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.

1. 서 론
2. 알 카시의 첨두아치 작도와 실용적 접근
    2-1. 수리학의 열쇠의 구성과 일관된 서술 방식
    2-2. 이슬람권 학술 전통과 현안 해결의 추구
3. 첨두아치의 규모 분류와 기하학적 특성
    3-1. 세 첨두아치의 규모별 높이비와 곡률 차이
    3-2. 규모 불특정 첨두아치의 상호 연관성 부재
4. 첨두아치의 건축 활용과 유형적 특성 공유
    4-1. 곡면구조 변환과 기념비적 건축 장치 적용
    4-2. 곡면구조의 단면선 규정과 조합 가능성 고려
    4-3. 세 아치의 클로버형 수용과 울룩벡의 선택
5. 결 론

• 최남섭(서울대학교 건설환경종합연구소 선임연구원, 공학박사) | Choi Nam-sub Corresponding Author