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

The changes occurring within a region on a plane coincide with the flow that occurs when circling its boundary. "Reading the invisible forces within from the experience of boundaries" - Mathematics 外周を一周する金の回廊＝境界の積分、中央の光る円形ホワイエ＝内部の渦、という構成 The golden line represents the boundary, the central activity and the open space represent the internal "vortex." "Circling the outer perimeter" and "activities within" become a single spatial structure. Mathematical Architecture space

In the world of architecture, defying gravity, a natural law, has long been both a dream and a challenge. Modern mathematical architecture translates abstract concepts such as chaos theory, topology, and higher-dimensional geometry into spatial ideas and visual forms, realizing innovative structural designs that transcend the conventional constraints of gravity. This article explores the possibilities of gravity-transcending structural design and provides a concrete explanati

"A mechanism in which a system behaves autonomously through information, control, and feedback." Input ↓ Information processing ↓ Behavior (Output) ↓ result ↓ feedback ↓ Enter again In architecture People gather ↓ The space reacts ↓ The light changes ↓ The wall opens ↓ The sound changes ↓ People move ↓ The architecture reacts again. A system that continuously changes its state through interaction with users. 人・都市・情報に応答し続ける、知的で開かれた文化装置 Architecture that acts like a living inte

"A smooth space is broken down by a single point, line, or plane, and a curved surface is where structure and meaning converge." Singularity Surface Architecture: Architecture where points of failure generate space. 滑らかさではなく、破綻を設計する建築 「空間のエラー」が神聖な中心 Mathematical Architecture space

The world of architecture is constantly evolving. In particular, new perspectives on architectural design that transcend gravity are creating innovative designs that go beyond the conventional framework of architecture by translating mathematical theories and abstract concepts into spatial ideas and visual forms. This article explores the forefront of architectural design using mathematical approaches such as chaos theory, topology, and higher-dimensional geometry, and explai

A mathematical and logical theory that considers "types of things" as "shapes of space." type = space Element = Point in space Equality = the path connecting two points Equality between equals = Transformation of roads This approach involves continuously deforming shapes without cutting or pasting them, and considering them to be the same. A cup is roughly equivalent to a donut; if deformed continuously, it will have the same structure. “変形し続ける空間”として読む理論 A new mathematical fo

The world of architecture is creating unprecedented and innovative spaces through the fusion of mathematical concepts and cutting-edge technology. In particular, attempts to apply abstract mathematical ideas such as chaos theory, topology, and higher-dimensional geometry to architecture to achieve gravity-defying, floating designs are attracting attention. This article will provide a detailed explanation of the applications and future prospects of these innovative architectur

Algebraic spaces that operate using multiplication It's not a "point," but a space created by ratios, magnifications, and scale transformations. Algebraic, lattice-based, controlled deformations The same structure, but on different scales, chains together in a multiplicative manner. Algebraic Torus Architecture　 Multiplicative Space / Scaling Geometry A cultural landscape where scales proliferate in a chain reaction. Mathematical Architecture space

This approach involves updating predictions and probabilities whenever new information becomes available. First prediction ↓ Obtain evidence ↓ Update your forecast The probability is updated each time more information is added. Architecture where space gradually learns and adapts to its optimal state. 無数の可能性が重なり合った形 "Probability Field Architecture" " Architecture is only possible because information is constantly being updated ." Mathematical Architecture space

The sense of time, rhythm, and changes that occur within living organisms 1. Body clock 2. Time for Growth 3. Seasonal Time 4. Metabolism time Time that manifests as changes in life 成長し、変化し、劣化し、回復し、季節に反応する空間 Biological time is "the structure of time that living organisms possess within themselves." Mathematical Architecture space

Geometry that "the space itself is in a state of collapse." "Self-intersecting architecture of space" 1. Central singularity 2. Self-penetrating traffic flow 3. The collapse of the front and back. "Space that collapses due to projection" Mathematics → Structure → Space → Experience "Space as a limit of perception" 自己交差型代数曲面 Mathematical Architecture space

A theory that considers "how short a program can be used to represent a given piece of information." For example, let's compare the following two: A 111111111111111111111111111111 this is, "Repeat 1 30 times" It can be explained briefly as follows: In other words, the amount of information is small. B 101001110100101101011000111010 The rules are not very clear, so we have no choice but to write it almost exactly as it is. In other words, there is a lot of information. The mor

"An invisible spatial structure generated by zero point placement" 1. Aperiodic resonance city 2. The Architecture of the "Invisible Order" 3. Become an architectural masterpiece of light. "The deep frequencies of the universe" 夜になると金色の光点群が浮遊する A hall that seems to have become a building in itself, a "space of resonance." Architecture that doesn't focus on form, but rather on conveying an invisible order . "Architecture like a constellation": The interior space of a gigantic

A quantity that measures how much the "true probability distribution" differs from the "approximated probability distribution". "The amount of extra information needed due to using the wrong model." "The discrepancy between the spatial use envisioned by the designer and the actual usage patterns." The difference between "predicted cities" and "actual cities" Architecture that optimizes probability distributions, rather than architecture that designs form. "An information syst

A space in which countless triangular orders are hyperbolically folded, resulting in a space that possesses perfect symmetry as a whole. Surfaces of genus 3 It has a topology with three holes. 168 symmetries It possesses the greatest symmetry among Riemann surfaces of genus 3. The number "168" is extremely important. Related to hyperbolic geometry It's easier to understand if you think of it not as a plane, but as an order in a space with negative curvature. 「3つの大きな空洞を持つ双曲的な文

"A theory that defines 'quantities' such as length, area, volume, and probability for very general spaces." Geometry → “shape” Topological space → "connection" Measure theory → "How much does it exist?" 1. Set XXX 2. σ-additive family (sigma algebra) 3. Measure μ\muμ Fourier analysis Quantum mechanics Chaos theory geometry information theory These connections lead to → probability theory → "designing density" → from "object" to "distribution field". 「空間内に何がどれくらい存在するかを見る」 Arch

"A three-dimensional object in which there is no distinction between inside and outside." 1️⃣ There is no front or back. 2️⃣ There are no boundaries. 3️⃣ In 4th dimension, they do not self-intersect. The sequence is: city → building → city → building. 「内外の連続」＋「有機的な膨張」 Landscape architecture Looking at the cross-sectional diagram makes the mechanism of a Klein bottle instantly clear. 建物に入った瞬間が存在しない 「街の中に“外”と“内”が存在しない都市」 　 "The city itself is inverting into space." The boundar

The shape changes depending on the viewpoint, and perspective, vanishing points, and depth themselves constitute the structure. Perspective / Vanishing Point / Infinite Horizon Architecture Projective Variety Architecture Parallel lines intersect at infinity. 射影多様体建築の原理 Mathematical Architecture space

Architecture is not merely the design of space; by applying mathematical principles and theories, it creates unprecedented and innovative forms and structures. In particular, translating abstract mathematical concepts such as chaos theory, topology, and higher-dimensional geometry into spatial ideas and visual forms has made it possible to create architectural designs that defy gravity and possess a sense of weightlessness. This article explores in detail the influence of mat