Search Results for ""

The circumcenter of mass is a concept that can be defined by analogy with one of the the constructions for the geometric centroid for the case of polygons. The geometric ...

Roughly speaking, isospectral manifolds are drums that sound the same, i.e., have the same eigenfrequency spectrum. Two drums with differing area, perimeter, or genus can ...

A function f(x) is said to have bounded variation if, over the closed interval x in [a,b], there exists an M such that |f(x_1)-f(a)|+|f(x_2)-f(x_1)|+... +|f(b)-f(x_(n-1))|<=M ...

The vector space generated by the columns of a matrix viewed as vectors. The column space of an n×m matrix A with real entries is a subspace generated by m elements of R^n, ...

Given a polygon with an even number of sides, the derived polygon is obtained by joining the points which are a fractional distance r along each side. If r=1/2, then the ...

There are many formulas of pi of many types. Among others, these include series, products, geometric constructions, limits, special values, and pi iterations. pi is ...

The arc length of the parabolic segment y=h(1-(x^2)/(a^2)) (1) illustrated above is given by s = int_(-a)^asqrt(1+y^('2))dx (2) = 2int_0^asqrt(1+y^('2))dx (3) = ...

The point S^' which makes the perimeters of the triangles DeltaBS^'C, DeltaCS^'A, and DeltaAS^'B equal. The isoperimetric point exists iff a+b+c>4R+r, (1) where a, b, and c ...

A perspective collineation in which the center and axis are not incident. The term was first used by Poncelet (Cremona 1960, p. ix).

In general, "a" calculus is an abstract theory developed in a purely formal way. "The" calculus, more properly called analysis (or real analysis or, in older literature, ...