Math Forum / Mathematics / Recreational Math / July 2009

The Traveling Salesman Problem addresses the problem of determining the
most efficient route for a salesman between the sets of cities he must
visit.
I am investigating a similar problem - that of Traveling Salesmen.

Let k be an integer greater than 1. Every natural number n can be
written as the sum of k-th powers of natural numbers. In 1770, Edward
Waring asked if for every such k, is there an integer s such that each
natural integer n can be written as the sum of at most s k-th powers of

I'm Charlie and I'm working on a project to gather URLs that contain
information on Math & Logic Puzzles. I'm doing this on a new web site
called Biggest And Best Sites. If you will click on:
Math & Logic Puzzles

Let C represent the collection of all unending (infinite) strings of
zeroes and ones, where both the zeroes and the ones occur an infinite
number of times. C is evidently unountable.
Let S belong to C. Let S(n) be an initial segment of  S, so that for

Find (i) the volume swept out by revolving the area bounded by the parabola y = 2x^2 and the line y = 2 about the y axis; (ii) the length of the arc bounding this area; (iii) the area swept out by this arc when it is revolved around 0y.

problem:
Service time is exponentially distributed with mean 30 minutes.
1st customer arrived at t=0 min.
2nd customer arrives at t=5 min

Find and prove the numerical value of the curvature at the point (x,y) of the ellipse (x^2/a^2) + (y^2/b^2) = 1.
What is the ratio of the greatest to the least curvature of the ellipse ?.

Thank you to posters arguing with me about the "perfect tweet" as I
locked down another variant of the perfect tweet which defines itself
in the tweet and then came up with another perfect tweet talking about
it:

First, no, this isn't a homework question.  I've run into a problem where
I need an understanding of Eigenvalues, have tried to read up on them
based on my limited knowledge of linear algebra, and bounced.  So I'm
working through an intro linear algebra text on my own.

A parabolic mirror is formed by revolving the part of the parabola y^2 = 4ax from x = 0 to x = h about the axis of the parabola. If the width of the mirror is 2k, show that the area of its surface is [(pi*k)/6h^2]*[(k^2+4h^2)^(3/2)-k^3]