Triangles are an ever present feature in nature, which the building construction industry duly echoes. However, an exact expression intended to offer the radiant field due to any triangle in an upright or inclined position had not been identified by previous research. In this case, the author has been able to solve by direct integration, the canonical expression of radiative transfer. This result alone confers a myriad of possibilities that had been inconceivable before, for studying in detail the three-dimensional heat transfer behavior of volumes and figures in which triangles do manifest, such as fins, windows, roof-gables and louvers of various kinds. Typically, shading devices, when tilted, give rise in their extremes to rhomboidal shapes which were difficult to take into account or had to be subject to discretization and subsequent Monte Carlo methods in order to perform an approximate calculation of their emission. This implied a lengthy and inexact procedure that induced many errors and consumed computing time. We can now avoid all the former downsides due to the advances hereby presented. As the novel expression can be converted into an algorithm it will be advantageously employed for simulation. This significant finding dovetails in the intricate puzzle of radiated heat and we believe that their consequences will greatly affect the conception and design of HVAC devices, aircraft manufacturing and specifically building or lighting industries among others.

unlike the volume, the expression for the surface area of a regular conoid has not yet been obtained by means of direct integration or a differential geometry procedure. As this non-developable form is relatively used in engineering, the difficulty to determine its surface, represents a serious shortcoming for several problems which arise in radiative transfer, lighting and construction, to cite just a few. In order to solve the problem, I conceived the surface as a set of linearly dwindling ellipses which remain parallel to a circular directrix, a typical problem appears when searching the length of such ellipses. I employed a new procedure which, in principle, consists in dividing the surface into infinitesimal elliptic strips to which we have successively applied Ramanujan’s second approximation for the longitude of the ellipse. In this manner, we can obtain the perimeter of any transversal curve pertaining to the said form as a function of the radius of the directrix and the position of the ellipse’s center on the X-axis. Integrating the so-found perimeters of the differential strips for the whole span of the conoid, an unexpected solution emerges through the newly found number psi (ψ) which seems like a refined approximation to the third decimal of Pi but derived from a definite integral equation. As the strips are in truth slanted in the symmetry axis, their width is not uniform and we need to perform some adjustments in order to complete the problem with sufficient precision, but this is discussed separately in the annexes. Relevant implications for mathematical symmetry applied to multifarious architectural and engineering forms can be derived from this finding

The exact determination of radiative exchanges between solids and surfaces has been a long sought-for question in heat transfer science. Being the canonical equation that rules such phenomena, a fourfold integral, it is extremely difficult to obtain an accurate solution like a formula or abacus. Over the last thirty years, the author has tried to integrate the canonical expression by sundry procedures and they have published two books and a dozen of articles on the matter, recently by virtue of computational geometry and graphic algorithms as a new way to solve the finite-difference problems that arise on complex geometries. In architectural engineering curved radiant emitters are customary since antiquity, especially in domes and vaults and their oculus, However, a consistent procedure to handle them was not readily available. The principles that are described hereby based on Cabeza-Lainez’ first principle for spherical fragments offer a complete panorama on the manner in which surface sources related or contained in spheres can be interpreted and accounted for without resorting to integration. The main advance is that a variety of unexplained problems of radiative heat transfer, applicable to aerospace engineering, meteorological, architectural and medical sciences can be sorted out as exactly as quickly.

Circles, semicircles and its derived circular sectors are ubiquitous both in human creations and in the natural realm. However, mathematically speaking they have always represented a certain level of enigma or even mysticism since ancient times for being such a perfect shape that enclosed the irrational value that we now call π. Such figure was relatively unknown until the seventeenth century; polymaths like Guarini even equated it, after so many centuries, to the Archimedes fraction of 22/7 or sometimes 25/8 which, giving a value 3.125 introduces a considerable degree of error; Eventually, Lambert had to demonstrate, well advanced the eighteenth century that π was actually an irrational number. In recent years, the author has worked with sections of spheres and other curved bodies as related to radiative heat transfer and applied to the finding of form factors pertaining to such special geometries, to the point of defining new postulates. The main theorems so far enunciated refer to the radiative exchange between circles and half disks, but recently the possibility to treat circular sectors has arrived, thanks to the research already conducted in which, by virtue of Cabeza-Lainez first postulate, we are able to know the form factor of any spherical segment over itself, discarding in this way, the former uncertainties that appeared when dealing with the inner side of spherical surfaces. As it is known, to find the exact expression of the configuration factor by integration alone is mostly a tedious task and the results are not readily available as it has been frequently proved. In the said problem of the circular sectors, the author could integrate the first two steps of the basic formulation for radiant exchange. Subsequently, the novelty of the procedure lies in introducing a finite differences approximation for the third and fourth integrals which still remain unsolved, once that we have been able to find the first and second integrals of the form factor. This possibility had not been identified by former research. This sole output provides us with an ample variety of scenarios previously unforeseen. As a consequence, we would be able to analyze with more precision but freely, the spatial transference of radiant heat for figures composed of circular sectors such as spherical sectors like quarters or octaves of spheres. Many architectural, industrial or aircraft modules and objects fall into this category. We already know that spherical shapes cannot be discretized with any accuracy as there are no spherical tiles of the same size, therefore we hope to overcome with our finding a persistent extent of error. In this situation we are able to reduce a considerable amount of hindrances in the progress of thermal radiation science, due to the advances hereby presented. As the new formulations found can be adapted for algorithms, they will be integrated in simulation procedures with significant avail. Our achievement may be considered timely in the effort invested to square the elements of mathematics for radiative transfer. Important sequels are already being derived for radiation in the entrance to tunnels, aircraft design, low-energy building construction and also lighting and HVAC industries to cite just a few.

Several problems of radiative transfer are yet unsolved because of the difficulties of the calculations involved in them, especially if the intervening shapes are geometrically complex. The main goal of our investigation in this domain is to convert the formulas that were previously derived, into a graphical interface based on the projected solid-angle principle. Such procedure is now feasible by virtue of several widely diffused programs for Algorithms Aided Design (AAD). Accuracy and reliability of the process is controlled by means of the analytical software DianaX developed at an earlier stage by the authors. With this new approach the often cumbersome procedure of lighting and thermal exchange calculations can be simplified and made available for the neophyte, with the undeniable advantage of reduced computer time.

The purpose of this article is to disclose the strenuous efforts of Laszlo Hudec in China and Antonin Raymond in Japan and India to create a modern architectural stance by heralding an incipient space syntax. In the turn of the 19th Century, for dynastic, politic and economic reasons, Eastern Asia had very little modern Architecture. It is a surprising fact that, out of happenstance, two European architects Antonin Raymond and Laszlo Hudec, had to intervene to remedy this situation, to the point of becoming 20th Century icons in Japan and China. Their fruitful careers spanned over thirty years and included locations, like Tamil Nadu or the Philippines. The Oriental territories were not an easy ground for the bold architectural achievements that they produced. Despite of faraway strangeness and uncountable personal losses, in revolutions and wars, which eventually forced them both to leave for the United States of America and never to return, they were successful in the manner of establishing a broad avenue for Modern Asian Architecture which is still recognisable today thanks to their systematic approach. However, theirs is an endangered heritage and the intention of this article is to be a just remembrance of in which way such actions could be performed, how they predated by many years a syntactic approach to architectural composition and why their legacy should be preserved.

Burkina Faso is a sub-Saharan African country with a high poverty rate that has quadruplicated its population in the last half fifty years, that is, from 4.5 to 18 million inhabitants. Such demographic changes together with an intense migration process from rural areas to large cities, among other issues, are contributing to a rapid process of socio-cultural transformation. In this context, changes in both traditional and contemporary housing are analyzed and a complete ther-mo-hygrometric evaluation is carried out by processing significant data from on-site measure-ments to shed new light on the response of the said dwellings to the environmental and local cultural values. Results show that the introduction of land ownership linked to climate change and the increasing scarcity of natural resources are forcing native ethnic groups to modify their traditional ways of life, threatening their subsistence. Consequently, we can prove that the new building typologies are not in the least suitable for the climatic conditions nor the rich cultural heritage of Burkina Faso. This fact, negatively affects the possibility of revitalizing vernacular and environmentally-oriented solutions for the contemporary world and the necessary advance to-wards a more sustainable architecture.

In 1944 the architect Antonio Gómez Davó designed and built a new house for Mr. Ferrer at Rocafort in the suburbs of Valencia (Spain). In this same year, Europe, America, Russia and even Japan were still at war and Spain was only recovering from its own intestine conflict. Therefore, architectural innovations and influences were scarce as was the circulation of specialized journals on the matter. But in many creations, like the ceramic vaults and the brise-soleil, Le Corbusier himself had declared his profound nostalgia from the Mediterranean, a Sea that he had come to appreciate in his travels to the “orient”. In the case of Gómez Davó, having been born and raised in a prominent family of Valencia he could not remain indifferent to the design features that appeared in the vernacular architecture of the area, specially the type of inclined louvers of Arabic descent, that covered bow-windows and balconies and which have come to be known in Spain as the Majorcan louvers; nowadays even employed by Rafael Moneo for instance at the extension of the Painter Miro Foundation. However, with so many difficult circumstances surrounding him, Gómez Davó could not get to the point of producing a ground breaking design based on solar assumptions for the whole façade of the building, instead when providing an entrance porch apt for spending life, meals and well deserved rest hours outdoors in the pure Mediterranean tradition, he ventured to construct a surprising perforated wall oriented to the South in order to control radiation in winter and provide shade in the summer while affording excellent light and superb conditions of ventilation. By means of our own devised simulation tools we have analyzed the conditions of the house and especially of such innovative brise-soleil at times reminiscent of Alvar Aalto solutions for day-lit roofs, which he was aware intuitively and by his own incipient study of solar geometry, that needed adaptation from so distant latitudes as Finland and Valencia. By outlining such unknown and bold precedent we contribute to revitalize the early and daring pioneers of solar architecture in peripheral Spain and Europe, at the birth of critic regionalism, a fact often disregarded in conventional history of Modern Architecture.

The beneficial effects of solar radiation on human health are well documented. One necessary mechanism triggers the production of vitamin D whose insufficiency has been linked to a variety of disorders like diabetes, hypertension and more recently amyloidosis and Alzheimer disease. However, there are few architectural designs capable on ensuring adequate provision of solar radiation inside buildings. Conventional fenestration is not sufficient to provide for significant doses of sunlight even to prevent seasonal affective disorder (SAD). In this paper we discuss the effect of new design alternatives for skylights, especially in the refurbishment of obsolete facilities. After such complex retrofit is executed, we have analyzed the performance of a building in warm and sunny climates as is the case of southern Spain. It has been considered as a priority the study of the factors that relate sunlight and energy, as well as, to a certain extent, other aspects like ventilation and insulation. Many architectural designs are presented as correct if the thermal requirements alone are met, even at the risk of later energy waste in lighting devices and visual or physical discomfort. On the other hand, large glazed areas allow more daylight into a space, but they may also allow excessive heat gains or losses which increase the air-conditioning cooling or heating load. To avoid these problems, we have considered the combined effect of daylight and energy from the beginning of the skylight design-process. A daylighting software based on configuration factors that we have apply in former researches to study the problems of direct sun over architectural structures have been used. This question cannot be treated adequately with conventional programs for overcast skies. The skylights have already been constructed and on-site measurements in the offices have been taken to complement the computer simulations data. The results show that it is possible to achieve energy saving and high radiation levels in winter without increasing heat loads during the summer. All this is considered beneficial to improve the condition of users with cognitive diseases as Alzheimer’s disease by virtue of adapted spaces.

The purpose of this article is to disclose the architectural proportions and nature of the Korean national treasure in Seokguram Grotto, Gyeongju. The authors compare its features with those of other ancient hypogeal or ashlar constructions and intend to rediscover its relevant hidden configuration and latent structural properties to show its uniqueness. The methods employed in the research belong initially to architectural design and composition to advance at a later stage, into the nuances of stone masonry, lighting effects or cohesive construction. In this discussion and thorough analysis, different philosophical and scientific subtleties come afloat. The results demonstrate a significant potential capable to be applied in part to recent architectural developments like Tadao Ando’s Buddha Hill in Hokkaido (2017) and the authors’ own project for a Buddhist monument.

With this article we would like to clarify the often-disregarded fact by virtue of which the European Missionaries in Asia acted as catalysts of a kind of nuanced acculturation named Accommodatio (adaptation). To a great extent they became harbingers of Culture and Science more than Faith itself to the dismay of many, including the Roman Church. Such cultural and scientific transference was actually two-pronged, for simultaneously they presented in Europe unique findings related to Language, e.g. the Chinese Characters (considered to be the sole natural language), Geography, Cosmology and even Governance. We would try to prove that such procedure contributed positively to the modern scientific notions of sustainability and to provide the kind of accoutrements that model the modern world as we know it.