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The general function y(a,b,c,d)=csin{pi/(b-a)[((b-a)x/d+a)^2-a^2]}.

A syllogism, also known as a rule of inference, is a formal logical scheme used to draw a conclusion from a set of premises. An example of a syllogism is modus ponens.

A mathematical object is said to be symmetric if it is invariant ("looks the same") under a symmetry transformation. A function, matrix, etc., is symmetric if it remains ...

A symmetry group is a group of symmetry-preserving operations, i.e., rotations, reflections, and inversions (Arfken 1985, p. 245).

A topological space fulfilling the T0-separation axiom: For any two points x,y in X, there is an open set U such that x in U and y not in U or y in U and x not in U. ...

A topological space fulfilling the T3-separation axiom: X fulfils the T1-separation axiom and is regular. According to the terminology of Alexandroff and Hopf (1972), ...

A topological space X fulfils the T1-separation axiom and is normal. A space fulfilling the T_4-separation axiom is said to be a T4-space.

A topological space fulfilling the T_4-axiom: X fulfils the T1-separation axiom and is normal. In the terminology of Alexandroff and Hopf (1972), T_4-space are called Tietze ...

A double point at which two (or more) osculating curves are tangent. The above plot shows the tacnode of the curve 2x^4-3x^2y+y^2-2y^3+y^4=0. The capricornoid and links curve ...

A knot equivalent to a polygonal knot. Knots which are not tame are called wild knots.