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A limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class. For example, the point is a degenerate case of the circle as ...

Differential algebra is a field of mathematics that attempts to use methods from abstract algebra to study solutions of systems of polynomial nonlinear ordinary and partial ...

An elliptic curve is the set of solutions to an equation of the form y^2+a_1xy+a_3y=x^3+a_2x^2+a_4x+a_6. (1) By changing variables, y->2y+a_1x+a_3, assuming the field ...

There exists a triangulation point Y for which the triangles BYC, CYA, and AYB have equal Brocard angles. This point is a triangle center known as the equi-Brocard center and ...

Erdős and Heilbronn (Erdős and Graham 1980) posed the problem of estimating from below the number of sums a+b where a in A and b in B range over given sets A,B subset= Z/pZ ...

Let a prime number generated by Euler's prime-generating polynomial n^2+n+41 be known as an Euler prime. (Note that such primes are distinct from prime Euler numbers, which ...

The extangents circle is the circumcircle of the extangents triangle. Its center function is a complicated 9th-order polynomial and its circle function is a complicated ...

Let T_n(x) be an arbitrary trigonometric polynomial T_n(x)=1/2a_0+{sum_(k=1)^n[a_kcos(kx)+b_ksin(kx)]} (1) with real coefficients, let f be a function that is integrable over ...

Special functions which arise as solutions to second order ordinary differential equations are commonly said to be "of the first kind" if they are nonsingular at the origin, ...

Let p>3 be a prime number, then 4(x^p-y^p)/(x-y)=R^2(x,y)-(-1)^((p-1)/2)pS^2(x,y), where R(x,y) and S(x,y) are homogeneous polynomials in x and y with integer coefficients. ...