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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

1355.0. "simple paper question" by HERON::BUCHANAN (combinatorial bomb squad) Wed Dec 12 1990 18:58

	An obvious thing which has never occurred to me before, concerning
one of the most common objects that we have around us:  an sheet of A4
paper.

	Let A,B,C & D be the corners of such a sheet, in clockwise order, 
where AB & DC are the long sides.   Fold the sheet so that D lies on AB.
The crease runs from A to E say, where E is a point on CD.   Now fold the
sheet a second time, so that E now lies on AB.

	*Where* on AB does E lie, and why?

Regards,
Andrew.
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1355.1GUESS::DERAMOSometimes they leave skid marks.Wed Dec 12 1990 19:3222
>>	Let A,B,C & D be the corners of such a sheet, in clockwise order, 
>>where AB & DC are the long sides.   Fold the sheet so that D lies on AB.
        
        There is more than one way to do that.
        
>>The crease runs from A to E say, where E is a point on CD.
        
        Okay.  You mean to fold it so that all of AD is along AB.
        
>>							       Now fold the
>>sheet a second time, so that E now lies on AB.
        
        Again, there is more than one way to do that.
        
>>	*Where* on AB does E lie, and why?
        
        Folding so that all of AE lies along AB, point E ended
        beyond B rather than between A and B.  Folding along the
        line bisecting CB results (of course) in E ending up on
        top of D (where the folded D sits on AB).
        
        Dan
1355.2crazed of ValbonneHERON::BUCHANANcombinatorial bomb squadWed Dec 12 1990 20:276
	Yeah, I'm working all night due to DECPresent letting me down, and
this flaky idea came to mind.   Dan's right, I'm folding AD onto AB, and
AE on to AB afterwards.   The mind wanders.

Regards,
Andrew.
1355.3Let's go for a Golden Ratio standard!IOSG::CARLINDick Carlin IOSG, Reading, EnglandThu Dec 13 1990 05:168
    If it's A4 paper then the answer is B. This follows from the SQRT(2)
    ratio of length to width for An paper. (This means that an A3 folds in
    half to give an A4, A4 -> A5 etc.) 
    
    Dan's paper probably isn't A4, which leads to the question of why US
    paper has the ratio approx 1.3
    
    Dick
1355.4GUESS::DERAMOSometimes they leave skid marks.Thu Dec 13 1990 08:455
        I think mine was 8 1/2 by 11 (both in inches).  It did
        occur to me afterwards to ask what the dimensions of an
        A4 sheet of paper were.  What are they?
        
        Dan
1355.7page size CSSE::NEILSENI used to be PULSAR::WALLYThu Dec 13 1990 12:538
Contrary to what .0 says, the availability of A4 paper depends a lot on your
geography.  I usually have a bit in my (US) office, from paper mail from
Europeans.  But I could not find any to measure.

The LN03 programmer's manual gives A4 size as 21 cm by 29.7, which is the 
sqrt(2) ratio.

I don't know why US paper is 8� by 11.