
Art Art and Architecture Forum  Math in our world, culture, buildings, natural wonders, nature, movies, music 
 LinkBack  Thread Tools  Display Modes 
February 6th, 2013, 07:00 PM  #1 
Senior Member Joined: Dec 2012 Posts: 450 Thanks: 0  drawing a closed figure
What ensures if you can draw a closed figure without lifting your hand off and without repeating through a line? I tried different conjectures but all of them failed for some figures. Please help me out... 
February 6th, 2013, 09:51 PM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 406  Re: drawing a closed figure Hello, mathmaniac! Quote:
An even vertex has an even number of paths leading out of it. An odd vertex has an odd number of paths leading out of it. If all the vertices are even, the figure is traceable. If there are any odd vertices, there must be exactly two of them. Otherwise, the figure is not traceable. Code: B A o * * * o * * * o C * * * * * * * * * * * * H o o D * * * * * * * * * * * * G o * * * o * * * o E F Code: A o * * * * E o * * * * * o B * * * * * * * * * o * * * F * * * * * * D o * * * * * o C Code: A o * * * * * o B * * * H * G o * * o * * o C * * * * * * F o * * o * * o D E  
February 7th, 2013, 05:08 PM  #3  
Global Moderator Joined: May 2007 Posts: 6,136 Thanks: 468  Re: drawing a closed figure Quote:
 
February 8th, 2013, 01:31 AM  #4 
Math Team Joined: Apr 2010 Posts: 2,770 Thanks: 356  Re: drawing a closed figure
What is connected? All vertices >= 2? If so, do you have an example that fails [color=#105287]soroban[/color]'s conditions for traceability?

February 8th, 2013, 01:22 PM  #5 
Global Moderator Joined: May 2007 Posts: 6,136 Thanks: 468  Re: drawing a closed figure
Two triangles not connected to each other. You can draw either one, but you need to lift the pencil to do both.

February 8th, 2013, 05:41 PM  #6 
Senior Member Joined: Dec 2012 Posts: 450 Thanks: 0  Re: drawing a closed figure
Thank you soroban,but i need time to check your conjecture.

February 9th, 2013, 01:48 AM  #7  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: drawing a closed figure Quote:
 
February 9th, 2013, 05:32 PM  #8 
Senior Member Joined: Dec 2012 Posts: 450 Thanks: 0  Re: drawing a closed figure
Have you got any proof for it?

February 9th, 2013, 09:27 PM  #9  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: drawing a closed figure Quote:
Quote:
Shouldn't we have even number of odd vertices for Hamiltonian ones? i.e. GP(5,2) is the Peterson graph. Where the number of odd nodes are 10 (not 2).  
February 13th, 2013, 09:10 PM  #10  
Senior Member Joined: Dec 2012 Posts: 450 Thanks: 0  Re: drawing a closed figure Quote:
 

Tags 
closed, drawing, figure 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Drawing xyz graph.  ohc4r3  Linear Algebra  1  March 17th, 2013 05:25 AM 
Closed set and closed ball  Vasily  Real Analysis  3  February 4th, 2013 01:49 PM 
Is the union of infinite disjoint closed sets closed?  03sqq  Real Analysis  4  November 13th, 2012 04:40 AM 
Drawing balls with repetition  butabi  Advanced Statistics  1  November 27th, 2011 09:19 AM 
How To Figure Gross With a Certain Net Figure  Al_Ch  Elementary Math  2  May 21st, 2009 05:53 PM 