# Math History: Konigsberg Bridge and Power Series

1. Nov 13, 2011

### Shackleford

For the first one, I said yes, you can add or remove a bridge to solve the problem. Each of the vertices has an odd order. If you add or subtract a bridge anywhere, you should then have an even number at two of the respective vertices. Since there are four vertices, two would have an odd order and two would have an even order, thus satisfying the requirement for being traversible.

http://i111.photobucket.com/albums/n149/camarolt4z28/1-3.png [Broken]

I'm rusty on series. I think for a function to be expressed as a power series, it has to be infinitely differentiable. The absolute value of x function is not differentiable at x = 0 and cannot be expressed as a power series.

http://i111.photobucket.com/albums/n149/camarolt4z28/2-3.png [Broken]

Last edited by a moderator: May 5, 2017