Trend Of Non-Euclidean Geometry

This article starts with the definition of the Euclidean Geometry and the Non-Euclidean Geometry. In the Euclidean Geometry, all the things in the world are abstracted into simple forms. The characteristics of this geometry are idealization, abstraction and simplification. Non-Euclidean Geometry is any geometry that is different from Euclidean Geometry. It extends the edge of geometry and makes it possible to describe the complex and flexural form. It brings out a dynamic and uncertain space instead of the static and certain space.Looking back to the development history of architecture, we find that the form of the buildings is always based on Euclidean Geometry until the modernism period. It is related to the way we observe the world. Along with the development of science and technology, people pay more attention to the complexity that presented widely in the world and change their simplification world view which is based on Newton's Mechanics and Euclidean Geometry. Gradually, buildings'form which is based on the Non-Euclidean Geometry become smoother. It is also related to the contemporary technology, science, philosophy and aesthetics.The analysis of the form, which is built on geometry, nature and biology, technique, art and narrative architecture, is trying to find out the deep-structure of the forms and the origin of the designs. I hope that we can benefit from it in our design. Finally, this article analyses the characteristic of this form built on dynamic, uncertain, harmonized with nature and absence of culture. And complexity of this form is discussed through aspects of non-linear, uncertain form and the paradox of rationality and irrationality.