Zhao Youqin (1271~1335) was a Chinese astronomer, mathematician, and Daoist who calculated the value of π, constructed astronomical instruments, conducted experiments with a camera obscura, and compiled an influential astronomical compendium.

赵友钦(1271~1335 )，天文学家、数学家、道士。赵友钦算出了圆周率的值，建造了天文仪器，做了小孔成像实验并编了一本有影响的天文学纲要。

Zhao was one of the patriarchs of the northern branch of the Quanzhen ("Complete Perfection") sect of Daoism.

赵友钦是全真教北宗掌门人之一。

His astronomical treatise Gexiang xinshu ("New Writing on the Symbol of Alteration") presents his cosmological theory featurfing a flat Earth inside a spherical Heaven, his explanation of the lunar and solar eclipses, and his experiments with a camera obscura to establish the relationship between the luminosity of an image of a source of light and the distance of the source from the pinhole.

赵友钦的天文学论文《革象新书》展示了他的宇宙理论(他认为天圆地方)、他对日月食的解释以及确定光源与小孔的距离与所成之像的亮度之间的关系的试验。

The book also describes his methods of remote surveying with gnomons to measure the distance from the Earth to the Sun, the Moon, and the stars, as well as his procedure for evaluating π using inscribed regular polygons of 4, 8, …, 16,384 sides.

这本书还描述了赵友钦用日晷测量地球与太阳、月亮和星星之间的距离的方法以及使用正多边形估算圆周率的程序。

Following Liu Hui(flourished c. 263), this is the second extant Chinese procedure for the evaluation of π.

这是刘徽之后，我国现存的第二个估算圆周率的程序。

Zhao stated that his goal was to confirm the value 355 / 113 obtained by Zu Chongzhi (429~500), yet his calculations may have allowed him to prove the validity of the better evaluation 3.1415926<π<3. 1415927, also obtained by Zu.

赵友钦说他的目标是确证祖冲之的355/113，但是他的计算却证明祖冲之估算的另一个值3. 1415926 < π <3.1415927是正确的。

The second extant book of Zhao, Xian Fo tongyuan ("On the Common Origins of [the Teachings of] Transcendentals and Buddhas"), is devoted to the so-called "Inner Alchemy," an esoteric discipline focusing on the attainment of immortality via respiratory and meditative practices.

赵友钦现存的第二本书是《仙佛同源》。这是一本“内丹”名著。内丹是一个抽象的学科，它集中处理通过呼吸和冥想练习达到长生不老的问题。

He designed several astronomical instruments; he used one of these to measure the difference in right ascension between two celestial bodies and another one to find the angular distance from the celestial north pole to a given star.

赵友钦设计了一些天文仪器;他用其中一个仪器测量两个天体的赤经差，用另一个仪器测北极与某颗星的角距离。