The saddle between two hills or mountains is the region surrounding the

saddle point In mathematics, a saddle point or minimax point is a Point (geometry), point on the surface (mathematics), surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero (a Critical point (mathematics), ...

, the lowest point on the line tracing the drainage divide (the col) connecting the peaks. When, and if, the saddle is navigable, even if only on foot, the saddle of a (optimal) pass between the two

massif A massif () is a principal mountain mass, such as a compact portion of a mountain range, containing one or more summits (e.g. France's Massif Central). In mountaineering literature, ''massif'' is frequently used to denote the main mass of an ...

s, is the area generally found around the lowest route on which one could pass between the two summits, which includes that point which is a mathematically when graphed a relative high along one axis, and a relative low in the perpendicular axis, simultaneously; that point being by definition the col of the saddle.

Topography

A saddle is the lowest area between two highlands ( prominences or peaks) which has two wings which span the divide (the line between the two prominences) by crossing the divide at an angle, and, so is concurrently the local highpoint of the land surface which falls off in the lower direction. That is, the

drainage divide A drainage divide, water divide, ridgeline, watershed, water parting or height of land is elevated terrain that separates neighboring drainage basins. On rugged land, the divide lies along topographical ridges, and may be in the form of a single ...

is a ridge along the high point of the saddle, as well as between the two peaks and so defines the major reference axis. A saddle can vary from a sharp, narrow gap to a broad, comfortable, sway-backed, shallow valley so long as it is both the high point in the sloping faces which descends to lower elevations and the low area between the two (or three or four.) flanking summits. Concurrently, along a different axis, it is the low point between two peaks, so as such, is the likely 'optimal' high point in a pass if the saddle is traversed by a track, road or railway.

Saddles and cols

The relationship between saddles and cols is not universally agreed upon. A col is sometimes defined as the lowest point on a saddle co-linear with the drainage divide that connects the peaks. Whittow describes a saddle as ''"low point or col on a ridge between two summits"'', whilst the

Oxford Dictionary of English The ''Oxford Dictionary of English'' (''ODE'') is a single-volume English dictionary published by Oxford University Press, first published in 1998 as ''The New Oxford Dictionary of English'' (''NODE''). The word "New" was dropped from the titl ...

implies that a col is the lowest point on the saddle. Monkhouse describes a saddle as a ''"broad, flat col in a ridge between two mountain summits."'' The term col tends to be associated more with mountain, rather than hill, ranges. The height of a summit above its highest saddle (called the key saddle) is effectively a measure of a hill's prominence, an important measure of the independence of its summit. Saddles lie on the line of the watershed between two

hill A hill is a landform that extends above the surrounding terrain. It often has a distinct summit, and is usually applied to peaks which are above elevation compared to the relative landmass, though not as prominent as Mountain, mountains. Hills ...

Structural geology

structural geology Structural geology is the study of the three-dimensional distribution of rock units with respect to their deformational histories. The primary goal of structural geology is to use measurements of present-day rock geometries to uncover informati ...

, a saddle is a depression located along the axial trend of an

anticline In structural geology, an anticline is a type of Fold (geology), fold that is an arch-like shape and has its oldest Bed (geology), beds at its core, whereas a syncline is the inverse of an anticline. A typical anticline is convex curve, c ...

Mathematical saddles

A 'saddle point' in

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

derives its name from the fact that the prototypical example in two dimensions is a

surface A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is ...

that ''curves up'' in one direction, and ''curves down'' in a different direction, resembling a riding

saddle A saddle is a supportive structure for a rider of an animal, fastened to an animal's back by a girth. The most common type is equestrian. However, specialized saddles have been created for oxen, camels and other animals. It is not know ...

or a

mountain pass A mountain pass is a navigable route through a mountain range or over a ridge. Since mountain ranges can present formidable barriers to travel, passes have played a key role in trade, war, and both Human migration, human and animal migration t ...

between two peaks forming a landform saddle.

Notes

References

{{Structural geology Landforms Oronyms Structural geology