A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Consider the region shown below. It is bounded by a regular hexagon whose sides are
of length 1 unit. Show that if any seven points are chosen in this region, then two of
them must be no further apart than 1 unit.
anonymous
 one year ago
Consider the region shown below. It is bounded by a regular hexagon whose sides are of length 1 unit. Show that if any seven points are chosen in this region, then two of them must be no further apart than 1 unit.

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0john will be here soon

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.4Oh this one seems interesting So we have a hexagon dw:1433602194782:dw God I hate drawing on this thing lol but regardless...work with me here

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.4What if we were to draw line from the center of the hexagon to each vertex? dw:1433602323521:dw Also labeled the fact that each side length is 1

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.4Now, if I could have drawn any better...you would see that this would actually make it so the hexagon is simply 6 equilateral triangles

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.4Now it wouldnt take too much visual to realize that if we choose 7 spots...any 7 random spots...at least 1 triangle will end up with 2 of those spots in it dw:1433602536119:dw 1 spot for each triangle...and then we have to put another one..so it would go with another triangle that already has a spot...okay thats fine

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.4Now if that is true, which it is, we can show from that that since those 2 points are within a triangle of side length 1...the distance between the two cannot be greater than 1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okayy ..i understand..thank you very much.. :) but how can we show it using pigeonhole principle ?

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.4If I remember correctly, Pigeonhole just states that if you try to put X items into a container of Y partitions...and X>Y then at least 1 partition will contain more than 1 X So we kinda did that here...if there are 6 partitions here...and we have 7 spots...since 7>6 then at least 1 triangle will have more than 1 point

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh okaayyy.. thank you veryyyy much.. :) :)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.