The term horse saddle is used, in contrast to monkey saddle, to designate a saddle point that is a minimax, that is to say a local minimum or maximum depending on the intersecting plane used. The monkey saddle has just a point of inflection. To see this, consider a line y = kx. Along this direction the surface becomes simply z = (1 − 3k2)x3, lacking any critical points.
Read more about this topic: Monkey Saddle
Famous quotes containing the words horse and/or saddle:
“We read that the traveller asked the boy if the swamp before him had a hard bottom. The boy replied that it had. But presently the traveller’s horse sank in up to the girths, and he observed to the boy, “I thought you said that this bog had a hard bottom.” “So it has,” answered the latter, “but you have not got half way to it yet.” So it is with the bogs and quicksands of society; but he is an old boy that knows it.”
—Henry David Thoreau (1817–1862)
“As the saddle makes the horse, so the tailor makes the man.”
—Chinese proverb.