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The zeros of the derivative P^'(z) of a polynomial P(z) that are not multiple zeros of P(z) are the positions of equilibrium in the field of force due to unit particles ...

For an arbitrary not identically constant polynomial, the zeros of its derivatives lie in the smallest convex polygon containing the zeros of the original polynomial.

If any of the roots of a polynomial are increased, then all of the critical points increase.

Let {f_n(x)} be a sequence of analytic functions regular in a region G, and let this sequence be uniformly convergent in every closed subset of G. If the analytic function ...

A circle surrounded by a square looks larger than the same circle surrounding a square.

The sum of the reciprocals of roots of an equation equals the negative coefficient of the linear term in the Maclaurin series.

A square number, also called a perfect square, is a figurate number of the form S_n=n^2, where n is an integer. The square numbers for n=0, 1, ... are 0, 1, 4, 9, 16, 25, 36, ...

Square line picking is the selection of pairs of points (corresponding to endpoints of a line segment) randomly placed inside a square. n random line segments can be picked ...

The term perfect square is used to refer to a square number, a perfect square dissection, or a factorable quadratic polynomial of the form a^2+/-2ab+b^2=(a+/-b)^2.

A number which is simultaneously square and triangular. Let T_n denote the nth triangular number and S_m the mth square number, then a number which is both triangular and ...