a² + b² = c² Right angles in architecture The very basic structure of space, including floors, walls, columns, and stairs. If we translate the resulting vector, which is the product of two directions of motion, into architectural terms... → A "diagonal structure" that penetrates orthogonal spaces This is a form where the "equation for length" has been transformed into a "relationship between spatial quantities." ピタゴラスの空間

A tool for counting and organizing the world Natural numbers = content of the letter; QR code = envelope "QR code = a cubic space of 0s and 1s" It's like walking through a mathematical formula. A three-dimensional program space created by a device that allows people to enter into information. 知的に挑発してくる都市空間

"Architectural Cross Section" as Differentiation: Extracting Change The process of extracting "changes at a particular moment or place" "Architectural Cross Section" as an Integral: Overlapping Spaces The process of "building a shape by accumulating tiny elements" "Program collisions" and "accumulation of discontinuous fragments" Building=∫(Culture+Commerce+Chaos)dz パラメトリック・デザイン

Nothing exists. 0 is the "boundary"... "an attempt to transform numbers into space." In calculus, if we consider 1/x, its value becomes ∞ as x → 0. 0 is "complete nothingness," ∞ is "complete excess"... 0 and ∞ are used in architecture. 「Zero Core – Infinite Field」 ０

The method using catenary curves is a truly unique approach that can be considered the epitome of structural aesthetics. The shape is deliberately derived by **"using gravity"**. The "tensile force" is directly replaced by the "compressive force," creating an ideal arch structure that doesn't require columns. 「樹状の柱」 The mirror-like basin at your feet reflects an inverted "framework of light," and the ideal structure comes to life as both reality and illusion within the sensib

A space made up of complex numbers, that is, x + iy instead of x, y. Perfect geometric balance... an ultra-complex donut on a cosmic scale Overhead view ○───○ / \ ○ ○ ○ \ / ○───○ Plane configuration courtyard ┌─────┐ │ Circulating Corridor │ Courtyard │ │Courtyard │ Exhibition room │ │ │ │ Circulating Corridor │ └──○──┘ courtyard Cross-sectional structure curved roof /￣￣＼ / \ ____／ ＼____ exhibition space ○ courtyard Structural system ╱╲╱╲╱╲ ╲╱╲╱╲╱ ╱╲╱╲╱╲ Light design ceiling

A tesseract is a cube with "one dimension added." Dimensional flow dimension shape 0 dimensions point 1D line 2D square 3D cube 4th dimension Tesseract A cube that has been stretched even further The spatial relationships are different from those of ordinary buildings. The room next door suddenly appears on a different floor. Going up leads to the side. The interior and exterior are continuous. Architecture with distorted spatial topology 連続するプログラム空間

Fractal Landscape A city structure where "shapes infinitely self-replicate"... self-similarity (fractal) An endless city, where the city continues on and on. One of the most complex shapes in the universe A structure in which cities grow like living organisms. マンデルブロ集合 都市 FRACTAL CITY Self-similar Urbanism

energy → matter → life → thought → culture Urban cross-section diagram Tokyo ||||||||||||||||||||| type of density Fukuchiyama ——————— horizontal spread Project ▲ Compressed density ⇒ Urban engine in front of the station → Architecture that allows you to experience urban transformation Urban Culture Accelerator City = Continuous Change Urban culture evolves through the accumulation of people, time and events. d/dt Fukuchiyama introduces a vertical articulator That accelerate

"A three-dimensional object in which there is no distinction between inside and outside." An extended version of the Möbius strip → The surface is connected → If we create it in our 3D space, we will inevitably break through it midway. When it becomes an architectural space As I was walking down the corridor Without realizing it It's on the back side of the building Neither the walls nor the floor are cut. A single continuous surface "Architecture where the interior and exter

Some complex functions are "contradictory in the ordinary plane." Instead of using a single flat surface, stack multiple flat surfaces on top of each other. Then, in the first order, √z = + and in the second order, √z = − can exist without contradiction. "Architecture where different levels of space exist within the same location." For example, a space where you enter the same door but end up on a different floor—like a "door to anywhere." "Create space to match the function"

A structure where space is made up of bundles of circles (fibers) → Link (chain link) state "One of the most beautiful geometric structures in the universe" ホップ・パビリオン "Imagination condition" category Set conditions Environment settings A city waterfront. The reflection of structures on the water's surface suggests the symmetry of $S^3$. lighting Twilight (blue hour). The setting is such that the afterglow from within highlights the overlapping curves. texture Parametric ribs

One of the most complex symmetries conceivable in the universe. Mathematics dealing with the symmetry of continuous transformations 248 fundamental symmetry directions → 8-dimensional symmetrical lattice → jewel-like structure Cosmic Gothic Structure Music, Art, Mathematics, Light, Silence 静かなコンクリートの宇宙 宇宙の星座

There is order, but no cycle. The golden ratio appears. A star-shaped pattern is created. No matter how much you expand it, it won't be the same cycle. Self-replicating urban structure → Order + Non-repetition Quasicrystal 迷う文化ホール

Strange Structure of Higher-Dimensional Spheres It's the same ball, but it's a different ball. An exotic sphere is a smooth manifold that has the same homotopy type (topological structure) as a normal sphere, but possesses a different smooth structure (differential structure). 一番理解しにくい構造 4次元球面のエキゾチック構造

A collection of chaotic solutions → "Butterfly Wings" It looks random, but it's not completely random → Chaos Butterfly effect The space between order and chaos

24 dimensions is → (x1, x2, x3, ..., x24) Space-scale urban grid A space that resonates deeply, a space with a heavy atmosphere, a space where you feel order in your body. Silence outside Inside is space 垂直方向の光の落とし方と素材の密度の対比 "The spirit of the place," "The texture of the materials," "The use of light and shadow," "Minimalism"

"The largest and most complex 'ultimate symmetric structure' ever found in the world of symmetry." "Extreme city of local order × global chaos" → "God of Symmetry" "An incomprehensible order" 光の挙動　と　内部透視