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 plane old stuffed cube


Best Answer plasmid, 27 September 2013 - 04:49 AM

If no one else is going to go after this one... I can give an answer based on, well, working in the spirit of the best solution the program could find. But I can't prove that there aren't any larger squares that can fit in the unit cube.

Spoiler for
Go to the full post


  • Please log in to reply
9 replies to this topic

#1 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5828 posts
  • Gender:Male
  • Location:New York

Posted 24 September 2013 - 02:44 AM

  What is the area of the largest square that can fit entirely within a unit cube? 


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

#2 Dariusray

Dariusray

    Newbie

  • Members
  • Pip
  • 7 posts

Posted 24 September 2013 - 03:25 AM

I just realized where I went wrong in my first guess...  I'll have to figure a different answer:

Spoiler for Estimation now...


Edited by Dariusray, 24 September 2013 - 03:34 AM.

  • 0

#3 phaze

phaze

    Senior Member

  • Members
  • PipPipPipPip
  • 1002 posts
  • Gender:Male

Posted 24 September 2013 - 03:26 AM

Spoiler for First guesses

  • 0
Perfecting Mafia suicide since August 2008

#4 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5828 posts
  • Gender:Male
  • Location:New York

Posted 24 September 2013 - 03:37 AM

I just realized where I went wrong in my first guess...  I'll have to figure a different answer:

Spoiler for Estimation now...

Since it's a unit cube, your answer simplifies (if I'm reading it correctly) to Sqrt(2) / 2 = .707.

This is smaller than a cube face. But maybe I don't interpret your answer correctly.


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

#5 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5828 posts
  • Gender:Male
  • Location:New York

Posted 24 September 2013 - 03:39 AM

Spoiler for First guesses

A little too large, but close. And the answer is in fact a rational number.

 

If it helps, there is a close relation to the question that asks whether a cube can be pushed through a square hole in a smaller cube.


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

#6 plasmid

plasmid

    Senior Lolcat

  • VIP
  • PipPipPipPip
  • 1430 posts
  • Gender:Male

Posted 25 September 2013 - 03:42 AM

So far the best that my horribly inefficient and possibly buggy java code came up with is an area of 1.0984. But it's still running.

I probably ought to have searched for a reasonably efficient Windows C compiler instead.

 

Unfortunately I don't see any easy way of modifying the code to work in 4 dimensions. Especially since it uses cross products which I don't think are defined in 4D.


  • 0

#7 plasmid

plasmid

    Senior Lolcat

  • VIP
  • PipPipPipPip
  • 1430 posts
  • Gender:Male

Posted 26 September 2013 - 02:42 AM

This is what my brute force approach came up with. If you look at the coordinates of the square that it fit into the unit cube, it should become clear how to imagine that it's oriented, and allow you to come up with a more analytical approach to solving the problem. Which I'm not going to attempt myself for now.

 

Spoiler for Coordinates for the vertices of the square
 
Spoiler for The Java code (obviously written by someone not used to naming conventions)
 
Spoiler for How to run the code on a Windows machine (if you're comfortable working from a command line and editing system environment variables)

  • 0

#8 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5828 posts
  • Gender:Male
  • Location:New York

Posted 26 September 2013 - 07:23 AM

Thanks for the programming detail.
I'm learning how to do java programming.

You get an area of 1.0984, a rational number.
But it can be bigger than that.
  • 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#9 plasmid

plasmid

    Senior Lolcat

  • VIP
  • PipPipPipPip
  • 1430 posts
  • Gender:Male

Posted 27 September 2013 - 04:49 AM   Best Answer

If no one else is going to go after this one... I can give an answer based on, well, working in the spirit of the best solution the program could find. But I can't prove that there aren't any larger squares that can fit in the unit cube.

Spoiler for

  • 0

#10 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5828 posts
  • Gender:Male
  • Location:New York

Posted 11 October 2013 - 08:47 PM

I'm late marking this one solved. Nice, clear approach.
  • 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