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In the above illustration, black dots appear to form and vanish at the intersections of the gray horizontal and vertical lines. When focusing attention on a single white dot, ...

A semicubical parabola is a curve of the form y=+/-ax^(3/2) (1) (i.e., it is half a cubic, and hence has power 3/2). It has parametric equations x = t^2 (2) y = at^3, (3) and ...

The Smale horseshoe map consists of a sequence of operations on the unit square. First, stretch in the y direction by more than a factor of two, then compress in the x ...

In a rectangular room (a cuboid) with dimensions 30^'×12^'×12^', a spider is located in the middle of one 12^'×12^' wall one foot away from the ceiling. A fly is in the ...

A short exact sequence of groups 0-->A-->B-->C-->0 (1) is called split if it essentially presents B as the direct sum of the groups A and C. More precisely, one can construct ...

A map projection obtained by projecting points P on the surface of sphere from the sphere's north pole N to point P^' in a plane tangent to the south pole S (Coxeter 1969, p. ...

A trapezoid is a quadrilateral with two sides parallel. The trapezoid is equivalent to the British definition of trapezium (Bronshtein and Semendyayev 1977, p. 174). An ...

To find the motion of a rectangular membrane with sides of length L_x and L_y (in the absence of gravity), use the two-dimensional wave equation ...

It is always possible to "fairly" divide a cake among n people using only vertical cuts. Furthermore, it is possible to cut and divide a cake such that each person believes ...

Cartesian coordinates are rectilinear two- or three-dimensional coordinates (and therefore a special case of curvilinear coordinates) which are also called rectangular ...