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There are nine possible types of isolated singularities on a cubic surface, eight of them rational double points. Each type of isolated singularity has an associated normal ...

Cayley's cubic surface is the unique cubic surface having four ordinary double points (Hunt), the maximum possible for cubic surface (Endraß). The Cayley cubic is invariant ...

A cyclide is a pair of focal conics which are the envelopes of two one-parameter families of spheres, sometimes also called a cyclid. The cyclide is a quartic surface, and ...

A two-player game, also called crosscram, in which player H has horizontal dominoes and player V has vertical dominoes. The two players alternately place a domino on a board ...

The envelope of the plane lx+my+nz=c, (1) where c is the speed of propagation of a wave in the direction (l,m,n) (i.e., l, m, and n are the direction cosines) is known as the ...

A hyperbolic paraboloid is the quadratic and doubly ruled surface given by the Cartesian equation z=(y^2)/(b^2)-(x^2)/(a^2) (1) (left figure). An alternative form is z=xy (2) ...

Let three similar isosceles triangles DeltaA^'BC, DeltaAB^'C, and DeltaABC^' be constructed on the sides of a triangle DeltaABC. Then DeltaABC and DeltaA^'B^'C^' are ...

The Kummer surfaces are a family of quartic surfaces given by the algebraic equation (x^2+y^2+z^2-mu^2w^2)^2-lambdapqrs=0, (1) where lambda=(3mu^2-1)/(3-mu^2), (2) p, q, r, ...

The Roman surface, also called the Steiner surface (not to be confused with the class of Steiner surfaces of which the Roman surface is a particular case), is a quartic ...

Given a triangle DeltaABC, construct the contact triangle DeltaT_AT_BT_C. Now extend lines parallel to the sides of the contact triangle from the Gergonne point. These ...