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A problem in the calculus of variations. Let a vessel traveling at constant speed c navigate on a body of water having surface velocity u = u(x,y) (1) v = v(x,y). (2) The ...

A negative integer is one of the integers ..., -4, -3, -2, -1 obtained by negating the positive integers. The negative integers are commonly denoted Z^-.

Any irreducible curve may be carried by a factorable Cremona transformation into one with none but ordinary singular points.

"Nordstrand's weird surface" is an attractive quartic surface given by the implicit equation It has 11 ordinary double points located at (2/5,0,0), (-2/5,0,0), ...

Place 2n balls in a bag and number them 1 to 2n, then pick half of them at random. The number of different possible sums for n=1, 2, 3, ... are then 2, 5, 10, 17, 26, ... ...

An algebraic surface of degree eight. The maximum number of ordinary double points known to exist on an octic surface is 168 (the Endraß octics), although the rigorous upper ...

The number sign # sometimes used in mathematics to indicate the number of a quantity satisfying some condition, e.g., #{n:n>1}. The symbol is also used to denote a primorial.

An open interval is an interval that does not include its end points. The open interval {x:a<x<b} is denoted (a,b), although the nonstandard notation ]a,b[ is sometimes also ...

The four of Hilbert's axioms which concern the arrangement of points.

The oriented matroid of a finite configuration of points extracts relative position and orientation information from the configuration. An oriented matroid can be described ...