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An algebraic surface with affine equation P_d(x_1,x_2)+T_d(x_3)=0, (1) where T_d(x) is a Chebyshev polynomial of the first kind and P_d(x_1,x_2) is a polynomial defined by ...

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 ...

Togliatti (1940, 1949) showed that quintic surfaces having 31 ordinary double points exist, although he did not explicitly derive equations for such surfaces. Beauville ...

The largest n such that |z_n|<4 in a Mandelbrot set. Points of different count are often assigned different colors.

Each centered convex body of sufficiently high dimension has an "almost spherical" k-dimensional central section.

The three diagonal points of a complete quadrilateral are never collinear.

S_n=sum_(i)eta_imu(E_i), where mu(E_i) is the measure of the set E_i of points on the x-axis for which f(x) approx eta_i.

Topological lower bounds in terms of Betti numbers for the number of critical points form a smooth function on a smooth manifold.

A geometry constructed without reference to measurement. The only primitive concepts are those of points and intermediacy. There are 10 axioms underlying ordered geometry.

Functions which have derivatives of all orders at all points and which, together with their derivatives, fall off at least as rapidly as |x|^(-n) as |x|->infty, no matter how ...