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 on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero (a critical point), but which is not a local extremum of the function ...

, 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 Pass, PASS, The Pass or Passed may refer to: Places * Pass, County Meath, a townland in Ireland * Pass, Poland, a village in Poland * Pass, an alternate term for a number of straits: see List of straits * Mountain pass, a lower place in a moun ...

between the two

massif In geology, a massif ( or ) is a section of a planet's crust that is demarcated by faults or flexures. In the movement of the crust, a massif tends to retain its internal structure while being displaced as a whole. The term also refers to a ...

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 (

prominence In topography, prominence (also referred to as autonomous height, relative height, and shoulder drop in US English, and drop or relative height in British English) measures the height of a mountain or hill's summit relative to the lowest contou ...

s 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 singl ...

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. 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 In topography, prominence (also referred to as autonomous height, relative height, and shoulder drop in US English, and drop or relative height in British English) measures the height of a mountain or hill's summit relative to the lowest contou ...

) is effectively a measure of a hill's

, 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 (topography), summit. Terminology The distinction between a hill and a mountain is unclear and largely subjective, but a hill is universally con ...

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 informatio ...

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

anticline In structural geology, an anticline is a type of fold that is an arch-like shape and has its oldest beds at its core, whereas a syncline is the inverse of an anticline. A typical anticline is convex up in which the hinge or crest is the ...

Mathematical saddles

A 'saddle point' in

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

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 The 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 kno ...

or a

mountain pass A mountain pass is a navigable route through a mountain range or over a ridge. Since many of the world's mountain ranges have presented formidable barriers to travel, passes have played a key role in trade, war, and both Human migration, human a ...

between two peaks forming a landform saddle.

Notes

References

{{Structural geology Landforms Oronyms Structural geology