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Titze's extension theorem
Values defined continuously within a closed subspace can be extended to the entire space while maintaining continuity, provided the conditions are favorable. This approach involves extending the "continuous conditions" such as light, temperature, sound, and density present in parts of existing buildings naturally into the city and surrounding space, rather than abruptly cutting them off at the boundary. 中央の明るいホールを「局所で定義された連続性」とし、屋根・床・テラス・階段・広場の水平レイヤーがそのまま外部へ拡張していく構成 A hall wh

Yuki
Aug 31 min read


Green's Theorem
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

Yuki
Aug 11 min read


Noter's Theorem
"The symmetry of natural laws gives rise to conservation laws." Symmetry is not about visual beauty, but a principle that determines what the world preserves. 対称性によって空間の安定が保存される The golden axis extending from the circular void at the top to the stage and the center of the audience seating is "the amount to be preserved". The surrounding balconies and radial acoustic ribs unfold symmetrically, and the movements, sounds, and lights of the audience all converge towards an unchan

Yuki
Jul 301 min read


Divergence Theorem
The amount of "flow" that is created and disappears within a given space is equal to the total amount of flow that enters and leaves the surface of that space. "What happens internally is reflected at the interface." 内部の「発散」が建築の外皮に現れる With the central stage as the "source" of emission, golden light and movement lines radiate from the floor to the audience, walls, and ceiling, finally exiting through vertical slits in the ceiling. The relationship where "the total amount produ

Yuki
Jul 291 min read


Jordan curve theorem
When you draw closed lines that do not intersect on a plane, the plane is always divided into an "inside" and an "outside". It is only by placing a continuous boundary that the concepts of "inside" and "outside" are created. ONE CONTINUOUS BOUNDARY CREATES INSIDE AND OUTSIDE. A single, non-intersecting closed curve forms the entire structure, clearly separating the central courtyard as the "inside" from the urban plaza as the "outside." The main entrance symbolizes the moment

Yuki
Jul 271 min read


Brouwer's fixed-point theorem
If you move a disc or sphere continuously without cutting or flying it, at least one point will always remain in its original position. There is at least one point where the "actual floor position" and the "position depicted on the map" perfectly coincide. Architecture where everything appears to be in motion, yet there is always one unmoving center. 黒い曲面屋根:連続的に変形する空間 A thin, golden light at the center of the stage is the "fixed point." Even though the entire surrounding spac

Yuki
Jul 261 min read
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