Caught in the headlight

The Wave is a sandstone rock formation located in the United States of America near the Arizona and Utah border on the slopes of the Coyote Buttes, in the Paria Canyon-Vermilion Cliffs Wilderness, on the Colorado Plateau. It is famous among hikers and photographers for its colorful, undulating forms, and the rugged, trackless hike required to reach it.

In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but which is not required to be straight. This entails that a line is a special case of curve, namely a curve with null curvature. Often curves in two-dimensional (plane curves) or three-dimensional (space curves) Euclidean space are of interest.

Various disciplines within mathematics have given the term different meanings depending on the area of study, so the precise meaning depends on context. However many of these meanings are special instances of the definition which follows. A curve is a topological space which is locally homeomorphic to a line. In everyday language, this means that a curve is a set of points which, near each of its points, looks like a line, up to a deformation. A simple example of a curve is the parabola, shown to the right. A large number of other curves have been studied in multiple mathematical fields.

The term curve has several meanings in non-mathematical language as well. For example, it can be almost synonymous with mathematical function (as in learning curve), or graph of a function (as in Phillips curve).

Coyote Buttes is a section of the Paria Canyon-Vermilion Cliffs Wilderness managed by the Bureau of Land Management (BLM), spanning extreme South Central Utah and North Central Arizona, just south of US 89 halfway between Kanab, Utah and Page, Arizona. It is divided into two areas: Coyote Buttes North and Coyote Buttes South. Visiting either of the Coyote Buttes areas requires purchasing a hiking permit.

The Coyote Buttes area is an exposure of cross-bedded aeolian Jurassic Navajo Sandstone. The variable coloration of the sandstones is a result of various iron oxide pigments within the layers. A dinosaur trackway or trample surface is found in the area and provides evidence of a variety of dinosaurs. The area includes dramatic swirling erosional rock formations such as The Wave.

The Wave and Buckskin Gulch share the Wire Pass Trailhead on House Rock Valley Road.