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Let p be a prime with n digits and let A be a constant. Call p an "A-prime" if the concatenation of the first n digits of A (ignoring the decimal point if one is present) ...

A congruence of the form f(x)=0 (mod n) where f(x) is an integer polynomial (Nagell 1951, p. 73).

A knot used to join the ends of two ropes together to form a longer length.

The difference of two complex numbers z=x+iy and z^'=x^'+iy^' is given by z-z^'=(x-x^')+i(y-y^'). In component form, (x,y)-(x^',y^')=(x-x^',y-y^').

An equation of the form y=ax^3+bx^2+cx+d where only one root is real.

A plane curve of the form y=x^n. For n>0, the curve is a generalized parabola; for n<0 it is a generalized hyperbola.

Given a Farey sequence with consecutive terms h/k and h^'/k^', then the mediant is defined as the reduced form of the fraction (h+h^')/(k+k^').

An extension of an arbitrary field F of the form F(sqrt(1+lambda^2)), where lambda in F.

A cross also called the tau cross or crux commissa, illustrated schematically above in polyomino form.

An amazing pandigital approximation to e that is correct to 18457734525360901453873570 decimal digits is given by (1+9^(-4^(7·6)))^(3^(2^(85))), (1) found by R. Sabey in 2004 ...