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Article

Architectural Characteristics of Different Configurations Based on New Geometric Determinations for the Conoid

Department of Architectural Composition, University of Seville, Av. Reina Mercedes 2, 41002 Sevilla, Spain
Academic Editors: Oleg Kapliński, Agata Bonenberg, Wojciech Bonenberg and Marco Lucchini
Buildings 2022, 12(1), 10; https://doi.org/10.3390/buildings12010010
Received: 6 December 2021 / Revised: 19 December 2021 / Accepted: 20 December 2021 / Published: 24 December 2021
(This article belongs to the Special Issue Architecture: Integration of Art and Engineering)
The aim of this article is to orient the evolution of new architectural forms offering up-to-date scientific support. Unlike the volume, the expression for the lateral area of a regular conoid has not yet been obtained by means of direct integration or a differential geometry procedure. In this type of ruled surface, the fundamental expressions I and II, for other curved figures have proved not solvable thus far. As this form is frequently used in architectural engineering, the inability to determine its surface area represents a serious hindrance to solving several problems that arise in radiative transfer, lighting and construction, to cite just a few. To address such drawback, we conceived a new approach that, in principle, consists in dividing the surface into infinitesimal elliptic strips of which the area can be obtained in an approximate fashion. The length of the ellipse is expressed with certain accuracy by means of Ramanujan’s second formula. By integrating the so-found perimeter of the differential strips for the whole span of the conoid, an unexpected solution emerges through a newly found number that we call psi (ψ). In this complex process, projected shapes have been derived from an original closed form composed of two conoids and called Antisphera for its significant parallels with the sphere. The authors try to demonstrate that the properties of the new surfaces have relevant implications for technology, especially in building science and sustainability, under domains such as structures, radiation and acoustics. Fragments of the conoid have occasionally appeared in modern and contemporary architecture but this article discusses how its use had been discontinued, mainly due to the uncertainties that its construction posed. The new knowledge provided by the authors, including their own proposals, may help to revitalize and expand such interesting configurations in the search for a revolution of forms. View Full-Text
Keywords: conoid; ellipse; calculus of surface areas; number psi; number Pi; parametric design; cubature architecture; design paradigms conoid; ellipse; calculus of surface areas; number psi; number Pi; parametric design; cubature architecture; design paradigms
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MDPI and ACS Style

Cabeza-Lainez, J. Architectural Characteristics of Different Configurations Based on New Geometric Determinations for the Conoid. Buildings 2022, 12, 10. https://doi.org/10.3390/buildings12010010

AMA Style

Cabeza-Lainez J. Architectural Characteristics of Different Configurations Based on New Geometric Determinations for the Conoid. Buildings. 2022; 12(1):10. https://doi.org/10.3390/buildings12010010

Chicago/Turabian Style

Cabeza-Lainez, Joseph. 2022. "Architectural Characteristics of Different Configurations Based on New Geometric Determinations for the Conoid" Buildings 12, no. 1: 10. https://doi.org/10.3390/buildings12010010

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