This new issue of the NNJ brings to us a discussion of shape, an argument that lies at the heart of many a discussion about the relationships between architecture and mathematics.

In Research Articles, Marco Frascari, an architect, and Elena Marchetti and Luisa Rossi Costa, both mathematicians, approach the issue of shape from their respective points of view, giving us, the readers, the advantage of a multi-dimensional examination of the subject. Marco Frascari focuses his lively and imaginative atttention on subject often viewed as too practical and concrete to be of much inspiration to the creative architect: the application of shape to structure. In A Light, Six-Sided, Paradoxical Fight, Marco examines the concept of "lightness" in overcoming the force of gravity, and how engineer Robert La Ricolais deployed the hexagonal shape to win the fight. The paradox consists in making a light structure with big, heavy members. What makes this article so original and so engaging is that in order to arrive at his conclusions about Le Ricolais's use the hexagonal shape as a structural tool, Marco takes the scenic route, visiting Leon Battista Alberti, Italo Calvino, Johannes Kepler, Louis Kahn, Medusa and Perseus, Ludovico Ariosto and Rabelais along the way.

Elena Marchetti and Luisa Rossi Costa teach a course in mathematics to architecture students at Milan's Polytechnic University. One of the tools they use in their course is linear algebra, a subject that would have surely made me groan initially had I been in their course as an architecture student. But their treatment of Johannes Itten's The Fire Tower has convinced me of the beauty of the argument, because just as the musician sees notes on the page and hears the music, the mathematician sees the matrices put together by Elena and Luisa and sees the lovely spiral form that becomes Itten's Fire Tower. Elena and Luisa don't limit themselves to merely generating the form, but have taken the time to trace the use of the spiral in the Bauhaus school, through painting and architecture. The Italian version of the article, La Torre del Fuoco, is also available in this new issue.

In the NNJ's Didactics section this issue, George Hart also examines the issue of shape, and what marvelous shapes they are! In In the Palm of Leonardo's Hand: Modeling Polyhedra, George discusses the appearance of Leonardo's illustrations of polyhedra in Luca Pacioli's De divina proportione. He then goes on to discuss how three-dimensional models of the polyhedra can be generated by today's new 3D printing technology equipment. George himself has written the programs that allow the 3D printing machines to create the polyhedra.

Our Geometer of the Geometer's Angle, Marcus the Marinite (aka Mark Reynolds), deals this issue with a very special shape, the Golden Section rectangle. In On the Triple Square and the Diagonal of the Golden Section, Marcus uses an initial Golden Section rectangle to generate a new "Triple Square" system. As always, Marcus provides a step-by-step procedure to construct the geometric system.

In Book Reviews, Michael Chapman reviews Architecture and Science, a compilation of essays dealing shape as related to topology in architecture, edited by Giuseppa di Cristina.

I am very much looking forward to the Nexus 2002 conference in Obidos, Portugal, 15-18 June 2002. The next issue of the NNJ, Summer 2002, will be dedicated to the conference.

Kim Williams