Architects: Oficina de Arquitectura X
Area: 125 m²
Year: 2022
Photography: Leonardo Méndez
Lead Architects: Nicole Jaquet, Felipe Ramirez Ilculese
Structure Consultants: Felipe Ramirez Ilculese
City: Asunción
Country: Paraguay
In Asunción, Paraguay, the architectural firm Oficina de Arquitectura X, under the leadership of Nicole Jaquet and Felipe Ramirez Ilculese, tackled a unique challenge. Tasked with optimizing space between party walls using a limited supply of bricks, the team devised a mathematical strategy to maximize the area while minimizing the perimeter. Their solution, rooted in geometric principles, produced a design centered around a prism with a square base—a shape proven to provide the most efficient use of space. This project, showcased through Leonardo Méndez’s vivid photography, highlights the synthesis of architectural creativity and mathematical precision. The result is not only a functional residential space but also an artistic expression of mathematical aesthetics in architecture.
“Everything is a number,” said Pythagoras. This project was driven by the challenge of using a finite number of bricks to construct a house between party walls while seeking to maximize the area and minimize the perimeter.
Ground floor plans and other visuals by Leonardo Méndez accompany the description of the solution: a deductive logical method. The first premise posits that any change in shape increases the surface area, and the second states that the only feasible shapes between party walls are rectilinear. The conclusion reached is that a pure prism with a rectangular base is optimal.
Mathematical equations further refine the design approach. Calculating area (Area = X.Y where Y = A/X) and perimeter (Perimeter = 2X + 2Y or P = 2X + 2A/X), a function for perimeter is derived and differentiated concerning X, setting the result to zero to solve for X, thus determining that Y = X, and the optimal shape is a square.
Further mathematical proofs using second derivatives establish that a square indeed provides the minimum perimeter for the maximum area. This theoretical solution materializes into the actual structure of a pure prism based on a square base, resting on a foundation slab that also serves as the floor. The design cleverly integrates geometric figures into the floor plan, anchored by a central pillar that organizes and defines the internal spaces.
The construction technique features walls and ceilings composed of visible ceramic bricks laid in a specified pattern (Brick laying type A), using a dry polymeric adhesive to minimize waste and eliminate undesired joints. The design ensures a meticulously managed lighting environment, enhancing the living experience within the mathematical constraints set out at the project’s conception.
In summary, the project not only questions whether numbers alone can define architecture or construction but also showcases how theoretical mathematics can directly influence practical architectural solutions.
Project Gallery
Project Location
Address: Dr. Adriano Irala, Ayolas, Asunción, Paraguay
Location is for general reference and may represent a city or country, not necessarily a precise address.
