I've Got The World On A String
Madeleine wishes to create the design above using a wooden board, nine nails, and a length of string. She will hammer the nails into the board (almost all the way), arranged as the vertices of a regular nonagon. She will then take the string, tie one end to one of the nails, then wrap the string around the nails repeatedly until every pair of nails has exactly one length of string connecting them.
Madeleine plans to use a piece of string 10 meters long. What is the farthest apart that she could place the nails at consecutive vertices of the nonagon?
Give your answer in millimeters, rounded to the nearest whole millimeter.
Details and Assumptions:
- The nails have negligible width, and none of the string is used up when it is wound around a nail.