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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

1749.0. "Circle disection" by AUSSIE::GARSON (nouveau pauvre) Sat May 15 1993 00:34

    Draw a circle. Let A be a point on the circle and let B be the point
    diametrically opposite A.
    
    Let n be an integer >= 2. (n=3 seems useful for sketching.)
    
    Define P[0] as A and P[n] as B and let P[0],...,P[n] be such that the points
    P[1],...,P[n-1] divide the diameter AB into n equal parts i.e. the
    distance between P[k] and P[k+1] is 1/n times the diameter. (Don't draw
    in the diameter.)

    Draw semi-circular arcs passing through P[0] and P[1], P[0] and P[2],
    ..., P[0] and P[n-1] where the arcs are all on the same side of the
    diameter AB.
    
    Now draw semi-circular arcs passing through P[1] and P[n], P[2] and
    P[n], ..., P[n-1] and P[n] where the second group of arcs are all on
    the same side of the diameter as each other but not on the same side of
    the diameter as the first group.
    
    The circle has now been divided into n regions.
    
    What can be said about the area of the regions?
T.RTitleUserPersonal
Name		DateLines
1749.1cryingHANNAH::OSMANsee HANNAH::IGLOO$:[OSMAN]ERIC.VT240Mon May 17 1993 10:2512

This problem is just *crying* for a picture of what the hell you're talking
about.

Anyone care to try to draw a nice one somehow for this notes file ?

Thanks.

/Eric
1749.2Generalized ying-yang?WIBBIN::NOYCEIt's the memory interface, stupid!Mon May 17 1993 11:2825
picture for n=4

      _-~~0~~-_
   .-'     \\`.`-.
  /         |\ `\ \
 /      ,-1'  |  | \
|    ,-'      |  |  |
|   /        /   |  |
|  |    ,-2-'    |  |
|  |   /        /   |
|  |  |      ,-'    |
 \  \ |  ,3-'      /
  \  `.\|         /
   `-_ `\\     _-'
      `-__4__-'




If we draw in the diameter, then the area under a semicircle of diameter k
is k^2 (times pi*r^2/2n).  The area between semicircle k and semicircle k-1
is k^2 - (k-1)^2 = 2k-1.  Each region consists of one part with diameter k
and one part with diameter n+1-k, with total area 2n -- all the regions have
the same area.
1749.3HANNAH::OSMANsee HANNAH::IGLOO$:[OSMAN]ERIC.VT240Mon May 17 1993 14:495

Great picture, thanks !

/Eric
1749.4AUSSIE::GARSONnouveau pauvreMon May 17 1993 20:186
    re .1
    
    Sorry, Eric, the artist in .2 must be made of sterner stuff than I.
    
    Those using the Notes DECwindows interface can view "pictures" directly,
    can't they? I don't use it myself.
1749.5we need pictures, badly !HANNAH::OSMANsee HANNAH::IGLOO$:[OSMAN]ERIC.VT240Tue May 18 1993 11:5420

It's of little value that decwindows notes can "view" pictures, if for the most
part it's inconvenient for user's to DRAW pictures.

I dream of a day when it's simple for all of us to both draw and view pictures
in notes.

The common uses I envision:

o	Sketches for math problems

o	Posting of a cartoon I liked in newspaper and want to share

o	Signing off with little pictures of ourselves (perhaps you've seen
	mine already)



/Eric
1749.6Digital has it nowAUSSIE::GARSONnouveau pauvreWed May 19 1993 00:5815
1749.8AUSSIE::GARSONnouveau pauvreMon May 24 1993 08:4711
    re .7
    
    as stated in .2.
    
    re .*
    
    To digress slightly, should we be encouraged to post DDIF diagrams
    (like .6) to clarify our postings? In the past I have refrained because
    it isn't fair to those without workstations. (Also, I don't like the
    Notes DECwindows interface.) But how many people don't yet have a
    workstation (or at any rate among those who note here)?
1749.9VMSDEV::HALLYBFish have no concept of fireMon May 24 1993 10:254
    I don't USE the workstation interface but would encourage DDIF postings
    anyhow...if it's important enough I'll switch over.
    
      John