A design proposal with triply periodic minimal surfaces

People has developed different types of communication methods in order to explain their works to another who is either collabration or customer. In the first ages people were using drawings and then common language and writing. Then people started to theorize some professions like maths, physics, chemistry and so on. Geometry which is evolved in order to understand objects in nature and their relations, is probably the most influential branch of knowledge for architecture. Because architects used goemetry for representing and building of their works. Geometry became one of the fundamental element which shapes architectural thought. Scientists like Euclid, Pythagoras, Archimedes, Leonardo Da Vinci and Descartes keep continiously develop geometrical principles which is used in architecture often. Planar geometry which is developed by one of the most important geometrician Euclid, used for agelong by people architects in order to smybolise things. Today with the impact of geometries that is not fitting Euclid's fifth postulate, also called non-Euclidean geometries, and computational design methods put architecture into another dimensions. Topics that needs specialists to implement like topological geometry, algeabric geometry, fractal geometry, differantial geometry become doable in architectural design thanks to tools of computational design. While architects are using these geometry topics, they also creates new problems that can be subject in geometric researchs. Geometry also plays a mayor role in architectural education. It can be said that students can produce what they do understand. As the all of the people we are teached geometry that is Euclidean from their childhood. So our geometrical thinking is shaped by Euclid's way of thinking. It can be said that architects and architecture students mostly designs in Euclid's way. In last few decades there are lots of discussions about what can be done with other geometries and what is the pros&cons of designs that is formed by these geometrical thoughts. Minimal surfaces are one of the common subject of differantial geometry. With their lots of physical advantages like using minimum material, the complex shapes they form is an interesting point for architects from the begining. At first, scientists and architects do physical experiments like shaping soap-bubble in order to set up rules of their shapes and geometrical explanations. The basic principle of minimal surfaces is the mean curvature of every point of this surface must be equal to zero, and also sum of the mean curvature values is equal to zero. With the aim of the computational techonologies, people solved more complex problems that is fitting this simple principle and bring out more complex examples of minimal surfaces. Frei Otto was the most important architecture who used physical experiments as an inspiration in his designs. He designed some of his well-noted projects like Roof of Munich Olimpic Stadium following to his experiments with soap bubbles. Periodic minimal surfaces that is based on continuum of minimality principle of these surfaces is a subject for not only geometry but also biology, chemistry etc. These surfaces were studied first at the last years of 19. century. After almost nine decades periodic minimal surfaces appealed to geometricians and space scientists. With the power of computer techonologies scientists find out lots of new periodic minimal surfaces. These surfaces also has lots of inspirations in sculpteral works. Some artists like Erwin Hauer, Carlos Séquin produced lots of pieces that is derived from periodic minimal surfaces. And also they contributed the geometrical basis of these minimal surfaces. In architecture, there are some designs and works especiallt made with Triply Periodic Minimal Surfaces. In this work these some examples are given according to what they form utmost. Some of these works used minimal surfaces because of their natural equilibrium, some of them used because they find their sculptural shape interesting and some of them used them trying to generate a systematic design with repetitions of periodic minimal surfaces. After research of geometrical basis and architectural use of Triply Periodic Minimal Surfaces this work tries to use Triply Periodic Minimal Surfaces not stickly to they are formed with their boundary shapes in geometrical definitions, but they deformed and derived in an architectural use for designing a space. The model developed in Rhino-Grasshopper with this logic, crates boundary shapes that is calculated as a subdivisons of a given polygonal area and derives Triply Periodic Minimal Surfaces that is defomered according to these boundary shapes. After designing this space out of periodic mnimal surfaces, a mean curvature analysis of these individual surfaces are examined in order to check if deformation breaks the gometrical concept of minimal surfaces or not. And also this study produces a physical model of this very last design by 3D printing the periodic surfaces.