Spiral geometry refers to the study of spiral shapes and their mathematical properties. Spirals can be found in nature, such as in the shells of snails or the arrangement of seeds in a sunflower. They can be classified into different types, including Archimedean spirals and logarithmic spirals, each with unique equations and characteristics. In mathematics, spirals are often represented in polar coordinates, where the distance from the center increases as the angle changes. This allows for the creation of beautiful patterns and designs, which are not only aesthetically pleasing but also have applications in fields like architecture and art.