0

In my graph theory book exercise,I found a problem that:

Prove that,World is not flat using Mathematics

enter image description here

This picture is used in the exercise,but no idea of applying it.

Hailey
  • 1,020
  • Did they provide you with the lengths of the lines? – god of llamas Jun 07 '16 at 11:31
  • http://math.stackexchange.com/questions/1816766 – Watson Jun 07 '16 at 11:32
  • What do you know about the Pythagorean theorem on a Euclidean plane? – Phillip Hamilton Jun 07 '16 at 11:37
  • 1
    I'm not sure this is really directly related to "graph theory". – Fabrice NEYRET Jun 07 '16 at 11:56
  • @FabriceNEYRET I think there is probably a graph theory proof related to the fact that K5 is not planar, but I'm not sure how exactly to do it. – Ian Jun 07 '16 at 11:57
  • @Ian For what it's worth K5 cannot be embedded into the sphere either. (There's a cute, short proof of this using the Euler characteristic that's a nice exercise, too.) – Travis Willse Jun 07 '16 at 12:21
  • On-topic: you can take three (not any three) of the distances to find a triangle. Given any of the other three, if the whole thing were planar, you'd be confining the fourth point to a circle. Given a fifth distance as well, you'd be confining the fourth point to be one of at most two points. Adding a sixth distance will thus typically be impossible (because there are only at most two admissible values of this sixth distance). I think this "two" corresponds to the possibility of the resulting quadrilateral being concave vs. convex. – Ian Jun 07 '16 at 12:25
  • Take a small region of the earth which is "locally 2-dimensional" and take four places in it that "nearly" provide the four vertices of a rectangle. For instance, take the four corners on the field of a soccer stadium. Then one clearly can connect these four places by streets/lines that do not intersect each other ($K_4$ is planar). Also, clearly, if we take a point at the opposite side of the earth, and connect it with the other four points in the shortest possible way (through the inner of the earth), then these lines will also not intersect each other or any of the previous lines. – lattice Jun 07 '16 at 12:52
  • So my idea for using graph theory would be: The earth cannot be planar, because $K_5$ is not planar. This is not quite related to the figure, but I do not see how 4 points and their distances on the earth should suffice to show that the earth is not planar using graph theory (i.e. letting them define a graph), since $K_4$ can be drawn on a plane. – lattice Jun 07 '16 at 12:54
  • 2
    @Watson Right observation : In fact Hailey has already asked this question 7 hours ago, and this question has been put "on hold". Please Hailey dont' do that, it is not a correct behavior. – Jean Marie Jun 07 '16 at 13:10
  • 1
    But doesn't my question a valid one ?I put it again as my previous question was put on Hold – Hailey Jun 07 '16 at 13:51
  • 2
    One of my question should be valid,both are either on hold or duplicate,now how can get the answer. – Hailey Jun 07 '16 at 14:11
  • 2
    Since you asked what to do to get an answer - if you read the on-hold banner in your other question, it gives an explanation. "This question is missing context or other details: Please improve the question by providing additional context..." If you click on the text "improve the question", this links brings you to the post (on meta) explaining how good questions should look and what are good ways to add missing context. – Martin Sleziak Jun 07 '16 at 14:25

0 Answers0