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"The" tetrahedral graph is the Platonic graph that is the unique polyhedral graph on four nodes which is also the complete graph K_4 and therefore also the wheel graph W_4. ...

"The" trifolium is the three-lobed folium with b=a, i.e., the 3-petalled rose curve. It is also known as the paquerette de mélibée (Apéry 1987, p. 85), with paquerette being ...

Consider the solid enclosed by the three hyperboloids specified by the inequalities x^2+y^2-z^2 <= 1 (1) y^2+z^2-x^2 <= 1 (2) z^2+x^2-y^2 <= 1. (3) This work dubs this solid ...

As defined by Gray (1997, p. 201), Viviani's curve, sometimes also called Viviani's window, is the space curve giving the intersection of the cylinder of radius a and center ...

All the propositions in projective geometry occur in dual pairs which have the property that, starting from either proposition of a pair, the other can be immediately ...

The set of terms of first-order logic (also known as first-order predicate calculus) is defined by the following rules: 1. A variable is a term. 2. If f is an n-place ...

An arithmetic progression, also known as an arithmetic sequence, is a sequence of n numbers {a_0+kd}_(k=0)^(n-1) such that the differences between successive terms is a ...

Erdős proved that there exist at least one prime of the form 4k+1 and at least one prime of the form 4k+3 between n and 2n for all n>6.

The conditional probability of an event A assuming that B has occurred, denoted P(A|B), equals P(A|B)=(P(A intersection B))/(P(B)), (1) which can be proven directly using a ...

The absence of contradiction (i.e., the ability to prove that a statement and its negative are both true) in an Axiomatic system is known as consistency.