Conference rusure::math

1073.0. "seasonal problem" by HERON::BUCHANAN (Andrew @vbo DTN 828-5805) Tue May 02 1989 17:34

                  I N T E R O F F I C E   M E M O R A N D U M

                                        Date:     02-May-1989 06:43pm ETE
                                        From:     BUXTON
                                                  BUXTON@ULYSSE@MRGATE@STATOS@VBO
                                        Dept:      
                                        Tel No:    

TO:  BUCHANAN@A1NSTC


Subject: A puzzle for you ....

DOCUMENT NUMBER: 009047                 PRINTED BY: STEVE BUXTON @VBE
                   I N T E R O F F I C E   M E M O R A N D U M
                                        Date:      02-May-1989 06:22 CET
                                        From:      STEVE BUXTON @VBE 
                                                   BUXTON.STEPHEN 
                                        Dept:      EAITG
                                        Tel No:    DTN: 828 / X: 5765

TO:  ~Remote Addressee~                   ( _NM%HERON::BUCHANAN )

CC:  Ian COWBURN @VBE                     ( COWBURN.IAN )

Subject: A puzzle for you ....

    Hi Andy,
    
        We (me, Liliane and Ian C.) went hiking yesterday and after a 
        long hard day got into a very serious and profound 
        conversation over a beer (as one does !). We came up with a 
        puzzle which doesn't seem too difficult but which does require 
        a little thinking-about with a mathematical type of brain. 
        Knowing your fondness for such puzzles (and given our extreme 
        sloth where brain-work is concerned) I took an action to pass 
        the problem on to you.
        
        We all got a little (!) sunburnt on the backs of our necks and 
        arms.
        
        The problem is "what kind of walk do we need to follow in 
        order to get an even sun-tan ?"
        
        We must assume that the Sun describes an arc in the sky 
        roughly East-West, somewhat less than overhead (i.e. we're not 
        at the equator and it's not midsummer's day). So what's the 
        optimum shape (and direction ?) of our all-tanning walk ?
        
        A thought that just occurred to me - if we only have one car 
        and therefore need to get back to the same place at the end of 
        this walk, is it possible to describe an all-tanning 
        "aller-retour" ??
        
        I'm sure you will appreciate the earth-shattering importance 
        of this problem, and thus give it your best efforts.
        
        Answers on a postcard please ........
    
    - Steve B.
    

	Tell them to take their clothes off and lie down.  After
	a while, turn over.  :-)

	Dan

Interested in just the horizontal component of our live-giving sun
or also the vertical component (in which case the walk will not be
a trivial and the advise in .1 seems the most appropiate)?
Or even worse: looking for the spherical integration of the sunlight
on the human body (which could be simplified by modelling the body
with a cylinder)?

    Let's assume the hikers are spherical.
    
    
    
    Sorry, I can't continue this with a straight face right now.

Sorry, I reacted before thinking. The solution is simple (not if you
want to end at the same place you started from): just walk from west
to east and in time symmetrical around mid-day (noon).