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From: ian@psuvax1.UUCP (Ian Parberry)
Newsgroups: net.math
Subject: a piece of folk-lore
Message-ID: <1799@psuvax1.UUCP>
Date: Tue, 17-Sep-85 15:43:11 EDT
Article-I.D.: psuvax1.1799
Posted: Tue Sep 17 15:43:11 1985
Date-Received: Fri, 20-Sep-85 05:39:04 EDT
Distribution: net
Organization: Pennsylvania State Univ.
Lines: 38

Great Moments in the History of Mathematics:

I heard the following story while an undergraduate in Brisbane in the late
seventies.  (It involves the well-known fly-and-bicycle problem, which
has for some time been a fashionable example of "lateral thinking".)

       A graduate student of a respected mathematician poses the following
    problem to the great man (hoping to catch him out):

    "A cyclist is exactly x miles from home.  She rides home at a constant
    speed of c miles per hour.  At the exact instant she starts out, a fly
    leaves the front wheel of her bicycle at i miles per hour (i>c),
    heading towards home.  When it reaches there, it turns around (in zero time)
    and heads back to the bicycle.  It flies backwards and forwards at the
    same speed between the bicycle and the house until the rider gets home.
    How far does the fly fly?"

       The Master replies, without pause, "ix/c miles".  Deflated, the student
    observes that "a surprising number of people miss the easy solution, and
    try to sum the infinite series of distances flown by the fly".  To which
    the puzzled mathematician replies, "But I did!".

Can anyone answer the following questions:
1.  Is this a true story, or just a piece of mathematical folk-lore?
2.  What is the origin of the fly-and-bicycle problem?  Assuming the story
    is true, did the student make it up? If not, who did?
3.  Who was the great mathematician?  (I've forgotten).
4.  Who was the student?  (I was never told).
5.  When and where did this (alleged) conversation occur?
6.  How was the original problem stated?  For example, every time I've heard the
    fly-and-bicycle problem, the person telling it has used different values
    for i, c and x.

-----------------------------------------------------------
Ian Parberry.
<allegra,ihnp4,atcgva,burdvax,purdue>!psuvax1!ian

Dept. of Computer Science, Penn. State University.


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