"Mathematics is the process of unifying disparate, localized pieces of information into a coherent, unified whole structure." ① Segmentation (local) ② Connection (restriction mapping) ③ Integration (gluing) "A collective building that retains differences in its components while perfectly aligning only its boundaries." ①形態 × ②構造 × ③運動 を統合 Core Geometry Mathematical Architecture space

"Geometric spaces with completely different shapes actually contain the same information." Space A Space B Geometry: Counting Curves Geometry for studying hole structure Space A Space B (Complex curve) ←→ (Complex hole) 鏡宇宙を移動する体験 Twin buildings with different shapes Architecture A Architecture B Organic forms full of curves linear Flowing Corridor Courtyard type Movement distance, line of sight, and spatial volume are in perfect agreement. Mathematical Architecture space

"The study of mathematically dealing with patterns of randomly (accidentally) placed points, lines, and surfaces." Mathematical modeling of random spatial structures 建築と都市の中間 "Cities are architecture that grow like living organisms." "Architecture that has come into existence" rather than "architecture that has been designed" Mathematical Architecture space

"A phenomenon where seemingly unrelated fields of mathematics coincide at an unbelievable level." Monstrous Moonshine The coefficients in the expansion of the modular function are as follows: 196884 = 196883 + 1 196883 → Dimensions of representation of monster groups 1 → Self-evident expression "Architecture where structure and light are perfectly aligned" 広大な都市広場の中央に、完全に無機質な黒い直方体が静かに立っている。 The surface appears flat at first glance, but upon closer inspection, countless irregu

Shapes that cannot be explained in ordinary dimensions (1D, 2D, 3D) Famous dimension ① Koch curve Dimensions: Approximately 1.26 dimensions ② Sierpinski triangle Dimensions: Approximately 1.58 dimensions ③ Cantor set Dimensions: Approximately 0.63 dimensions "Architecture where scale collapses" 建物 ≒ 地形 ≒ 宇宙構造 Prompt 1 fractal architecture based on Hausdorff dimension, recursive self-similar structure, infinite detail facade, multi-scale geometry, organic yet mathematical form