The discussion over the proper relationships between architecture and mathematics isn't new. Its roots are quite ancient. But as a discussion, it is far from being limited to the theoretical, and the issues raised at the beginning are as valid for architects today as they were for architects of the past. This Summer 2001 issue of the Nexus Network Journal will make that abundantly clear.

Do architects use use geometry or do they use number? Michele Sbacchi undertakes a discussion of how the conflict between the geometric and analytic, as embodied by Euclid's Elements on the one hand and Plato's Timaeus on the other, had a great influence on architectural theory in the seventeenth century. Euclidism and Theory of Architecture looks at how Euclidean geometry, eclipsed by Pythagorean numerology in the fifteenth and sixteenth century, is resurrected to a poisition of supreme importance in the architectural treatises of the seventeenth century.

Of the Gothic age, Michele Sbacchi writes, "We can believe that during the Middle Ages, to make architecture, the Euclidean lines, easily drawn and visualized, were most often a good alternative to more complicated numerological calculations." In his research article in this issue, Han Vandevyvere provides us with a catalogue of how Euclidean geometrical constructions were used to govern the construction of Gothic Town Halls in and around Flanders, 1350-1550. An important aspect of this study is its adhesion to fundamental principles governing modern analyses of extant historical structures. Vandevyvere outlines his set of criteria in the beginning of his paper. They will be a valid point of reference for anyone wishing to perform similar analyses.

Leonard Eaton brings us up to the twentieth century with his look at how architects and engineers managed to resolve the problem of indeterminate structures in reinforced concrete in the 1950s. For a manageable solution, they turned to Hardy Cross and the "Moment Distribution Method". A brilliant engineer, Cross's method was not only a valuable practical application, but teaches some interesting lessons about approximation as well. Here is a "concrete" (forgive the pun) examples of the relationships between architecture and mathematics.

Michael Leyton takes us from the concrete back to the abstract with his Nested Symmetries. Author of Symmetry, Causality, Mind, Leyton explores how symmetry operations can lie at the heart of architectural compositions. This is the first part of a two-part series first published in VisMath, the online journal for symmetry.

In the Didactics column this month, Roger Herz-Fischler presents Proportion in the Architectural Curriculum, with a chapter exerpted from his book Space, Shape and Form /An Algorithmic Approach, developed for a course in architecture and mathematics that he taught at the School of Architecture, Carlton University, 1973-1984. The present chapter will be an important resource for teachers and students, both for the references it contains and for the methodology it sets forth.

Proportion in the Architectural Curriculum? Did someone mention the Golden Section? Well, Marcus the Marinite, our resident geometer of the Geometer's Angle, does in his column for this issue. Marcus (aka Mark Reynolds) introduces a fine method for generating the regular heptagon from the equilateral triangle and pentagon, an original construction that constitutes a significant discovery.

Karim Abdul Bangura has reviewed the new edition of George Gheverghese Joseph's book, Crest of the Peacock, for this issue of the NNJ. The book ably deals with ethnomathematics, and Bangura's review contains some interesting reflections on this subject. George Joseph is already known the the Nexus community, having presented a paper entitled Geometry of Vedic Altars at the Nexus '96 conference (published in Nexus: Architecture and Mathematics).

Finally, John Sharp has written a review of the exhibit Making Buildings, now on tour in the United Kingdom. The artists and architects who participate in the exhibit show, perhaps sometimes unintentionally, just how interrelated architecture and mathematics are. If you are traveling in the UK this summer and fall, you might be able to catch the exhibit; dates and places are listed at the end of the review. But if you are traveling, don't forget to stop at an Internet cafe so you can read the NNJ! You won't want to miss any of our regular features: the Virtual Library, Submission Guidelines and the Nexus Network Journal Bookshop.

Have a great summer, and please e-mail me with questions or comments.

Kim Williams, Editor-in-Chief