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A sextic surface given by the implicit equation 4(x^2+y^2+z^2-13)^3+27(3x^2+y^2-4z^2-12)^2=0.

A homotopy from one embedding of a manifold M in N to another such that at every time, it is an embedding. The notion of isotopy is category independent, so notions of ...

The keratoid cusp is quintic algebraic curve defined by y^2=x^2y+x^5. (1) It has a ramphoid cusp at the origin, horizontal tangents at (0,0) and (-6/(25),(108)/(3125)), and a ...

The Labs septic is a septic surface having 99 ordinary double points, which is the maximum number known for any septic surface.

The Lebesgue identity is the algebraic identity (Nagell 1951, pp. 194-195).

Given a map f from a space X to a space Y and another map g from a space Z to a space Y, does there exist a map h from X to Z such that gh=f? If such a map h exists, then h ...

If a compact manifold M has nonnegative Ricci curvature tensor, then its fundamental group has at most polynomial growth. On the other hand, if M has negative curvature, then ...

A manifold is said to be orientable if it can be given an orientation. Note the distinction between an "orientable manifold" and an "oriented manifold," where the former ...

The quintic surface given by the equation x^2+y^3+z^5=1 was considered by S. Plouffe (pers. comm., Dec. 21, 1998) and here dubbed the peninsula surface. It has been dubbed ...

The pentanacci constant is the limiting ratio of adjacent pentanacci numbers. It is the algebraic number P = (x^5-x^4-x^3-x^2-x-1)_1 (1) = 1.96594823... (2) (OEIS A103814), ...