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A reducible fraction is a fraction p/q such that GCD(p,q)>1, i.e., p/q can be written in reduced form. A fraction that is not reducible is said to be irreducible. For ...

Let R+B be the number of monochromatic forced triangles (where R and B are the number of red and blue triangles) in an extremal graph. Then R+B=(n; 3)-|_1/2n|_1/4(n-1)^2_|_|, ...

The second Yff triangle is the Cevian triangle DeltaA^'B^'C^' of the second Yff point. The area of the second Yff triangle is Delta=(u^3)/(2R), where R is the circumradius of ...

A smooth map f:S^1->R^3 whose image has singularities. In particular, in the theory of Vassiliev's knot invariants, singular knots with a finite number of ordinary double ...

A polynomial equation whose roots all have negative real parts. For a real quadratic equation z^2+Bz+C=0, the stability conditions are B,C>0. For a real cubic equation ...

The locus of points whose first polars with regard to the curves of a linear net have a common point. It is also the locus of points of concurrence of line polars of points ...

The Suzuki group is the sporadic group Suz of order |Suz| = 448345497600 (1) = 2^(13)·3^7·5^2·7·11·13. (2) It is implemented in the Wolfram Language as SuzukiGroupSuz[].

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 ...

With n cuts of a torus of genus 1, the maximum number of pieces which can be obtained is N(n)=1/6(n^3+3n^2+8n). The first few terms are 2, 6, 13, 24, 40, 62, 91, 128, 174, ...

The triquetra is a geometric figure consisting of three mutually intersecting vesica piscis lens shapes, as illustrated above. The central region common to all three lenses ...