arrête

Arête is a term used in geometry and geography. In geometry, an arête refers to the sharp edge or ridge formed by the intersection of two planes or faces. This concept is commonly encountered in the study of polyhedra, where edges are the line segments connecting vertices. A more specific geometrical term is a "ridge line," which is the line where two non-parallel planes intersect.

In geography and glaciology, an arête is a sharp, narrow mountain ridge that is typically formed when two glaciers erode a mountain. As the glaciers move down opposite sides of the mountain, they carve out valleys, leaving a steep, knife-like ridge between them. This process is known as glacial erosion. Arêtes are often found in glaciated mountain ranges, such as the Alps, the Himalayas, and the Andes. They can be challenging to traverse and are often sought after by mountaineers. The formation of an arête is a gradual process, dependent on the erosive power of glaciers and the geological structure of the mountain. Over time, the repeated freeze-thaw cycles and the movement of ice further sharpen and refine these ridges.