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The quartic curve given by the implicit equation (x^2-a^2)(x-a)^2+(y^2-a^2)^2=0, (1) so-named because of its resemblance to a tooth. The bicuspid curve has cusps at (a,-a) ...

A binary quadratic form is a quadratic form in two variables having the form Q(x,y)=ax^2+2bxy+cy^2, (1) commonly denoted <a,b,c>. Consider a binary quadratic form with real ...

A set of curvilinear coordinates defined by x = (asinhv)/(coshv-cosu) (1) y = (asinu)/(coshv-cosu) (2) z = z, (3) where u in [0,2pi), v in (-infty,infty), and z in ...

One of the symbols { and } used in many different contexts in mathematics. Braces are used 1. To denote grouping of mathematical terms, usually as the outermost delimiter in ...

In complex analysis, a branch (also called a sheet) is a portion of the range of a multivalued function over which the function is single-valued. Combining all the sheets ...

A bridged graph is a graph that contains one or more graph bridges. Examples of bridged graphs include path graphs, ladder rung graphs, the bull graph, star graphs, and ...

The Brocard inellipse is the inconic with parameters x:y:z=1/a:1/b:1/c, (1) giving the trilinear equation ...

If n=1,2 (mod 4), and the squarefree part of n is divisible by a prime p=3 (mod 4), then no difference set of order n exists. Equivalently, if a projective plane of order n ...

A set of positive integers S is called sum-free if the equation x+y=z has no solutions x, y, z in S. The probability that a random sum-free set S consists entirely of odd ...

In general, the pedal curve of the cardioid is a slightly complicated function. The pedal curve of the cardioid with respect to the center of its conchoidal circle is the ...