Nexus Network Journal

This year, 2009, is being celebrated as the International Year of Astronomy. According to the mission statement, this “is a global effort initiated by the International Astronomical Union and UNESCO to help the citizens of the world rediscover their place in the universe through the day- and night-time sky, and thereby engage a personal sense of wonder and discovery” (you can read more on the IYA2009 website, http://www.astronomy2009.org/). Architecture and urban design are deeply rooted in astronomy, as the papers in this special issue demonstrate.

It is commonly believed that the longitudinal axes of churches extend exactly in an east-west direction. However, thorough investigations have shown that this is not always correct; rather, both southern and northern deviations of up to about 25° can occur. The angular deviation between the church axis and true east is called the Holy Alignment. This present study presents the possibility that the nave is oriented towards the direction of the sun-rising point on the name day of the patron saint of the church. If several saints share the patronage, the Holy Alignment equals the algebraic sum of the angular distances for each saint. The orientation of a nave can be analyzed by means of common mathematical relations used in geodesy, astronomy and gnomonics. In order to perform such an anlysis, it is necessary to know the history of the patronage of the church; the Gauss-Krüger coordinates of the ground plan; and characteristic astronomical quantities at the time the church was built. A calculated example with the saints Andrew, James and Philip for the year 980 illustrates the analysis.

An appendix deals with the influence of atmospheric refraction on the apparent altitude of the sun near the horizon.

The present paper discusses various implications suggested by a thirteen hundred year old stone masonry structure, built by Queen Sun-Duk of the Silla Dynasty, regarding astronomy, religion, symbol, mathematics in architectural form and construction. The name of the 9.1 m tall stone tower, Chum-Sung-Dae, implies its use as celestial observatory and it is claimed to be the oldest one existing in Asia. Although there have been some disagreements about its function as an observatory, this claim is generally accepted in the absence of any evidence to the contrary. No matter what the original function was, Chum-Sung-Dae has been unanimously acknowledged as the product of then state-of-the-art technology. What makes Chum-Sung-Dae so unique and particular among coeval buildings in stone masonry is in its elegant, multiple curvatures. Furthermore, the geometry of Chum-Sung-Dae is reported to embody a notable numerical significance. The absence of mortar between stone layers and sides indicates that the load transfer mechanism of the tower is dependent upon the frictional resistance due to gravity. All these features will be discussed, with an emphasis on the mathematical analysis and interpretation.

The architectural complexes composed by the two main pyramids of Giza together with their temples are investigated from an interdisciplinary point of view, taking into account their astronomical alignments as well as their relationships with the visible landscape. Combining already known facts together with new clues, the work strongly supports the idea that the two complexes were conceived as parts of a common project.

One of the most enigmatic megalithic buildings of Italy is the structure which lies on the S. Erasmo hill near Cesi, in Umbria, a huge complex encompassing an area of around 8000 square meters and enclosed by refined cyclopean walls. Although its date is uncertain, suggested dates comprise the Iron Age and archaic period, down to the third century B.C. The building’s function is also uncertain. usually identified as a fortified structure, in fact there is a megalithic platform at the southern end of the enclosure which could have served as foundation of a temple or palace and, from the top of Monte Torre Maggiore, a complex of temples dating from the fourth century B.C. overlooks the hill. Similar combinations of megalithic buildings resting half-way to temples placed on high peaks are known to exist. In order to clarify the function of this structure and its position in relation to the surrounding landscape, with particular attention to its visibility and to the directions of visibility from the complex, as well as to the possible astronomical alignments, we present a multi-disciplinary approach to the study of the S. Erasmo complex, which includes the mapping of the sky at the various possible epochs of construction, the creation of a digital model of the landscape in forms of digital maps using Geographic Information System technologies, and a 3D model using various 3D software packages.

Ghiyâth al-Dîn Jamshîd Kâshânî (al-Kâshî) is the prominent mathematician and astronomer of ninth/fifteenth century of Islamic civilization who founded the scientific methodology in practical and theoretical knowledge of mathematics in architecture. He played a significant role in the interaction and concurrence among mathematicians and architects, by addressing the relation between architecture and mathematics in two areas of knowledge, theoretical and practical, the latter itself including theoretical practice and practical practice. this paper addresses the question of how Kâshânî’s research has led to the foundation of the first theoretical basis for the application of mathematics in architecture in the form of easily practicable solutions for drawing, and measuring different types of ceilings, arches, vaults, domes, and ornaments, as well as estimating required materials. Further, we will discuss how his knowledge in mathematics and astronomy were utilized in management, design and construction of Samarkand observatory and its astronomical instruments. By exploring how the mathematical knowledge of a Persian scientist was utilized in architecture and craftsmanship, we will shed some light on the hidden layers of Kâshânî’s architectural life, who until now has been considered only a mathematician and astronomer.

The Story of Science is a book series by Joy Hakim of which the first three volumes are now available — Aristotle Leads the Way (2004), Newton at the Center (2005) and Einstein Adds a New Dimension (2007) — and three more are planned. The books represent an on-going project aimed at teaching science in a way that is both specific and interdisciplinary. Kim Williams discussed the project and its goals with author Joy Hakim and art scholar Sabine Russ, who chose the illustrations for the books.

Two recent projects for a frist-year course in drawing for architecture students have been organized by Sylvie Duvernoy, Michela Rossi and Kay Bea Jones. The first, a four-phase program centering around a tour of the architecture of the Midwest in the United States, was implemented in Spring 2008. The second, a day-long seminar on designs for temporary architecture, took place in December 2008. In both, the use of mathematical concepts to provide an underlying organization for the generation of architectural form was fundamental.

The zodiac is widely known as a band of twelve celestial constellations. It also contains a mathematical model for cosmographic depiction, based on observations of the sun, moon, and visible planets as they traverse the celestial ecliptic. Here wee consider the zodiac as a timepiece or calendar; how this system of planets and constellations emerges from elementary geometric patterns; and how these patterns inform the symbols of the zodiac and frame our world view.

According to Robert Tavernor, a flaw that plagues contemporary life is the lack of belief in the idea expressed in these words of Protagoras, the pre-Socratic philosopher and original Sophist, of whose work only a few fragments, such as the one quoted above, survive. The humanistic culture of which he was a participant in founding no longer survives in a vital way in the modern world. Yet Protagoras is one of the few significant figures relevant to the history of Western measuring systems whose thought has not been brought to bear on the topic in this fascinating, and, ultimately, moving book by Robert Tavernor. Conspicuous by their absence, perhaps the familiarity of Protagoras’s words argued for their exclusion from this closely argued book, whose goal is to take one of the most prosaic and familiar of all modern human tools, the metric system of measurement, and suggest the depth of meaning that lies dormant in treating this subject solely in an instrumental fashion, as an aspect of technological advancement. His title clearly echoes the famous aphorism while suggesting a sly inversion of its meaning. Yet it may be Protagoras’s reputation as the precursor of relativism that places him outside of Tavernor’s concerns, for in the history of measurement precision of mutually agreed upon standards has perforce always been the goal, and any confusion on this issue would be counterproductive.

Sylvie Duvernoy reports on the seventh international, interdisciplinary Nexus conference for architecture and mathematics.

Valentina Filemio reports on a 2008 exhibit in Turin, Italy, that focussed on architects Guarino Guarini, Filippo Juvarra and Alessandro Antonelli.