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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

495.0. "The equator hoop problem." by THEBUS::KOSTAS (Kostas G. Gavrielidis <o.o> ) Sat May 31 1986 22:15

    The question is often asked:
    
        "If a hoop that fits perfectly around the earth's equator 
        is cut and lengthened by inserting  one  inch, will it still
        fit so tightly that even a knife blade cannot be slipped 
        under it?"
    
    
    Enjoy,
    
    Kostas G.
T.RTitleUserPersonal
Name		DateLines
495.1An inch goes a long ways!VAXRT::BRIDGEWATERSun Jun 01 1986 03:396
    No.  If the equator and hoop encircling it are both assumed to
    be circles, the hoop after having been lengthened by an inch
    will have a little less than 1/6 (1/2pi) inch clearance above
    the equator at every point on the equator.
    
    - Don
495.2Some calculations related...THEBUS::KOSTASKostas G. Gavrielidis <o.o> Tue Jun 03 1986 12:2727
    The inch seems so small an addition to the equator's twenty five
    thousand miles, that a hasty judgement often leads to an affirmative
    answer to this question.
    
    Let's see,
    
      if the earth's circumference is  C  inches 
      and the radius is   R  inches,
    
      then     2*(pi)*R = C
      and      R = C/(2*pi).
    
      When the circumference is increased to  C+1  inches,
      the radius is incresed to  (C+1)/(2*pi),
      more by  1/(2*pi)  inches
           or  .159  inches.
    
      So the lengthened hoop could be raised more than  1/8
      of an inch all around the equator.
    
    Note: The same amount of raising occurs when one inch 
          is added to any hoop, however large or small.
    
    Enjoy,
    
    Kostas G.