CTK Exchange
Front Page
Movie shortcuts
Personal info
Awards
Reciprocal links
Terms of use
Privacy Policy

Interactive Activities

Cut The Knot!
MSET99 Talk
Games & Puzzles
Arithmetic/Algebra
Geometry
Probability
Eye Opener
Analog Gadgets
Inventor's Paradox
Did you know?...
Proofs
Math as Language
Things Impossible
My Logo
Math Poll
Other Math sit's
Guest book
News sit's

Recommend this site
Manifesto: what CTK is about Search CTK Buying a book is a commitment to learning Table of content Things you can find on CTK Chronology of updates Email to Cut The Knot Recommend this page

CTK Exchange

Subject: "Math Layout"     Previous Topic | Next Topic
Printer-friendly copy     Email this topic to a friend    
Conferences The CTK Exchange Middle school Topic #109
Reading Topic #109
AEROX
guest
 Jan-31-05, 08:04 PM (EST)
 
"Math Layout"
 
   I am having some trouble figuring out a way to make a layout of a cube I have to draw different ways to amke a cube and do not understand?


  Alert | IP Printer-friendly page | Reply | Reply With Quote | Top
alexb
Charter Member
1905 posts		 Jan-31-05, 08:08 PM (EST)
Click to EMail alexb Click to send private message to alexb Click to view user profileClick to add this user to your buddy list  
1. "RE: Math Layout"
In response to message #0
 
   How many square sides has a cube? Cut as many as you need out of paper. All must be equal in size. Put two of the squares so that they share an edge. Attach one to the other by a sticky tape. Place this two on a cube. Think where you can attach a third square to the first two so that you'd be able to flatten out all the three. Repeat for the fourth square and as needed.


  Alert | IP Printer-friendly page | Reply | Reply With Quote | Top
Layout
guest
 Feb-04-05, 11:36 AM (EST)
 
2. "RE: Math Layout"
In response to message #0
 
   Well you could draw a square then about in the middle and up draw another. Connect the squares together with lines. Hope this helps, really simple sorry if you already knew that and it didnt help much!


  Alert | IP Printer-friendly page | Reply | Reply With Quote | Top
GEB
guest
 Mar-02-05, 06:00 PM (EST)
 
3. "RE: Math Layout"
In response to message #2
 
   If you know there are 6 squares that make up the cube, how many unique ways could you arrange these 6 squares so they would still fold up into a cube?
Having played for a while, can you start thinking of a system that would help you check?


  Alert | IP Printer-friendly page | Reply | Reply With Quote | Top
alexb
Charter Member
1905 posts		 Mar-02-05, 11:46 PM (EST)
Click to EMail alexb Click to send private message to alexb Click to view user profileClick to add this user to your buddy list  
4. "RE: Math Layout"
In response to message #3
 
   >If you know there are 6 squares that make up the cube, how
>many unique ways could you arrange these 6 squares so they
>would still fold up into a cube?
>Having played for a while, can you start thinking of a
>system that would help you check?

Of the top of my head:

Think of the cube as a graph with 8 vertices, 12 edges and 6 faces. Its dual graph is the octahedron, a graph with 6 vertices and 12 edges, each vertex being of degree 4. What you are looking for is the number of spanning trees on the octahedron (as a graph). Any such spanning tree has 5 = 6 - 1 edges. Thus the upper bound on your number is C(5, 12) - 12 choose 5. This is not the exact number as there are spanning subgraphs that contain cycles.


  Alert | IP Printer-friendly page | Reply | Reply With Quote | Top
Silver_dragon
guest
 Oct-23-06, 10:08 PM (EST)
 
5. "RE: Math Layout"
In response to message #0
 
   I am having the same question, but I know that there are 11 ways total. IF ANYONE KNOWS THE WAYS, PLEASE SHOW ME!!!


  Alert | IP Printer-friendly page | Reply | Reply With Quote | Top

Conferences | Forums | Topics | Previous Topic | Next Topic

You may be curious to have a look at the old CTK Exchange archive.
Please do not post there.

Copyright © 1996-2018 Alexander Bogomolny

Search:
Keywords:

Google
Web CTK