Angles in a convex pentagon?

Tom Shermer shermer at cs.sfu.ca
Mon May 28 13:28:18 PDT 2001


You can get an angle approaching pi + arccos(1/4) > pi + pi/3
by the following method:
	1) Construct an equilateral not-strictly-convex pentagon
	    with EA and AB colinear, and BC and CD colinear.
	2) Wiggle it. (shrink the appropriate edges slightly,
	    causing slight changes in the angles).
	    
	    Tom

	
> Date: Fri, 18 May 2001 14:21:41 +0200 (MEST)
> From: Jobst Heitzig <heitzig at mbox.math.uni-hannover.de>
> X-Sender: nhabheit at unics
> To: compgeom-discuss at research.bell-labs.com
> Subject: Angles in a convex pentagon?
> MIME-Version: 1.0
> X-Scanning-Notification: This email was scanned in its path for viruses and 
certain attachments may have been dropped
> 
> Does anyone know whether the following is true in a convex pentagon ABCDE:
> Given that EA>AB>BC and CD<DE<EA, the angle sum DEA+EAB is at most 4*pi/3.
> 
> I tried hard but could neither prove nor disprove it :-)
> 
> Jobst Heitzig
> 
> 
> 
> -------------
> The compgeom mailing lists: see
> http://netlib.bell-labs.com/netlib/compgeom/readme.html
> or send mail to compgeom-request at research.bell-labs.com with the line:
> send readme
> Now archived at http://www.uiuc.edu/~sariel/CG/compgeom/maillist.html.


-------------
The compgeom mailing lists: see
http://netlib.bell-labs.com/netlib/compgeom/readme.html
or send mail to compgeom-request at research.bell-labs.com with the line:
send readme
Now archived at http://www.uiuc.edu/~sariel/CG/compgeom/maillist.html.



More information about the Compgeom-announce mailing list