ [Bose, Morin, van Renssen, and Verdonschot. The Theta-5-graph is a spanner. Computational Geometry, 2015.]

翻译：我们显示$\frac{ \ sin\ left (\ frac{ 3\ pi} 10\\\ right)\\ sin\ left (\ frac{ 2\ pi} 5\\ right)\ sin\ left (\ frac{ 3\ pi} 10\\\\ right) <5. 70$ 的上括号, 在 $\ Theta_ 5 graphy 的宽度比例上显示, 上括号为 $9. 96 美元上括号上下有改进 [Bose, Morin, van Renssen, 和 Verdonschot]。 Theta-5 graph is a spanner. computational 几何方法, 2015]