# Hanging picture on the wall with two nails

There's picture which we have to hang on the wall with two nails. The two ends of a string are attached to both of the upper edges of the picture.

a) How do we have to hang the picture if it falls (under the influence of the gravity) to the ground as soon as one of the nails is pulled out of the walls. Make a sketch and explain your approach.

b) The string which is pulled by the weight can be interpreted (by projection onto the wall) as a path in C{a,b}, where the midpoints of the nails lie in a,b ∈ C. Determine the winding number of path from (a) around each of the two nails. Is the path null-homotopic?

c) Can we find such a way of hanging also for n ≥ 3 nails?

• What have you tried so far?? Have you made a diagram? please include your own thoughts. – The Integrator May 18 '18 at 18:30

Try the Pochhammer contour[ http://dlmf.nist.gov/5.12.F3.mag][1] you can see that it is not null homotopic and has winding number 0 around each point obviously.

• Yep. That contour works. – David G. Stork May 18 '18 at 20:46