# Mathematics And Saddle

By: James Monahan

Usually the term saddle makes us think about the seat in a horse back or the seat in a bicycle or in a motorcycle.

In horseback riding, the saddle is the seat that horse riders use to keep themselves firmly sitting upon the horse's back. It is attached to the horse using a girth and a wide strap. The wide strap will go around the horse to keep the seat from moving.

It is most important that the saddle will keep both horse and rider comfortable to avoid injury to both of them. Saddles may either be English saddles or Western saddle depending on what purpose they are used for.

An English Saddle is used for Polo, Racing, Jumping, Show, Dressage, Park, Show or it can be an All Purpose Saddle. Western Saddles on the other hand are used for Trail, Endurance, Pleasure, Barrel and Roping activities. While Sidesaddles, Australian saddles and Military saddles do not fall into either category.

Although this is true, as is a saddle is also a meat part of mutton, lamb, venison or veal that is from both sides of the animal consisting of its unseparated meat from its rib to its leg or that it could mean the passage found between the low area of hills or mountains.

In construction terms, a saddle is a piece of wood that serves as a decoration covering sections of different materials or heights.

But as weird as it may seem, the term saddle is also connected with mathematics. In this field, a saddle point is a point of one or more valuables (commonly known as function).

Tat is both stationary point (this is a part of calculus that explains the parallelism of tangent to the x ? axis of the graph or when the plane tangent is parallel to the surface of the XY plane.

In the saddle point, the funcion of its single variable is the point where zero is its first derivative, the second derivative on this case, changes the sign. To better explain it, in the example the funtion of y = x3 has the same point as the origin.

The reason that a saddle point is called as such, because in a function with two or more variables, the two dimensional topological space (surface) looks like a saddle that is curving up in one or more directions and also curves down in one or more direction (kind of like a mountain passage or saddle).

In a contour line, the saddle point is apparent by the contour that seems to intersect itself. Example, a saddle point can be recognised in two mountains or hills separated by a high pass. At the top of this pass, one will be able to see a figure eight-like contour that forms the saddle.

For two variables with a real function mathematics used the Hessian matrix to have 2x2 matrix. This is a function that has a curving down pattern along the x and a curving up pattern along the y thus creating the saddle point.,

Also, there is what we call the saddle point approximation where in the steepest descent method is used to approximate integrals.

Saddle points are not only found in mathematics, physics also have their own saddle points. Between electron in solid and electrons in liquid, the wet electrons are considered the saddle point.

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James Monahan is the owner and Senior Editor of SaddlePlace.com and writes expert articles about saddles.