Some Solutions for Some of Najm al-Dawla’s Propositions in his Usūl Awāʾil Hindisa wa ʿAmalīyāt Ān, Drawing of Regular Polygons and their Application in Tile and Architecture

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Najm al-Dawla in his Usūl Awāʾil Hindisa wa ʿAmalīyāt Ān (Principles of Elementary Geometry and its Operation), Chapter Three, has divided a circle into a number of unproven issues and has come up with simple and innovative ways to draw them. In this paper, the problems are proven and their application in tile and architecture was explained. 1. Divide circle environment into 7, 14 and 15 equal parts; 2. Divide the circle into 5, 8, 10, 11 and 16 equal parts; 3. Divide circle environment into 9, 13 and 19 equal parts; 4. Divide circle environment into 17 equal parts; 5. Divide the circle into n equal parts; 6. Calculate the area of a lagoon, which there is no accessible to its inside; 7. Drawing an egg

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نجم الدوله، عبدالغفار. (1317ق). اصول اوائل هندسه، تهران، دارالخلافه تهران، چاپ اول.
آقایانی چاووشی، جعفر. (1384ش). «مقایسۀ روش‌های ابوالوفای بوزجانی، لئوناردو داوینچی و آلبرش دورر در ترسیم پنج ضعلی منتظم». آینۀ میراث، دورۀ جدید، سال سوم، بهار، پیاپی 28، ص1-21.
ـــــــــــــــــ . (1385ش)، «مقایسۀ روش‌های ابوالوفای بوزجانی و ابوریحان بیرونی در ترسیم نه ضلعی منتظم». آینۀ میراث، دورۀ جدید، سال چهارم، شمارۀ چهارم، زمستان، پیاپی 35، ص5-23.

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