L'articolo di Alicia Imperiale 

1. Cosa succede con le nuove geometrie topologiche?

(What happens with the new topological geometries?)

New topological geometries fundamentally change how architects think about, design, and construct space. Traditional Euclidean geometry relied on fixed shapes like lines, planes, and volumes. Topological geometry, by contrast, emphasizes continuous, flexible, and dynamic forms that can be manipulated and deformed without losing their essential properties.

With the advent of digital tools like NURBS-based modeling systems (e.g., Alias, Maya), architects now have the ability to explore fluid, interconnected surfaces that reflect a shift from static forms to designs that embrace complex curvature and dynamic relations. These geometries:

• Allow for seamless transitions between inside and outside, inspired by mathematical models like the Möbius strip or Klein bottle, where boundaries blur.

• Emphasize smoothness and continuity, rejecting rigid distinctions like structure vs. ornament.

• Reflect cultural and technological shifts, representing interconnectedness and fluidity in the modern world.

In practice, these geometries enable new forms of architecture that are more organic and dynamic, challenging the static, orthogonal forms of the past.

2. Le varie forme di relazionare il piano, la superficie, le nuove superfici?

(What are the various ways of relating the plane, the surface, and the new surfaces?)

The relationship between planes and surfaces has evolved dramatically due to digital tools and shifting architectural paradigms. Here are some key ways these relationships manifest:

1. From Plane to Continuous Surface:
   
   

   • Traditional architecture often treated surfaces as static, flat planes defining space. New approaches view surfaces as dynamic and flexible, capable of morphing and adapting to forces, functions, and contexts.

   • The shift emphasizes continuity, where planes and surfaces no longer have clear boundaries but instead blend into one another seamlessly.

2. Interaction Between Structure and Ornament:
   
   

   • Surfaces are no longer mere decorative layers; they often integrate with the building’s structural system. This challenges classical distinctions and reflects the idea of depth as an extension of the surface.

3. Digital Animation and Fluid Design:
   
   

   • Programs like Maya and Alias allow architects to design surfaces influenced by forces and movement, creating forms that are time-based. For example, rather than defining a plane as static, architects can simulate how it might shift or flow over time.

4. Topology and Contextual Adaptation:
   
   

   • New surfaces interact with their environment in a more organic way, adapting to site-specific conditions like wind, light, and human movement. This results in adaptive geometries that are both functional and expressive.