"A polygon with an infinite number of sides" "Apeirogon" comes from the Greek words apeiros (infinity) + gonia (horn). "A way of thinking that views a circle as a 'polygon that is infinitely divided'" 終わらない回廊都市 ● Architecture with an endless corridor ● Deconstruction of a circular hall ● Architecture where only the boundary exists Mathematical Architecture space

"A phenomenon where a state changes suddenly, almost as if it's flying, after having been changing slowly." The form "cusp" Space is gradually compressed. In a sense, "the view suddenly opens up." The flow of movement suddenly branches or reverses. Architecture that creates a continuous space, yet the experience is discontinuous. 連続変化 → 突然の空間ジャンプ The ball is in a valley. The terrain gradually changes. At a certain moment, it jumps into another valley. This "jumping" becomes

The outer space becomes incredibly complex. Strange topology 絡まり地獄 Hilbert Hotel Architecture A crazy space Mathematical Architecture space

It's continuous (not interrupted), yet it can't be differentiated anywhere (the slope cannot be defined). A space where details continue endlessly f(x)=n=0∑∞​ancos(bnπx) Curved surfaces vibrate infinitely; slabs become fractalized ; light creates abnormal shadows. Mathematical Architecture Mathematical Architecture space

"Cities may appear random, but in reality, they are made up of self-similarity (fractals) and nonlinearity (chaos)." ① Hierarchical design of scale 👉 This creates a "comfortable atmosphere" ② Network optimization 👉 Resilient to disasters and congestion ③ Blurring of boundaries 👉 Spaces with chaotic "fluctuations" "Designing growth rules" 「建築というより小都市」 "A cultural hall without a central point"

"A geometric space for treating time and space as a single entity." 4th dimension (3-dimensional space + time) → The very stage of the theory of relativity → "A collection of trajectories extended in the time direction" "A coordinate system of the universe that includes time" Mathematical Architecture 's "Riemannian Manifold Architecture"