# 矢 (幾何)

## 公式

${\displaystyle r^{2}=\left({\tfrac {1}{2}}l\right)^{2}+\left(r-s\right)^{2}.}$

{\displaystyle {\begin{aligned}s&=r-{\sqrt {r^{2}-{\tfrac {1}{4}}l^{2}}},\\[10mu]l&=2{\sqrt {2rs-s^{2}}},\\[5px]r&={\frac {s^{2}+{\tfrac {1}{4}}l^{2}}{2s}}={\frac {s}{2}}+{\frac {l^{2}}{8s}}.\end{aligned}}}

${\displaystyle s=r\operatorname {versin} \theta =r\left(1-\cos \theta \right)=2r\sin ^{2}{\frac {\theta }{2}}.}$

## 近似值

${\displaystyle s\approx {\frac {l^{2}}{8r}}.}$

${\displaystyle a\approx l+{\frac {2s^{2}}{r}}\approx l+{\frac {8s^{2}}{3l}},}$

## 參考文獻

1. ^ Shaneyfelt, Ted V. 德博士的 Notes About Circles, ज्य, & कोज्य: What in the world is a hacovercosine?. Hilo, Hawaii: University of Hawaii. [2015-11-08]. （原始内容存档于2015-09-19）.
2. ^ 弓形高. Yahoo奇摩字典. [2023-12-28]. （原始内容存档于2023-12-28）.
3. Woodward, Ernest. Geometry - Plane, Solid & Analytic Problem Solver. Problem Solvers Solution Guides. Research & Education Association (REA). December 1978: 359. ISBN 978-0-87891-510-1.
4. ^ van Brummelen, Glen Robert. Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry. Princeton University Press. 2013 [2015-11-10]. ISBN 9780691148922. 0691148929.
5. ^ sagitta. 牛津英語詞典 (第三版). 牛津大學出版社. 2005-09 （英语）.
6. ^