Advanced International Journal for Research

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Volume 7 Issue 5
September-October 2026

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Application of Geometrical Induction For Building Construction

Author(s) Dr. Chung S Lee, Brendon M Son, Daniel M Kim, Ellie H Kim
Country United States
Abstract This paper develops a rigorous interpretation of geometrical induction for building construction. The term is used here to mean the controlled extension of a verified geometric building unit, bay, floor, façade cell, or structural module from stage k to stage k+1 under a repeatable set of dimensional, structural, interface, and constructability rules. This interpretation combines the logic of mathematical induction with modular coordination, parametric geometry, Building Information Modeling (BIM), Design for Manufacture and Assembly (DfMA), and off-site construction. The proposed framework begins with a base construction unit P(1), defines a geometric transformation T that creates P(k+1) from P(k), and requires invariant constraints—such as grid alignment, load-path continuity, connection compatibility, dimensional tolerances, egress continuity, and service-zone coordination—to remain satisfied at every extension. Worked applications are presented for repetitive floors, an L-shaped block model, façades, trusses, and volumetric modules. The paper concludes that geometrical induction is most useful not as a substitute for engineering analysis, but as a design-control principle that converts repeated building geometry into verifiable rules.
Keywords geometrical induction, mathematical induction, modular construction, BIM, DfMA, parametric design, prefabrication, geometric recursion
Field Mathematics
Published In Volume 7, Issue 5, September-October 2026
Published On 2026-09-25
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E-ISSN 3048-7641
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