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The closed plane curve that crosses itself once and consists of one lobe on each side of the intersection. It can be viewed as a circle with a half twist. The fundamental ...

When applied to a system possessing a length R at which solutions in a variable r change character (such as the gravitational field of a sphere as r runs from the interior to ...

Given a convex plane region with area A and perimeter p, then |N-A|<p, where N is the number of enclosed lattice points.

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.

The parameter r in the exponential equation of population growth N(t)=N_0e^(rt), where N_0 is the initial population size (at t=0) and t is the elapsed time.

A nowhere-neat dissection in which squares of the same size are not allowed to share any part of a side.

Let G be a group with normal series (A_0, A_1, ..., A_r). A normal factor of G is a quotient group A_(k+1)/A_k for some index k<r. G is a solvable group iff all normal ...

The octahemioctacron is the dual polyhedron of the octahemioctahedron U_3 and Wenninger dual W_(68). When rendered, the octahemioctacron and hexahemioctacron appear the same.

An almost integer is a number that is very close to an integer. Near-solutions to Fermat's last theorem provide a number of high-profile almost integers. In the season 7, ...

The Euler numbers, also called the secant numbers or zig numbers, are defined for |x|<pi/2 by sechx-1=-(E_1^*x^2)/(2!)+(E_2^*x^4)/(4!)-(E_3^*x^6)/(6!)+... (1) ...