Zhào Yǒuqīn 趙友欽
Style name Zǐgōng 子恭, sobriquet Yuándūzǐ 緣督子 — known to his contemporaries as Yuándū xiānshēng 緣督先生 (Master Yuándū). Sòng Lián’s 宋濂 preface gives his personal name variously as Jìng 敬 or Yǒuqīn 友欽. Native of Pòyáng 鄱陽 (in modern Jiāngxī), tenth-generation descendant of Zhào Yuánzuǒ 趙元佐, Prince of Hàn of the Northern Sòng — and thus a member of the Sòng imperial clan in Yuán-period diaspora. Astronomer, mathematician, optical experimenter, and Daoist priest of the Quánzhēn 全真 school, in which he became a patriarch; in 1329 he ordained Chén Zhìxū 陳致虛 (the Shàngyángzǐ 上陽子) as his successor.
He withdrew from worldly life early, retired for ten years on the East Sea coast, and devoted himself to the Zhōuyì (compiling tens of thousands of words of commentary, since lost), to alchemy (Jīndān zhènglǐ 金丹正理, Yuándūzǐ xiānfó tóngyuán lùn 緣督子仙佛同源論, Sānjiào yīyuán 三教一源 — all lost), to calendrical computation (Tuībù lìchéng 推步立成 — lost), and to the synthesis-and-experimental treatise Géxiàng xīnshū 革象新書 — the only work that survives. The Géxiàng xīnshū contains his celebrated camera-obscura (“pinhole image”) experiment using two arrays of candles and a perforated board: he documented systematically that aperture size, source intensity, and screen distance govern image brightness independently of aperture shape — the earliest experimental optics in Chinese science. He also computed an improved value of π by the method of inscribed regular polygons (the same Liú-Huī-style method, but pushed to higher orders).
Two parallel transmissions of the Géxiàng xīnshū survive: the original 5-juan recension passed through his disciple Zhū Huī 朱暉 to Zhāng Rùn 章濬, who obtained a preface from Sòng Lián 宋濂 and printed it (KR3f0005); and Wáng Yī 王禕’s 2-juan early-Míng abridgment (KR3f0004). Both were included in the Sìkù quánshū under the precedent of the Xīn / Jiù Tángshū (parallel admission of two recensions of one work).