TEXT

al-Risālat al-Muḥīṭiyyah

Title (arabic)

الرسالة المحيطيّة

Title (translit)

al-Risālat al-Muḥīṭiyyah

Alias

al-Muḥīṭiyya

Author

Created

827H/1424J

Language

Arabic

Subject

Notes

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.

ismi_id

499858

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.