A spherical surface that looks like a "sphere" but behaves in an "abnormally messy" way in space. The surface is infinitely intricate. A seemingly endless series of tiny thorns and ribs. The distinction between "inside" and "outside" is intuitively broken down. The internal structure becomes incredibly complex. The sense of spatial continuity is broken. The concept of "boundaries" goes haywire. "Architecture that is closed yet open" アレクサンダーのホーンド球面 Infinite Horn Corridor

Architecture is not merely the construction of space; it is deeply intertwined with mathematical principles. In particular, translating abstract mathematical concepts such as chaos theory, topology, and higher-dimensional geometry into spatial ideas and visual forms makes it possible to create architectural designs that defy gravity and possess a sense of weightlessness. This article explores the connection between architecture and mathematics , providing concrete insights u

"A single line, yet a mysterious curve that completely fills the entire plane." space-filling curve 「回廊＝建築全体」 A structure that defies intuition: "lines become surfaces" space Mathematical Architecture

It's not something that can be cut with a knife. "Something that goes against intuition" The trick of the spatial structure itself → "Manifold and topological architecture" The discrepancy between "space," "infinity," and "rules" バナッハ＝タルスキー "Destruction of spatial preservation" Mathematical Architecture space

"The space takes on a different shape each time." for example: Waves on the water's surface → constantly changing shape Clouds → Boundaries are random Cracks → Spreading irregularly Random walk (how a drunk person walks) Fractals (self-similar random shapes) Random graph (network) 迷宮型文化施設 (Incredibly beautiful) (Cosmic) (The city is shaking) Conflict between different programs

A world of "not smooth spaces" Thinking in terms of distance and measure Viewing in terms of extremes and scales Approach it probabilistically Treat as a discrete structure "A space where you can't find peace anywhere." 「世界は本当に滑らかなのか？」 Differentiable = Ideal/Smooth Not differentiable = realistic, rough, complex 👉 Non-differentiable geometry is **"geometry that is close to reality"**