Non-Euclidean painting refers to an artistic style or approach that utilizes non-Euclidean concepts and principles in visual representation. Euclidean geometry, developed by the Greek mathematician Euclid, is the traditional form of geometry that studies the properties and relationships of figures in flat and three-dimensional space. In contrast, non-Euclidean geometry refers to various geometric systems that do not adhere to Euclid's postulates, such as hyperbolic geometry and elliptic geometry. These alternative geometric systems have different concepts of straight lines, angles, and curvatures, and may allow for the existence of figures and structures that are not possible in Euclidean geometry. In the context of painting, non-Euclidean painting can explore and represent forms and spaces that challenge the conventions of Euclidean geometry. This can include depictions of distorted figures and objects, unconventional perspectives, non-Euclidean geometric shapes, and visual illusions that play with perception.