"Infinity has varying degrees of magnitude." Cantor Dust fractal topology infinite structure All of these originate from Cantor's set theory. "A city that exists, yet hardly exists." 「都市を削ることで現れる都市」 Cantor Group Mathematical Architecture space

A fractal structure in which circles are infinitely packed together. A fractal shape in which tiny circles increase infinitely. Fractals + Number Theory = Apollonian City デカルトの定理曲線都市 Galaxy cluster ↓ galaxy ↓ Star cluster ↓ fixed star ↓ planet Soddy–Gossett theorem 銀河分布・泡宇宙構造・重力レンズ構造 Mathematical Architecture spce

"The surface with the smallest area under the same boundary conditions" → soap film Dividing space infinitely periodically Smoothly continuous curved surface A maze-like structure full of holes The famous Schwarz surface Schwarz D surface Schwarz Psur Gyroid (Diamond surface) (Primitive surface) (A close relative discovered after Schwartz's discovery) 三次元迷路の曲面 The entire building is a single curved surface A gigantic sculpture of continuous curved surfaces 空間の骨格 Gyzo structu

Fractal shapes created from iterative calculations using complex numbers Dragon type, Seaweed type, Flame type, Coral type Simple mathematical formulas → infinitely complex forms = principles of nature フラクタル植物のような建築 The basics of chaos theory Mathematical Architecture space

Instead of using force directly, it uses kinetic energy T and potential energy V. L = T − V The most natural flow of space エネルギー差が形を決める建築 Kinetic energy T = flow of people Potential energy V = weight of space Energy Valley ラグランジュ文化ホール Mathematical Architecture space

Geometry where you can draw infinitely many parallel lines A curved surface that expands into space, like a saddle (horse saddle). 宇宙の形 一般相対性理論 カオス理論 フラクタル 無限空間 hyperbolic city Poincaré disc-shaped hyperbolic city Mathematical Architecture :