The study aims to analyze the geometric characteristics of the pointed arches proposed by Al-Kāshī in his book "Miftāḥ al-Ḥisāb" (Key of Arithmetic) and investigate their planning principles, architectural application, and typological characteristics. Al-Kāshī completed this significant work in 1427 and dedicated it to Ulugh Beg, a Timurid Sultan in Samarkand. In the ninth chapter, titled "Al-‘Imārāt wa al-Abnīya" (Amīr’s Mansion and Building), Al-Kāshī sought to measure the surface areas and volumes of barrel vaults (Azaj) and domes (Qubba). To achieve this, he proposed five kinds of pointed arches (Ṭāq) and analyzed their drawing methods and composition principles. The Īwān and Qubba structures, which are curved architectural elements, hold significant importance in Islamic architecture. However, previous research has predominantly focused on comparing the drawings in Al-Kāshī's book with historical buildings, neglecting the inherent characteristics of the drawings themselves. This study intends to contribute to a deeper understanding of Al-Kāshī's remarkable work and shed light on the geometric aspects of monumental structures in the Timurid Period.