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A point of a function or surface which is a stationary point but not an extremum. An example of a one-dimensional function with a saddle point is f(x)=x^3, which has f^'(x) = ...

A point where a curve intersects itself along four arcs. The above plot shows the quadruple point at the origin of the quadrifolium (x^2+y^2)^3-4x^2y^2=0.

A point where a curve intersects itself along three arcs. The above plot shows the triple point at the origin of the trifolium (x^2+y^2)^2+3x^2y-y^3=0.

A point, such as interior points of a disk, such that (px)(py)=[const], where p is the chord length.

A fixed point is a point that does not change upon application of a map, system of differential equations, etc. In particular, a fixed point of a function f(x) is a point x_0 ...

A pivot point of a curve is a fixed point Q such that points P lying on the curve and their (isogonal, isotomic, etc.) conjugates are collinear with Q.

The fixed point with respect to which a pedal curve or pedal triangle is drawn.

A point that lies on one of the sides of a triangle but is a not vertex.

The point in the plane with Cartesian coordinates (1, 1).

A K-rational point is a point (X,Y) on an algebraic curve f(X,Y)=0, where X and Y are in a field K. For example, rational point in the field Q of ordinary rational numbers is ...