Semerkand Astronomi ve Matematik Ekolünün Osmanl 'ya Etkisi: Ulu Bey'in Sinüs 1ºyi Yakla k Belirleme Yöntemi (2013)
Bir, Atilla (Author)
Kaçar, Mustafa (Author)
Osmanli Bilimi Arastirmalari: Studies in Ottoman Science
Volume: 14, no. 2
Issue: 2
Pages: 48-66
Edition Details: Translated title: [The influence of the Samarkand school of astronomy and mathematics on the Ottomans: Ulugh Beg's approximate method of calculating sinus 1º]
Language: Turkish
In his Zij, Ulugh Beg (1393-1449) pointed to the importance of calculating the exact value of sin 1º which is needed for the calculation of the sine and tangent tables. He says that nobody before him has given its exact value and that he has written a treatise accounting for his calculation of sinus 1ºand the above mentioned tables. The work Ulugh Beg referred is the Treatise for determining the sine of 1º by Ghiy th al-D n al-K sh 's method. In the present article, we investigate how Ulugh Beg derived sin 1º and compared his result with the one given by Ptolemeus. Ulugh Beg derived sin 1º value from the geometrically known cords of the (1 - 1/16)º, (1 + 2/16)º and (1 - 4/16)º = 45 angles. The approximate value he calculated is sin 1º@1P 2 49 43(3) 13(4) 5(5) 30(6)@ 0,0174524 1/4 expressed in sexagesimal system.This value is much better than the Ptolemeus' value, who used two times the half formulas for sin 3º and then took the average value of sin (3/2)º = 0,01745130 and sin (3/4)º = 0,01745279. Far in advance of his time, the recursive method used by Kad zade gave in few steps the exact value for sin 1º, a method which can be evaluated as a very modern approach. Key words: Ulugh Beg, zij, sinus 1º, astronomical tables, geometrical method, angle trisection.
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