Geometry is an integral part of design from start to finish.
Just think about it. Architects use geometry to study and divide space. As well as draft detailed building plans. Builders and engineers rely on geometric principles to create structures safely. Designers apply geometry (along with color and scale), to make the aesthetically pleasing. Applying geometry in design is unavoidable.
We have plenty of examples of creative applications of geometry. From the elaborate patterns found within Islamic architecture. To also the complex fractals in Pollock’s drip paintings.
To the clean lines of modern interiors. Why is geometry such an enduring foundation of our work? Because how can we apply it in ways. Not only appeal to our senses but also to our sense of well-being.
Short answer — look to nature.