300 AnswersTherefore, four times 28 gives us 112 inches as its length. And the area of the
space enclosed by the curve and the straight line AB is exactly three times the
area of the circle. Therefore, the enclosed space on either side of the circle is
equal in area to the circle.- A FAMOUS PARADOX
Of course, every part of the wheel revolves round the axle at a uniform
speed, and, therefore, in the case of a fixed wheel, such as a grindstone, the
answer is in the negative. But in the case of a bicycle wheel in motion along a
road it is an undoubted fact that what is the upper part for the time being al-
ways moves faster through space than the lower part. If it did not do so, no
progress would be made and the cyclist would have to remain as stationary
as the grindstone.
Look at our diagram and you will see the wheel in four different positions
that occur during one complete revolution from A1 to A 4 • I have earlier ex-
plained the peculiar curve, called a common cycloid, that is described by a
point on the edge of the tire. The curve is shown here for two points at A1and B 1. Note that in a half-revolution A1 goes to A3 and B1 to B 3 , equal dis-
tances. But neither point moves throughout at a uniform speed. This is at
once seen if we examine the quarter-revolution, where A1 has only moved as
far as A2, while B1 has gone all the way to B 2 • We thus see that a point on
the rim moves slowest through space when at the bottom, and fastest when
near the top.
And here is a simple practical way of demonstrating it to your unbelieving
friends without the aid of my diagrams. Draw a straight line on a sheet
of paper and lay down a penny with the base of Lincoln's head on the line.
Now make the penny run along the line a very short distance to the right and
then to the left. That the base hardly leaves the original point on the line,