In mathematics, a saddle point is a point in the domain of a function that is a stationary point but not a local extremum. The name derives from the fact that the prototypical example in two dimensions is a surface that curves up in one direction, and curves down in a different direction, resembling a saddle or a mountain pass. In terms of contour lines, a saddle point in two dimensions gives rise to a contour that appears to intersect itself.
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 at the stationary point is the matrix
which is indefinite. Therefore, this point is a saddle point. This criterion gives only a sufficient condition. For example, the point is a saddle point for the function but the Hessian matrix of this function at the origin is the null matrix, which is not indefinite.
Saddle Point (53°1′S 73°29′E / 53.017°S 73.483°E / -53.017; 73.483Coordinates: 53°1′S 73°29′E / 53.017°S 73.483°E / -53.017; 73.483) is a rocky point separating Corinthian Bay and Mechanics Bay on the north coast of Heard Island in the Antarctic.
The terminus of Challenger Glacier is located at the eastern side of Corinthian Bay, close west to Saddle Point. To the east of Challenger Glacier is Downes Glacier, whose terminus is located at Mechanics Bay, between Saddle Point and Cape Bidlingmaier.
The name was applied by American sealers at Heard Island following their initiation of sealing there in 1855.
This article incorporates public domain material from the United States Geological Survey document "Saddle Point" (content from the Geographic Names Information System).
Is this what you waited for for
A chance to take the floor
With my head
'Cause no one else is hanging on
The people who stood are long gone
You've free reign
And my blood runs cold
That someone you could have known
Would wish you to dust and bones
Hemorrhaging
What now you tell me I'm wrong
Play on my trust like you've always done
It won't fly
I had to watch people leave
Don't recall you there to comfort me
So don't lie
Light the sky
Take me homewards
All this time
Moving forwards (x3)
Light the sky
Take me homewards