xn + yn + zn + wn = 0 "An entity where pure mathematical formulas themselves have become space." "The Topological Universe Created by Mathematical Formulas" ① Algebraic geometry We construct spaces from polynomials. ② Complex Geometry The shape of the complex number space. ③ Hodge Theory Analysis of the "information layer" within a space. ④ Mirror symmetry Connection to superstring theory. ⑤ Arithmetic geometry The fusion of integers and space. Spatial characteristics 1. Perf

"In a sufficiently large system, 'order' will inevitably emerge." “An order that appears without design.” 1. A pattern emerges despite the random arrangement. 2. Cities unilaterally acquire a "core" 3. "Necessity within coincidence" exterior Giant random grid city countless units Seemingly chaotic However, partial symmetry will always appear. The golden light reveals an "unavoidable structure". Interior Random passage labyrinthine circulation However, walking always converges

"No other point can be found within the circumcircle of any triangle." "The most beautiful triangular network" "A structure that resembles the natural world" Not Designed. Generated. "Architecture born from relationships" 「生活の点配置から住空間が生成される」 Computational Geometry Delaunay House If it's a cultural hall, it becomes "architecture of connection" = "large-scale spatial network". ひとつの箱ではなく、結ばれた公共空間 Mathematical Architecture space

Architecture is becoming "biological." Architecture changes based on its "state" rather than its "purpose." Growing due to congestion Extinction due to depopulation Mutation through activity Evolves through connection “進化する建築” How do vacation homes multiply? How it multiplies internally 時間的可変性 Now, let's create a desert island using this math game. Autonomous Grid Architecture Mathematical Architecture space

“A mathematical fingerprint for distinguishing knots” "The way space is intertwined" Intersection of traffic flow Eye contact Penetration of the atrium Loop cycle Multilayer connection “Topological fingerprint” 1. Exterior Multiple loops penetrate Intersecting continuum "I don't know which is the front." 2. Introspection The flow of movement remains tangled. The seating area and the corridor are in phase connection. The feeling of upside down being reversed 3. Cross-section S

An equation that smooths out the "uniformity of curvature and shape" of space over time. Wrinkled surface → Uniform shape → Heat diffusion in space → Curvature is smoothed out The shape of space changes over time. Previously proposed architecture　“Chaos → Order” Thinking of it as a city Topology × Time × Curvature Consider it as a bridge (Tokyo to New York) 過去 → 遷移 → 均一 Consider it as an underground space 時間を持った建築 Surgery Architecture Mathematical Architecture space "If you l