Re: Aaahhh... I can't believe this
- From: "OwlHoot" <ravensdean@xxxxxxxxxxxxxx>
- Date: 18 Mar 2007 10:31:09 -0700
On Mar 18, 8:59 am, alertj...@xxxxxxxxxxxxxx wrote:
Well,
The situation is a case in which you tie a rope around earth's equator
(around 40,000 km) and you increase the length of the rope by one
metre. How much should you increase the radius of earth so that the
new loop fits perfectly (slack=0). Guess how much ? Dont calculate !
Answer is sixteen centimetres(1/2pi).
and the important thing is that the answer is always 16 cm even when
the body under consideration is Sun,moon or a bicycle tyre.
2.pi.R=C
2.pi.(R+dR)=(C+dC)
dR=dC/2.pi
Anyone has more of such difficult to believe questions ?
Lets share
Jean
Another golden oldie - Obviously x^2 + y^2 can't be expressed as
a product of algebraic factors (with real coefficients) like
x^2 - y^2 can. So you'd think the same is true of the similar
looking sum of squares x^4 + 4.y^4.
But x^4 + 4.y^4 = x^4 + 4.x^2.y^2 + 4.y^4 - 4.x^2.y^2 =
(x^2 + 2.y^2 - 2.x.y).(x^2 + 2.y^2 + 2.x.y) ..
In the late 19th century, someone called Landry spent several
months trying to factorize (2^58 + 1)/5 (or some very similar
number - I'm quoting that from memory) by manual calculations.
What a shame he forgot about the x^4 + 4.y^4 factorization above!
Cheers
John R Ramsden
.
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