Abstract: Architecture and music are inextricably linked no matter from internal structure or external form of expression, as the most dominant and leading basic discipline, mathematics is always using its incomparable logic and the axiomatic collection model to influence and promote the development and transformation of architecture and music creation. Based on the theoretical knowledge of natural science and aesthetics, taking the most representative ancient Greek and Baroque periods in the history of natural science and culture in the West as examples, combining visual pictures and digital models to explore a variety of translation models between mathematics, architecture and music, summarize the theories and characteristics of the aesthetic connection of architecture, music, and mathematics in different periods, to provide new ideas and application models for better realization of cross-border design.

Key words: architecture, music, mathematics, aesthetic connection, landscape design