Search Results for ""

The term isocline derives from the Greek words for "same slope." For a first-order ordinary differential equation y^'=f(t,y) is, a curve with equation f(t,y)=C for some ...

A fractal curve, also called the C-curve (Gosper 1972). The base curve and motif are illustrated below. Duvall and Keesling (1999) proved that the Hausdorff dimension of the ...

The Lorentzian function is the singly peaked function given by L(x)=1/pi(1/2Gamma)/((x-x_0)^2+(1/2Gamma)^2), (1) where x_0 is the center and Gamma is a parameter specifying ...

A theorem that can be stated either in the language of abstract algebraic curves or transcendental extensions. For an abstract algebraic curve, if x and y are nonconstant ...

det(i+j+mu; 2i-j)_(i,j=0)^(n-1)=2^(-n)product_(k=0)^(n-1)Delta_(2k)(2mu), where mu is an indeterminate, Delta_0(mu)=2, ...

For elliptic curves over the rationals Q, the group of rational points is always finitely generated (i.e., there always exists a finite set of group generators). This theorem ...

In three dimensions, a parallelepiped is a prism whose faces are all parallelograms. Let A, B, and C be the basis vectors defining a three-dimensional parallelepiped. Then ...

A number of fractal curves are associated with Peano. The Peano curve is the fractal curve illustrated above which can be written as a Lindenmayer system. The nth iteration ...

The term perimeter refers either to the curve constituting the boundary of a lamina or else to the length of this boundary. The perimeter of a circle is called the ...

A beautiful general theorem of which the following two statements are special cases (Coxeter and Greitzer 1967, pp. 99-100). 1. If DeltaABC and DeltaA^'B^'C^' are two ...