2
votes
2answers
37 views

Do I have this right Trip integrals

Just finished my proof of the volume of a cone using trip integrals. I think I noticed something. Wonder if I got it right. The first integral defines the line/curve, the second defines the area ...
5
votes
2answers
192 views

The area problem!

We have to find area of the quadrilateral formed by joining the point of intersection of the four quarter circles that are drawn from each vertex in a unit square. $\hspace{4cm}$ The challenge is ...
1
vote
1answer
82 views

Measuring how monotonically “staircase-like” a set of values is

A bit of a bizarre question here -- I'm looking for assistance in generating a robust metric to measure how monotonically "step-wise" a series of values is. The set must not start or end at a specific ...
10
votes
4answers
1k views

Ten soldiers puzzle

This is a puzzle from one popular book called "The Man Who Counted: A Collection of Mathematical Adventures",author is Malba Tahan. How to arrange ten soldiers in five lines in such a way that each ...