The curve of a mountain is like the curve of a frown! Turn that frown upside down and get back in the saddle instead! Saddles have beautiful views, nice breezes in summertime, and are great places to have lunch. It's well known that saddles are preferred travel routes for wildlife. (Ever see a bear on a peak? Of course not!)
Please help us compile the official list. Like the Hundred Peaks, there are some (Islip Saddle...ahem) that are easier than others (Gunsight Notch anyone?)
Gaps and notches count, so long as they fit the mathematical regulations for Indefinite Hessians. This is all quite simple to understand:
(source: http://en.wikipedia.org/wiki/Saddle_point)A simple criterion for checking if a given stationary point of a real-valued function F(x,y) of two real variables is a saddle point is to compute the function's Hessian matrix at that point: if the Hessian is indefinite, then that point is a saddle point. For example, the Hessian matrix of the function z = x2 − y2 at the stationary point (0,0) is the matrix
which is indefinite. Therefore, this point is a saddle point. This criterion gives only a sufficient condition. For example, the point (0,0) is a saddle point for the function z = x4 − y4, but the Hessian matrix of this function at the origin is the null matrix, which is not indefinite.
Saddle Bagging can obviously be combined with Peak Bagging, or Near Peak Bagging, and some saddles are worthy enough hikes on their own (such as Icehouse Saddle, Dawson Saddle, and that cool one between Icehouse and Cucamonga Peak.) Discover one, and we'll name it after you!
Thank you for your attention in this very serious matter and we look forward to your comments and suggestions.
i'll bring the popcorn.