Jump to content


Welcome to BrainDen.com - Brain Teasers Forum

Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account.
As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends.

Of course, you can also enjoy our collection of amazing optical illusions and cool math games.

If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top.
If you have a website, we would appreciate a little link to BrainDen.

Thanks and enjoy the Den :-)
Guest Message by DevFuse
 

Photo
* * * * - 1 votes

Central Area


Best Answer bonanova, 29 April 2014 - 11:38 AM

Since I inspired this, ^_^ I guess I should solve it.

 

Spoiler for Here goes

Go to the full post


  • Please log in to reply
9 replies to this topic

#1 BMAD

BMAD

    Senior Member

  • Members
  • PipPipPipPip
  • 1664 posts
  • Gender:Female

Posted 28 April 2014 - 01:28 AM

inspired by one of Bonanova's past problems:

 

What proportion of the area of a regular n-gon is closer to its center than to any edge?


  • 0

#2 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5627 posts
  • Gender:Male
  • Location:New York

Posted 28 April 2014 - 04:16 AM

Spoiler for looks like

  • 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#3 BMAD

BMAD

    Senior Member

  • Members
  • PipPipPipPip
  • 1664 posts
  • Gender:Female

Posted 28 April 2014 - 02:21 PM

Spoiler for looks like

 

 Are you sure?  For some reason I am finding my area to be rounder in shape.


Edited by BMAD, 28 April 2014 - 02:23 PM.

  • 0

#4 BMAD

BMAD

    Senior Member

  • Members
  • PipPipPipPip
  • 1664 posts
  • Gender:Female

Posted 28 April 2014 - 04:44 PM

.


Edited by BMAD, 28 April 2014 - 04:45 PM.

  • 0

#5 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5627 posts
  • Gender:Male
  • Location:New York

Posted 28 April 2014 - 05:22 PM

You're right. I drew a ray from the center and took the midpoint.

But that doesn't fit the question. I'll give it more thought.


  • 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#6 m00li

m00li

    Junior Member

  • Members
  • PipPip
  • 71 posts

Posted 28 April 2014 - 08:23 PM

I second Bonanova's first response. 


  • 0

#7 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5627 posts
  • Gender:Male
  • Location:New York

Posted 29 April 2014 - 11:38 AM   Best Answer

Since I inspired this, ^_^ I guess I should solve it.

 

Spoiler for Here goes


  • 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#8 BMAD

BMAD

    Senior Member

  • Members
  • PipPipPipPip
  • 1664 posts
  • Gender:Female

Posted 29 April 2014 - 02:14 PM

hmm well it does appear to be approaching 1/4 so maybe that is the limit.


  • 0

#9 m00li

m00li

    Junior Member

  • Members
  • PipPip
  • 71 posts

Posted 29 April 2014 - 10:34 PM

awesome problem and solution  :thumbsup:


  • 0

#10 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5627 posts
  • Gender:Male
  • Location:New York

Posted 29 April 2014 - 11:15 PM

hmm well it does appear to be approaching 1/4 so maybe that is the limit.

 

Yes of course for the circle the locus of equidistant points is a circle with half the radius and thus 1/4 the area.

The mistake of the first guess was to apply that reasoning to a polygon.

 

m00li, agree it is an interesting problem, much deeper than first appearance.


  • 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users