98 Geometrical Problems- SHARING A GRINDSTONE
Three men bought a grindstone twenty inches in diameter. How much must
each grind off so as to share the stone equally, making an allowance of four
inches off the diameter as waste for the aperture? We are not concerned with
the unequal value of the shares for practical use-only with the actual equal
quantity of stone each receives.- THE WHEELS OF THE CAR
"You see, sir," said the automobile salesman, "at present the fore wheel of
the car I am selling you makes four revolutions more than the rear wheel in
going 120 yards; but if you have the circumference of each wheel reduced by
three feet, it would make as many as six revolutions more than the rear wheel
in the same distance."
Why the buyer wished that the difference in the number of revolutions be-
tween the two wheels should not be increased does not concern us. The
puzzle is to discover the circumference of each wheel in the first case. It is
quite easy.
- A WHEEL FALLACY
Here is a curious fallacy that I have found to be very perplexing to many
people. The wheel shown in the illustration makes one complete revolution
in passing from A to B. It is therefore obvious that the line (AB) is exactly
equal in length to the circumference of the wheel. What that length is cannot
be stated with accuracy for any diameter, but we can get it near enough for
all practical purposes. Thus, if it is a bicycle wheel with a diameter of 28 inches,
we can multiply by 22 and divide by 7, and get the length-88 inches. This is
a trifle too much, but if we multiply by 355 and divide by 113 we get 87.9646,
which is nearer; or by multiplying by 3.1416 we get 87.9648, which is still more
nearly exact. This is just by the way.
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