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The inverse curve of the lituus is an Archimedean spiral with m=2, which is Fermat's spiral.

When a pair of non-incident edges of a tetrahedron is chosen, the midpoints of the remaining 4 edges are the vertices of a planar parallelogram. Furthermore, the area of this ...

The symmetry operation (x,y,z)->(x,y,-z), etc., which is equivalent to 2^_, where the bar denotes an improper rotation.

A tensor g whose discriminant satisfies g=g_(11)g_(22)-g_(12)^2>0.

If n>19, there exists a Poulet number between n and n^2. The theorem was proved in 1965.

Let a general theta function be defined as T(x,q)=sum_(n=-infty)^inftyx^nq^(n^2), then

A polynomial in a single variable, e.g., P(x)=a_2x^2+a_1x+a_0, as opposed to a multivariate polynomial.

Vorobiev's theorem states that if F_l^2|F_k, then F_l|k, where F_n is a Fibonacci number and a|b means a divides b. The theorem was discovered by Vorobiev in 1942, but not ...

Wilker's inequalities state that 2+(16)/(pi^4)x^3tanx<(sin^2x)/(x^2)+(tanx)/x<2+2/(45)x^3tanx for 0<x<pi/2, where the constants 2/45 and 16/pi^4 are the best possible ...

Gives a matrix representation b_i of a braid group in terms of (n-1)×(n-1) matrices. A -t always appears in the (i,i) position. b_1 = [-t 0 0 ... 0; -1 1 0 ... 0; 0 0 1 ... ...