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A tree is planted at each lattice point in a circular orchard which has center at the origin and radius r. If the radius of trees exceeds 1/r units, one is unable to see out ...

A parallelogram polyomino is a polyomino such that the intersection with every line perpendicular to the main diagonal is a connected segment. The number of parallelogram ...

For a system of n first-order ordinary differential equations (or more generally, Pfaffian forms), the 2n-dimensional space consisting of the possible values of ...

The vector r from the origin to the current position. It is also called the position vector. The derivative of r satisfies ...

A reducible fraction is a fraction p/q such that GCD(p,q)>1, i.e., p/q can be written in reduced form. A fraction that is not reducible is said to be irreducible. For ...

Let R+B be the number of monochromatic forced triangles (where R and B are the number of red and blue triangles) in an extremal graph. Then R+B=(n; 3)-|_1/2n|_1/4(n-1)^2_|_|, ...

A sorting algorithm which makes n passes over a set of n elements, in each pass selecting the smallest element and deleting it from the set. This algorithm has running time ...

When a prime l divides the elliptic discriminant of a elliptic curve E, two or all three roots of E become congruent (mod l). An elliptic curve is semistable if, for all such ...

The locus of points whose first polars with regard to the curves of a linear net have a common point. It is also the locus of points of concurrence of line polars of points ...

The swastika curve is Cundy and Rollett's (1989, p. 71) name for the quartic plane curve with Cartesian equation y^4-x^4=xy and polar equation ...