the Saddle

A saddle, in math, is a surface that curves upward in one direction and downward in another, resembling a horse’s saddle. Imagine a shape like a Pringles potato chip or a saddle on a horse: it bends up along one axis and down along the perpendicular axis. This creates a point called a saddle point, where the surface is flat but not a peak or valley. Saddles are important in calculus for analyzing how functions behave, especially when studying where a surface changes from increasing to decreasing or vice versa.