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A field of extremals is a plane region which is simply connected by a one-parameter family of extremals. The concept was invented by Weierstrass.

(Deltau)_i^2=(u_i-u^_)^2, where u^_ is the average of {u_i}.

The term "integral" can refer to a number of different concepts in mathematics. The most common meaning is the the fundamenetal object of calculus corresponding to summing ...

The sinc function sinc(x), also called the "sampling function," is a function that arises frequently in signal processing and the theory of Fourier transforms. The full name ...

The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any ...

Modus tollens is a valid argument form in propositional calculus in which p and q are propositions. If p implies q, and q is false, then p is false. Also known as an indirect ...

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 ...

A "curve" (i.e., a continuous map of a one-dimensional interval) into a two-dimensional area (a plane-filling function) or a three-dimensional volume.

An acnode, also called an isolated point or hermit point, of a curve is a point that satisfies the equation of the curve but has no neighboring points that also lie on the ...

A quartic curve that resembles the symbol for the zodiacal sign Capricorn given by the implicit equation a^2x^2(x^2+y^2)-b(ay-x^2-y^2)^2=0, where a>0, b>a^2. The curve ...