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Let a graph G have exactly 2n-3 graph edges, where n is the number of graph vertices in G. Then G is "generically" rigid in R^2 iff e^'<=2n^'-3 for every subgraph of G having ...

As Gauss showed in 1812, the hyperbolic tangent can be written using a continued fraction as tanhx=x/(1+(x^2)/(3+(x^2)/(5+...))) (Wall 1948, p. 349; Olds 1963, p. 138).

The Lyons group is the sporadic group Ly of order |Ly| = 51765179004000000 (1) = 2^8·3^7·5^6·7·11·31·37·67. (2) It is implemented in the Wolfram Language as LyonsGroupLy[].

The Maclaurin-Bézout theorem says that two curves of degree n intersect in n^2 points, so two cubics intersect in nine points. This means that n(n+3)/2 points do not always ...

If a_1, a_2, a_3, ... is an artistic sequence, then 1/a_1, 1/a_2, 1/a_3, ... is a melodic sequence. The recurrence relation obeyed by melodic series is ...

A graph G is called d-polytopal if there exists a d-dimensional convex polytope P such that the vertices and edges of G are in a one-to-one incidence-preserving ...

The projective special linear group PSL_n(q) is the group obtained from the special linear group SL_n(q) on factoring by the scalar matrices contained in that group. It is ...

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 ...