Any flat map can be colored using a maximum of four colors, provided that adjacent regions are not the same color. "The first famous theorem proven by a computer" 隣接関係そのものが建築の形を決める The walls and ceiling are divided like a "three-dimensional map" using gold, crimson, blue-green, and purple acoustic panels. The four colored polygonal regions are continuous from the outer shell to the ceiling, walls, seating area, and circulation paths. Mathematical Architecture space

Fractal shapes are always uniquely determined as a "combination of reduced copies". "By repeatedly shrinking, moving, and rotating a single architectural unit, the whole converges into a stable, self-similar form." The fundamental principle that makes all self-similar architecture possible 中央へ向かって形が無限に収束して見える部分が、定理における「唯一のフラクタル・アトラクター」を表現 The stage itself becomes the "attractor" in Hutchinson's theorem. Hutchinson's repetition principle is an architectural principle that inte

MATHEMATICAL ARCHITECTURE SERIES PART I — MATHEMATICAL ORDER Architecture generated from mathematics. Chaos.Fractals.Minimal Surfaces.Aperiodic Order.Symmetry & Lattices. A 55-page visual book exploring how mathematics becomes architecture, space, and atmosphere. Now available on Gumroad: https://shomei.gumroad.com/l/scyaok PART I — MATHEMATICAL ORDER Created for architects, designers, artists, and computational thinkers. #Architecture #ComputationalDesign #Mathematics #Digit

The curvature of the entire surface and the number of holes are strictly linked. Differential geometry and topology Localized curvature ⟷ Number of holes in the entire curved surface Gauss–Bonnet Architecture — Total Curvature TOTAL CURVATURE HALL Positive curvature encloses the hall. Negative curvature opens it to the city. Geometry changes. Topology remains. The building's overall topological structure can be felt even from the inside. Beyond its interesting shape, Gauss-B

It is possible to uniquely construct a number that satisfies several conditions simultaneously. for example, When divided by 3, the remainder is 2. When divided by 5, the remainder is 3. When divided by 7, the remainder is 2. We will search for a number that satisfies all of the following conditions. The smallest answer is 23 . 23≡2(mod3),23≡3(mod5),23≡2(mod7) And importantly, if the numbers do not have any common divisors, like 3, 5, and 7, the answer is 3×5×7=1053\times5\ti

It is possible to determine whether many convex regions "have a common part as a whole" using only a small number of combinations. When you choose any three things, there is always a common element. A central point or shared space exists that satisfies all conditions. A theorem for finding the commonality of the whole from local overlaps. 複数の凸状ボリュームが重なり、中央の金色に光る共有アトリウムへ収束する The golden light represents the "common area" of each domain. Spaces with different uses exist independ