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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 ...

A quartic algebraic curve also called the peg-top curve and given by the Cartesian equation a^4y^2=b^2x^3(2a-x) (1) and the parametric curves x = a(1+sint) (2) y = ...

A map defined by one or more polynomials. Given a field K, a polynomial map is a map f:K^n->K^m such that for all points (x_1,...,x_n) in K^n, ...

A projective space is a space that is invariant under the group G of all general linear homogeneous transformation in the space concerned, but not under all the ...

A simple closed curve on a sphere that is not necessarily a great circle but merely intersects as a great circle would (Billera et al. 1999).

The radius of curvature is given by R=1/(|kappa|), (1) where kappa is the curvature. At a given point on a curve, R is the radius of the osculating circle. The symbol rho is ...

The real part R[z] of a complex number z=x+iy is the real number not multiplying i, so R[x+iy]=x. In terms of z itself, R[z]=1/2(z+z^_), where z^_ is the complex conjugate of ...

The reciprocal of a real or complex number z!=0 is its multiplicative inverse 1/z=z^(-1), i.e., z to the power -1. The reciprocal of zero is undefined. A plot of the ...

A recurrence plot is defined as a plot of the quantity R(t,tau)=H(epsilon-||f(t)-f(tau)||), where H(x) is the Heaviside step function and ||f|| denotes a norm. A recurrence ...

A polygon that can be dissected into n smaller copies of itself is called a rep-n-tile. The triangular polygonal spiral is also a rep-tile. The above figure shows the zeroth ...