Architecture can be viewed not merely as a physical "thing," but as a "continuous space" where boundaries blend together, surfaces transform, and space flows without interruption. This perspective transcends conventional architectural concepts and invites us into the world of mathematical architecture, incorporating mathematical structures and topology. This time, we will introduce a new perspective on architecture centered on continuity and topology, along with specific meth

"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

"The phenomenon in which the boundary grows according to the gradient of the field." 1. Dendritic crystals (snow crystals) 2. Electric discharge (lightning) 3. The boundary between oil and water "The most unstable, yet the most natural" 「空間が自己生成する」 拡散律速凝集 CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=641439 サフマン・テイラー不安定性 By Claire Trease, Kingston University - Own work, CC BY-SA 4.0,https://commons.wikimedia.org/w/index.php?curid=45344174 Now let's consider sk

"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

As an ebook nears completion, anticipation grows, along with thoughts about its content and how it can be used. In particular, ebooks dealing with themes gaining attention in contemporary design fields, such as #Parametric Design, #Generative Art, and #Algorithmic Architecture, become valuable learning resources for students and creators. This article will introduce the appeal of an ebook nearing completion and offer practical ways to utilize it. What is the appeal of ebooks?

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