| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
The question is often asked:
"If a hoop that fits perfectly around the earth's equator
is cut and lengthened by inserting one inch, will it still
fit so tightly that even a knife blade cannot be slipped
under it?"
Enjoy,
Kostas G.
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 495.1 | An inch goes a long ways! | VAXRT::BRIDGEWATER | Sat May 31 1986 23:39 | 6 | |
No. If the equator and hoop encircling it are both assumed to
be circles, the hoop after having been lengthened by an inch
will have a little less than 1/6 (1/2pi) inch clearance above
the equator at every point on the equator.
- Don
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| 495.2 | Some calculations related... | THEBUS::KOSTAS | Kostas G. Gavrielidis <o.o> | Tue Jun 03 1986 08:27 | 27 |
The inch seems so small an addition to the equator's twenty five
thousand miles, that a hasty judgement often leads to an affirmative
answer to this question.
Let's see,
if the earth's circumference is C inches
and the radius is R inches,
then 2*(pi)*R = C
and R = C/(2*pi).
When the circumference is increased to C+1 inches,
the radius is incresed to (C+1)/(2*pi),
more by 1/(2*pi) inches
or .159 inches.
So the lengthened hoop could be raised more than 1/8
of an inch all around the equator.
Note: The same amount of raising occurs when one inch
is added to any hoop, however large or small.
Enjoy,
Kostas G.
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