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In the plane, a closed curve is a curve with no endpoints and which completely encloses an area.

A fractal curve of infinite length which bounds an area twice that of the original square.

Of all convex n-gons of a given perimeter, the one which maximizes area is the regular n-gon.

Given a convex plane region with area A and perimeter p, then |N-A|<p, where N is the number of enclosed lattice points.

The dual of Brianchon's theorem (Casey 1888, p. 146), discovered by B. Pascal in 1640 when he was just 16 years old (Leibniz 1640; Wells 1986, p. 69). It states that, given a ...

A point is a 0-dimensional mathematical object which can be specified in n-dimensional space using an n-tuple (x_1, x_2, ..., x_n) consisting of n coordinates. In dimensions ...

The shoelace formula, also known as Gauss's area formula, the shoelace algorithm, shoelace method, or surveyor's formula, is a name sometimes given to the polygon area ...

An affine variety V is an algebraic variety contained in affine space. For example, {(x,y,z):x^2+y^2-z^2=0} (1) is the cone, and {(x,y,z):x^2+y^2-z^2=0,ax+by+cz=0} (2) is a ...

The term "vesica piscis," meaning "fish bladder" in Latin, is used for the particular symmetric lens formed by the intersection of two equal circles whose centers are offset ...

Algebraic geometry is the study of geometries that come from algebra, in particular, from rings. In classical algebraic geometry, the algebra is the ring of polynomials, and ...