Geometry+in+Modern+Art


 * M.C. Escher** was a [|Dutch] [|graphic artist]. He is known for his often [|mathematically] inspired [|woodcuts], [|lithographs], and [|mezzotints]. These feature [|impossible constructions], explorations of [|infinity], [|architecture], and [|tessellations].

Mathematical Art of M.C. Escher Here's a PowerPoint used for middle and high school students

We have seen two different geometries so far: Euclidean and spherical geometry. Geometry is meant to describe the world around us, and the geometry then depends on some fundamental properties of the world we are describing. Objects that live in a flat world are described by Euclidean (or flat) geometry, while objects that live on a spherical world will need to be described by spherical geometry. In two dimensions there is a third geometry. This geometry is called **hyperbolic geometry**. If Euclidean geometry describes objects in a flat world or a plane, and spherical geometry describes objects on the sphere, what world does hyperbolic geometry describe? Like spherical geometry, which takes place on a sphere, hyperbolic geometry takes place on a curved two dimensional surface called **hyperbolic space**. We will describe hyperbolic space in several different ways. In Escher's work, hyperbolic space is a distorted disk. All of the angels in [|Circle Limit IV (Heaven and Hell)] live in hyperbolic space, where they are actually the same size, as do the devil figures. The image that Escher presents is a distorted map of the hyperbolic world. You can explore Escher's hyperbolic Circle Limit prints and get an introduction to hyperbolic geometry in the [|Escher's Circle Limit Exploration]
 * Hyperbolic Space **

More Hyperbolic Geometry Art by Escher