PS Good and maybe even true story about summing series
Supposedly someone asked J von Neumann about the following
problem
Suppose two trains start out from two stations that are 200 hundred miles
apart. The trains are going 20 miles per hour and 30 miles per hour.
A (speedy) bird leaves the front of one train and heads for the other
at 100 miles per hour. WHen he reaches the second train he immediately
reverses direction and heads back to the other train and when he reaches
that one he again reverses and heads back towards the other thus
zigzagging back and forth until the trains meet in the middle of the 200
mile piece of track.
The question is , how far does the bird fly up to the moment that the
trains meet.
von Neumann thought for only a very brief moment and said
"400 miles"
The person who had posed the problem looked embarrassed and said
"Most mathematicians over look the obvious nethod [that the trains
meet in 4 hours since the distance between them is diminishing at 50
mikes per hour and the bird has thus flown for 4 hours at one hundred
miles per hour] and they start summing up the infinite series of bird
flights."
von Neumann looked annoyed and said
"Yes of course, that is how I did it--summed the infinite series".
I do not know whether this story is true, but here is one that really is
supposed to be
Someone went up to Steinmetz and asked him what was the
volume
of three radius 1 cylinders intersecting at right angles.
Steinmetz said , I have never thought about it (only very short pause)
but the answer
seems to me to be 8(2-sqrt 2)
This is elementary, but doing it in one's head very fast...
well, some people are really smart!
Robert
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