Using Definite Integrals to Estimate Curved Areas and Volumes of Domes and Architectural Structures

Merouge N. Kadhem

Authors

Merouge N. Kadhem Karbala Directorate of Education, Ministry of Education, Iraq

Keywords:

Definite integrals, Architectural geometry, Dome structures, Curved surface estimation, Volume calculation

Abstract

Curved architectural forms mark the finest achievement of structural engineering in architecture. For centuries, the design is one of many that continues to admire contemporary architectural history. Their structural and spatial efficiency has been a journey through domes, arches, and vaults. In architectural planning, structural analysis and estimating the cost of materials, accurate estimation of surface areas and volumes is very important. Geometric formula alone suffices to give an exact solution of simple geometric shapes only like a sphere or cylinder. But most building structure has complex curves that requires math modeling. The definite integral is a mathematical instrument for estimating the area and volume of structures with irregular curves. The use of definite integrals to find the curved surface areas and volumes of domes in architecture is examined in this study. This paper provides a summary of integral mathematics, including the definite integral, proofs and applications for architectural geometry. Spherical domes, parabolic domes and elliptical domes are some examples of dome structures whose mathematical models have all been studied. Other topics covered are the disk method, shell method, and surface of revolution for volumes and surface areas of solids of revolution. Instances from both historical and contemporary architecture are offered to show how calculus based estimation can assist engineering choices in architectural design. A series of practical numerical approximations have also been presented to indicate that definite integrals can be used in construction. The definite integral is thus an important connection between mathematics and architecture, allowing for the ability to estimate areas and volumes of more complex curved structures. These techniques assist designers and engineers to develop cost-effective systems, maximize resource utilization, and advance structural modelling.

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