Circle Puzzles 99Now the inner circle (the large hub in the illustration) also makes one
complete revolution along the imaginary dotted line (CD) and, since the line
(CD) is equal to the line (AB), the circumference of the larger and smaller
circles are the same! This is certainly not true, as the merest child can see at
a glance. Yet, wherein lies the fallacy?
Try to think it out. There can be no question that the hub makes one com-
plete revolution in passing from C to D. Then why does not CD equal
in length its circumference?
- A FAMOUS PARADOX
There is a question that one is per-
petually hearing asked, but to which
I have never heard or read an answer
that was satisfactory or really con-
vincing to the ordinary man. It is this,
"When a bicycle is in motion, does
the upper part of each wheel move
faster than the bottom part near the
ground?" People who are not accus-
tomed to the habit of exact thought
will invariably dismiss the subject
with a laugh, and the reply, "Of
course not!" They regard it as too
absurd for serious consideration. A wheel, they say is a rigid whole, revolving
round a central axis, and if one part went faster than another it would simply
break in pieces.
Then you draw attention of your skeptic to a passing cart and ask him to
observe that, while you can clearly distinguish the spokes as they pass the
bottom, and count them as they go by, those at the top are moving so fast
that they are quite indistinguishable. In fact, a wheel in motion looks some-
thing like our rough sketch, and artists will draw it in this way. Our friend
has to admit that it is so, but as he cannot explain it he holds to his original
opinion, and probably says, "Well, I suppose it is an optical illusion."
I invite the reader to consider the matter: Does the upper part of a wheel
move faster than the lower part?