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The horizontal line segment in the above figure appears to be shorter than the vertical line segment, despite the fact that it has the same length.

Given two intersecting lines, the two nonadjacent angles with the same vertex are said to be vertical angles. One can easily prove that vertical angles are congruent. Some ...

An abstract machine that is implemented in software is termed a virtual machine.

A set of identities involving n-dimensional visible lattice points was discovered by Campbell (1994). Examples include product_((a,b)=1; ...

The partial differential equation iu_t+[(1+|u|^2u)^(-1/2)u]_(xx)=0.

Wagner's theorem states that a graph is planar iff it does not contain K_5 or K_(3,3) as a graph minor.

For R[mu+nu]>0, |argp|<pi/4, and a>0, where J_nu(z) is a Bessel function of the first kind, Gamma(z) is the gamma function, and _1F_1(a;b;z) is a confluent hypergeometric ...

The satellite knot of an unknot twisted inside a torus.

The second-order ordinary differential equation y^('')+[A+Bcos(2x)+Ccos(4x)]y=0.

For any point P on the boundary of an ordinary ball, find a neighborhood of P in which the intersection with the ball's boundary cuts the neighborhood into two parts, each ...