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The happy end problem, also called the "happy ending problem," is the problem of determining for n>=3 the smallest number of points g(n) in general position in the plane ...

A hexagon tiling is a tiling of the plane by identical hexagons. The regular hexagon forms a regular tessellation, also called a hexagonal grid, illustrated above. There are ...

The Tschirnhausen cubic is a plane curve given by the polar equation r=asec^3(1/3theta). (1) Letting theta=3tan^(-1)t gives the parametric equations x = a(1-3t^2) (2) y = ...

A plane curve discovered by Maclaurin but first studied in detail by Cayley. The name Cayley's sextic is due to R. C. Archibald, who attempted to classify curves in a paper ...

An angle theta drawn on the coordinate plane is said to be in standard position if its initial side lies on the positive x-axis so that its vertex coincides with the origin ...

Given a function f(x) plotted in the Cartesian plane as y=f(x), the average rate of change (or average rate of change function) of f from x to a is given by ...

Let X_1,X_2 subset P^2 be cubic plane curves meeting in nine points p_1, ..., p_9. If X subset P^2 is any cubic containing p_1, ..., p_8, then X contains p_9 as well. It is ...

Using a set of corners of a solid that lie in a plane to form the polygon vertices of a new polygon is called faceting. Such polygons may outline new faces that join to ...

A shell bounded by two similar ellipsoids having a constant ratio of axes. Given a chord passing through a homeoid, the distance between inner and outer intersections is ...

The symmetry operation corresponding to a rotation followed by an inversion operation, also called a rotoinversion. This operation is denoted n^_ for an improper rotation by ...