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A topological two-sphere in three-space whose exterior is not simply connected. The outer complement of Antoine's horned sphere is not simply connected. Furthermore, the ...

An aperiodic monotile, also somewhat humorously known as an einstein (where "einstein" means "one stone", perhaps generalizable to "one tile," in German), is a single tile ...

A surface of revolution defined by Kepler. It consists of more than half of a circular arc rotated about an axis passing through the endpoints of the arc. The equations of ...

The approximation problem is a well known problem of functional analysis (Grothendieck 1955). It asks to determine whether every compact operator T from a Banach space X to a ...

"Arabic numerals" are the numerical symbols 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0. Historically, Indian numerals evolved in Arab usage roughly 1000 A.D., and there was rare ...

Also known as araneidan, this curve owes its name to its spider-like shape. It is given by the polar equation r=a(sin(ntheta))/(sin[(n-1)theta]), where a>0 and n>2 is an ...

Arc length is defined as the length along a curve, s=int_gamma|dl|, (1) where dl is a differential displacement vector along a curve gamma. For example, for a circle of ...

An Archimedean circle is a circle defined in the arbelos in a natural way and congruent to Archimedes' circles, i.e., having radius rho=1/2r(1-r) for an arbelos with outer ...

The Archimedean duals in general have many stellations. The following table extracted from Webb gives a partial enumeration. In the table, E denotes counts of enantiomorphous ...

Enclose a sphere in a cylinder and cut out a spherical segment by slicing twice perpendicularly to the cylinder's axis. Then the lateral surface area of the spherical segment ...