al-Risālah al-Muḥīṭiyyah

Title (arabic)

الرسالة المحيطيّة

Title (translit)

al-Risālah al-Muḥīṭiyyah










A treatise on the circumference that determines the parameters of successively inscribed and circumscribed polygons inside and around a circle, in order to calculate the value of Pi to 16 decimal fractional units. Kāšī's calculations are performed in sexagesimal numberation for a circle with a radius of 60. The results are expressed in sexagesimal and decimal fractions.



Literature References

İhsanoğlu, Ekmeleddin, and Boris Rozenfeld. 2003. Mathematicians, Astronomers And Other Scholars Of Islamic Civilisation And Their Works (7Th-19Th C.). Istanbul: Research Centre for Islamic History, Art, and Culture.

P. 270 (no. 802), M3.

Saliba, George. 2012. “Kāši, Ḡiāṯ-Al-Din”. In Encyclopaedia Iranica, 64-67. New York: Encyclopaedia Iranica Foundation, Inc.
Dena: Fihristwāra-Yi Dastniwishthā-Yi Īrān. 2010. 12 vol.. Tehran: Muṣṭafā Dirāyatī.

9:197. There are 7 witnesses listed for this work in repositories in Mashhad, Shiraz, and Tehran.

Luckey, Paul L. 1953. Der Lehrbrief Über Den Kreisumfang (Ar-Risāla Al-Muhītīya) [Jamshīd Ibn Masʻūd Al-Kāshī]. Abhandlungen Der Deutschen Akademie Der Wissenschaften Zu Berlin. Klasse Für Mathematik Und Allgemeine Naturwissenschaften. Jahrgang 1950 Nor. 6. Berlin: Akademie-Verlag.

German translation.

Azarian, Mohammad K. 2010. “Al-Risāla Al-Muhītīyya: A Summary”. Missouri Journal Of Mathematical Sciences 22 (2): 64-85.
al-Kāshī, Jamshīd ibn Mas‘ūd. 2013. A Facsimile Edition Of The Autograph Manuscript (Ms 5389, Holy Shrine Library, Mashhad, Iran). Tehran: Mīrāth Maktūb.
Youschkevitch, A. P., and B. A. Rosenfeld. 1973. “Al-Kāshī”. In Dictionary Of Scientific Biography, 7:255-62. New York: Charles Scribner's Sons.
Hogendijk, Jan P. 2009. “Al-Kāshī's Determination Of Pi To 16 Decimals In An Old Manuscript”. Zeitschrift Für Geschichte Der Arabisch-Islamischen Wissenschaften 19.