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An R-module M is said to be unital if R is a commutative ring with multiplicative identity 1=1_R and if 1m=m for all elements m in M.

Calabi's triangle is the unique triangle other that the equilateral triangle for which the largest inscribed square can be inscribed in three different ways (Calabi 1997). ...

A congruent number can be defined as an integer that is equal to the area of a rational right triangle (Koblitz 1993). Numbers (a,x,y,z,t) such that {x^2+ay^2=z^2; ...

The ding-dong surface is the cubic surface of revolution given by the equation x^2+y^2=(1-z)z^2 (1) (Hauser 2003) that is closely related to the kiss surface. The surface can ...

The Maltese cross curve is the cubic algebraic curve with Cartesian equation xy(x^2-y^2)=x^2+y^2 (1) and polar equation r=2/(sqrt(sin(4theta))) (2) (Cundy and Rollett 1989, ...

The first Strehl identity is the binomial sum identity sum_(k=0)^n(n; k)^3=sum_(k=0)^n(n; k)^2(2k; n), (Strehl 1993, 1994; Koepf 1998, p. 55), which are the so-called Franel ...

The map which takes points on the surface of a sphere S^2 to their antipodal points.

A determinant appearing in Padé approximant identities: C_(r/s)=|a_(r-s+1) a_(r-s+2) ... a_r; | | ... |; a_r a_(r+1) ... a_(r+s-1)|.

Exchanges branches of the hyperbola x^'y^'=xy. x^' = mu^(-1)x (1) y^' = -muy. (2)

(1) Based on or involving trial and error. (2) Convincing without being rigorous.