Comments on: That’s impossible!

By: sean

sean — Fri, 03 Oct 2008 18:07:20 +0000

that’s an amazing result. I can’t fault it but i also can’t really believe it is true. It just goes against any intuitive thought on the problem.

By: Adrian Mac

Adrian Mac — Fri, 15 Aug 2008 00:18:26 +0000

I’ve only just heard this paradox and likewise thought ‘that can’t be right’. But a pencil and paper proved me wrong.

In trying to convince my son I thought of a persuasive visualisation.

Assuming the rope runs through the poles, don’t add one meter to the rope, add 25cm four times – at both poles and at the equator (both sides) then the four ‘segments’ (arcs) can lift apart and away from the earth’s surface by about the amount the calculations show.

That visualisation persuaded him. And, finally, me.

By: links for 2008-05-13 « Tom Altman’s Wedia Conversation

links for 2008-05-13 « Tom Altman’s Wedia Conversation — Tue, 13 May 2008 11:33:15 +0000

[...] That’s impossible! | Math-Blog (tags: math paradox) [...]

By: bob saget

bob saget — Mon, 12 May 2008 06:55:56 +0000

wait. this does sound impossible!

So, if the world had a 32 cm bigger diameter, you’d only need one more meter of rope to wrap it…

*thinks* actually that kind makes sense… because adding 1 meter to the circumference would increase the size by that ammount.

The thinking relies on making the 1 meter sound like the small measurement adjustment causing a huge 16cm change.

By: Antonio Cangiano

Antonio Cangiano — Sun, 11 May 2008 23:02:23 +0000

Yes Enginerd, the areas are obviously very different. The pardox is limited to the width of the gaps.

By: Enginerd

Enginerd — Sun, 11 May 2008 22:46:46 +0000

The width of the gap might be constant, but the area wouldn’t be. It would be
pi*( (r+1)^2 – r^2) = pi*(2*r + 1), which clearly depends on r. Simply asking how the two gaps compare is a bit vague.

I think the real issue is that when you picture the problem, the gaps look different. A 16 cm wide gap doesn’t seem like much next to the radius of the Earth, but it seems like a lot next to the radius of a golf ball.