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
- - - - -

A pentagon in a pentagon in a pentagon


  • Please log in to reply
7 replies to this topic

#1 BMAD

BMAD

    Senior Member

  • Members
  • PipPipPipPip
  • 1702 posts
  • Gender:Female

Posted 22 February 2013 - 05:42 AM

Conjecture: As long as each of the two smaller pentagons are formed by joining the midpoints of the next larger pentagon, the two ratios of the areas will always be equal and the two ratios of the perimeters will always be equal, no matter what shape the largest pentagon has.

 

Under what conditions is this true?


  • 0

#2 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5918 posts
  • Gender:Male
  • Location:New York

Posted 22 February 2013 - 05:54 AM

Conjecture: By saying "whatever shape the pentagon has" you are not limiting the discussion to regular pentagons.

 

True?


  • 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
  • 1702 posts
  • Gender:Female

Posted 22 February 2013 - 05:56 AM

Conjecture: By saying "whatever shape the pentagon has" you are not limiting the discussion to regular pentagons.

 

True?

yes.  any pentagon


  • 0

#4 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5918 posts
  • Gender:Male
  • Location:New York

Posted 22 February 2013 - 06:46 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

#5 BMAD

BMAD

    Senior Member

  • Members
  • PipPipPipPip
  • 1702 posts
  • Gender:Female

Posted 22 February 2013 - 01:41 PM

Spoiler for Looks like


Not all them.
  • 0

#6 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5918 posts
  • Gender:Male
  • Location:New York

Posted 23 February 2013 - 09:47 PM

Spoiler for Looks like

Not all them.

 

I'm not making any progress. Any tips for analyzing this?


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

#7 BMAD

BMAD

    Senior Member

  • Members
  • PipPipPipPip
  • 1702 posts
  • Gender:Female

Posted 24 February 2013 - 12:39 AM

Spoiler for help

  • 0

#8 BMAD

BMAD

    Senior Member

  • Members
  • PipPipPipPip
  • 1702 posts
  • Gender:Female

Posted 25 February 2013 - 01:00 AM

Spoiler for help

 

Spoiler for help2


  • 0




0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users