Search Results for ""

Let R be a plane region bounded above by a continuous curve y=f(x), below by the x-axis, and on the left and right by x=a and x=b, then the volume of the solid of revolution ...

Let f and g be nonnegative and continuous functions on the closed interval [a,b], then the solid of revolution obtained by rotating the curves f(x) and g(x) about the x-axis ...

Given a metric g_(alphabeta), the discriminant is defined by g = det(g_(alphabeta)) (1) = |g_(11) g_(12); g_(21) g_(22)| (2) = g_(11)g_(22)-(g_(12))^2. (3) Let g be the ...

A topology induced by the metric g defined on a metric space X. The open sets are all subsets that can be realized as the unions of open balls B(x_0,r)={x in X|g(x_0,x)<r}, ...

A sequence defined from a finite sequence a_0, a_1, ..., a_n by defining a_(n+1)=mex_(i)(a_i+a_(n-i)), where mex is the mex (minimum excluded value).

A derived polygon with side ratios chosen as r=1/2 so that inscribed polygons are constructed by connecting the midpoints of the base polygon. For a triangle P, the ...

Given order statistics Y_1=min_(j)X_j, Y_2, ..., Y_(N-1), Y_N=max_(j)X_j with sample size N, the midrange of the random sample is defined by MR=1/2(Y_1+Y_N) (Hogg and Craig ...

The series with sum sum_(n=0)^infty1/(F_(2^n))=1/2(7-sqrt(5)), where F_k is a Fibonacci number (Honsberger 1985).

The number 1000000=10^6. While one million in the "American" system of numbers means the same thing as one million in the "British" system, the words billion, trillion, etc., ...

If a compact manifold M has nonnegative Ricci curvature tensor, then its fundamental group has at most polynomial growth. On the other hand, if M has negative curvature, then ...