Topology is a field that studies the differences in shape between loops (knots) of strings in space. Famous knot Trefoil knot (three-leaf knot) The simplest non-trivial knot Figure-eight knot (a knot shaped like the number eight) It will never be the same shape as the Trefoil. Jones polynomial The "fingerprint" of a knot What is a knot? Circle S1S1S1 embedded in 3D space R3\mathbb{R}^3R3 Knot Culture Hall Möbius Knot Opera House Mathematical Architecture space

● Spatial structure A long hall Cut out the center The remaining part is also cut in the middle. Repeat that infinitely Splitting in a fractal pattern ● Architectural features ① Fractal Corridor ② Chapel of Light ③ Infinite Altar ● Architectural philosophy mathematics religious space infinite set God countless points people emptiness The realm of God "God dwells in infinite emptiness." Mathematical Architecture space

The world of mathematics gives rise to shapes as complex as the universe. The formula is unusually simple Yet infinite complexity When you zoom in, a new world appears forever. The boundaries are infinitely complex. 都市の中に都市があり、その中にまた都市がある A city like a galaxy 都市全体が巨大なフラクタル迷宮 Mathematical Architecture space

● Spatial structure A long hall Cut out the center The remaining part is also cut in the middle. Repeat that infinitely Splitting in a fractal pattern ● Architectural features ① Fractal Corridor ② Chapel of Light ③ Infinite Altar ● Architectural philosophy mathematics religious space infinite set God countless points people emptiness The realm of God "God dwells in infinite emptiness." Mathematical Architecture space

A space that expands infinitely within a circle, yet visually it appears to be contained within a finite circle— a rather不思議 (mysterious/strange) space. ① Straight lines curve ② Distorted sense of distance ③ Infinitely many parallel lines A visualization of hyperbolic geometry 有限の円に見えるけど、内部は無限に広がる曲がった空間 "The center is stable, while the outer perimeter can extend infinitely." Endless corridor Space with gravity at its center A city that stretches outwards Mathematical Archit

"A space created by gathering all the 'shapes (structures)' that satisfy certain conditions, and then classifying and organizing them." "A space in which geometric and algebraic objects are classified by 'grouping similar objects together as one.'" ● Circle Moduli ● Moduli of a donut (torus) Not "space itself," but "space of space." "A space that uses differences in shape as coordinates." Mathematical Architecture space