Now add exactly one foot to the rope's length and support it above ground equally around the globe.
How far is the rope above the ground?
Surprisingly, almost two inches! (1.90985...).
Let's wrap a rope around a orange, then lenghten it by one foot. How far is the gap?
Again, about two inches!
Try a ping pong ball. Same result!
Strangely believe it! The answer is independent of the size of the sphere
Explanation: Let C = the circumference of the earth.
Then C = the original length of the rope and C+1 the extended length.
Let r be the earth's radius and R be the new radius of the rope after extension.
But C = 2 * pi * r and C+1 = 2 * pi * R
and R = (C + 1) / (2 * pi)
and r = C / (2 * pi)
or: R - r = 1 / (2*pi) = 0.159... (feet) or 12 * 0.159 inches.
The doors are marked A, B and C. You choose A.
The host then opens door B which reveals a dollar bill.
He then asks you if you want to stay with your first choice, door A, or switch to door C.
What do you do? Well, the odds of winning the million dollars if you stay with A is 1/3. But the odds of winning if you switch to door C is 2/3!
Strangely believe it.
Here are the possibilities:
Original door selected A A A B B B C C C Location of $1,000,000 A B C A B C A B C Door opened by the host B/C C B C A/C A B A A/B Do not switch -------- WIN LOSE LOSE LOSE WIN LOSE LOSE LOSE WIN Switch ---------------- LOSE WIN WIN WIN LOSE WIN WIN WIN LOSESo if you DON'T switch, you will win 3 times and lose 6 times, but if you DO switch, you will win six times and lose three. Surf over here for another explanation.
Does this speed seem credible? How would you test it (without setting up 303,000 dominos)?
(Left to the inginuity of the reader)
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