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A curve also known as the Gerono lemniscate. It is given by Cartesian coordinates x^4=a^2(x^2-y^2), (1) polar coordinates, r^2=a^2sec^4thetacos(2theta), (2) and parametric ...

For a general quadrilateral with sides of length a, b, c, and d, the area K is given by (1) where s=1/2(a+b+c+d) (2) is the semiperimeter, A is the angle between a and d, and ...

The n-ball, denoted B^n, is the interior of a sphere S^(n-1), and sometimes also called the n-disk. (Although physicists often use the term "sphere" to mean the solid ball, ...

A number taken to the power 2 is said to be squared, so x^2 is called "x squared." This terminology derives from the fact that the area of a square of edge length x is given ...

Fatou dust is a Fatou set for a point outside the underlying set. Such a set has zero area and has an infinite number of disconnected components.

The area of a rational right triangle cannot be a square number. This statement is equivalent to "a congruum cannot be a square number."

Let a plane figure have area A and perimeter p. Then Q=(4piA)/(p^2)<=1, where Q is known as the isoperimetric quotient. The equation becomes an equality only for a circle.

The area of the dodecagon (n=12) inscribed in a unit circle with R=1 is A=1/2nR^2sin((2pi)/n)=3.

A broad area of mathematics connected with functional analysis, differential equations, index theory, representation theory, and mathematical physics.

A pseudocylindrical map projection which distorts shape, area, scale, and distance to create attractive average projection properties.