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Wired Equator

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Wired Equator - Back to the Cool Math Games

The circumference of the Earth is approximately 40,000 km. If we made a circle of wire around the globe, that is only 10 meters (0.01 km) longer than the circumference of the globe, could a flea, a mouse, or even a man creep under it?

This old topic is locked since it was answered many times. You can check solution in the Spoiler below.

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Wired Equator - solution

It is easy to compare R and new R (original perimeter = 2xPIxR, length of wire = 2xPIx(new R)) and find out that the result is about 1.6 m. So a smaller man can go under it and a bigger man ducks.

The circumference of the globe is approximately 40,000 km. If we made a circle of wire around the globe, that is only 10 metres longer than the circumference of earth (Edit: circumference of globe), could a flea, a rabbit or even a man creep under it?

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it sounds like you are saying that the wire is oly 10 meters long

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Wired Equator - Back to the Logic Puzzles

The circumference of the globe is approximately 40 000 km. If we made a circle of wire around the globe, that is only 10 metres longer than the circumference of earth, could a flea, a rabbit or even a man creep under it?

Wired Equator - solution

It is easy to subtract 2 equations (original perimeter = 2xPIxR, length of wire = 2xPIxR + 2xPIx(new R)) and find out that the result is 10m/(2xPI), which is about 1.6 m. So a smaller man can go under it and a bigger man ducks.

I’m confused. Are you saying that adding 10 Meters of wire to a perfectly measured 40,000 km of wire that fit snuggly around the planet would give you enough freed up space to elevate the wire 1.6 meters off the ground?? The way the question is worded is " If we made a circle of wire around the globe, that is only 10 meters longer than the circumference of earth" Does that mean you are then using 40,010 meters of wire??? I would think that 10 meters of wire compared to 40,000 would gain you such a microscopic amount it would be almost impossible to measure..

Sorry for the ignorance..

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Unbelievable as it may seem, but it is so. Radius of circle made of 40,000 km and 10 meters long wire is just about 1.6 meters longer than the radius of circle made of 40,000 km long wire.

But feel free to prove the opposite.

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Yeah, this is because the ratio of the input to the output in terms of circumference and radius is 2Pi.

So if you feed it (change in distance) 10m of circumference you will get (change in distance) 1.6m radius. The rest of the puzzle is just there to confuse peops.

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Yeah, this is because the ratio of the input to the output in terms of circumference and radius is 2Pi.

So if you feed it (change in distance) 10m of circumference you will get (change in distance) 1.6m radius. The rest of the puzzle is just there to confuse peops.

Yeah! What HE said!...lol

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No it does not mean having a wire of 40,010 meters but 40,000.01 km. But still, the 0.01km change leaves room for children to walk around.

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No it does not mean having a wire of 40,010 meters but 40,000.01 km. But still, the 0.01km change leaves room for children to walk around.

Well, I suppose the only way I am going to understand how that is possible is to learn Algebra this afternoon, and well, Needless to say, that’s not going to happen.. I am just trying to picture it on perhaps a smaller scale. If you have a basketball, and it is exactly 25 inches in diameter, and you have a piece of string 25.1 inches long.... AHHHH WAIT...lol I DO THIS EVERYTIME. I figure it out when talking about how I can't figure it out. lol

It's the shear scale of the planet that makes such a small amount NOT SO SMALL <--- Moron Math

I would think that placing the string around the basketball would free it up a small amount, but a few feet off the ground IS a small amount with the size of this planet. I SEE,,,, Thanks!

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There are actually a few other solutions that should be irrefutable based on the wording of the question (although they still feel like cheating). None of them even require the wire to be longer than the circumference.

First, the problem assumes, though it doesn't say so explicitly, that the earth is spherical. Earth is more like a sphere that has been squished in several ways -- I'm not an expert on this, but it may not even be a perfect or near-perfect ellipsoid. So it has several varying circumferences, depending on where you measure it, and I'm not sure the term circumference even actually applies. But assuming you measured the distance around the earth where it was largest, you could easily wrap the wire around at some other circumference-like spot even without making it 10 meters longer and have lots of extra creeping-under room.

But, assuming a different earth that is actually spherical, there is nothing that says your wire has to go around the globe _at_its_great_circle_, or above its circumference. In fact, you could use a wire shorter than the circumference of the earth, and have plenty of room to travel under it, if it were only wrapped around the earth at some other circle than the earth's great circle.

Finally, assuming that the earth is essentially spherical and that the wire does in fact go around over its circumference, the wire can be pulled as tight as one can imagine pulling it (without breaking the wire or slicing into the earth, of course) and there will be SOME point at which any living thing should be easily able to creep under it. Examples are mountain valleys and bodies of water. If you bend the wire so that it follows the ground along these places, then it would have to be much longer than otherwise, so there is some ambiguity about what the circumference of the earth actually means. Earth is not a smooth surface by any standards.

But still, those feel like cheating answers somehow.

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Well, the way I make it is

C= 40000000M therefore (Cx3.142857143/2=r) the Radius is 62857142.86 M

C= 40000000 + 10 is C = 40000010M therefore the radius is 62857158.57 M

62857142.86 - 62857158.57 is 15.71428571M.

Your answer of 1.6 M would be correct if the wire were only 1 M longer.

Or have I missed it completely?

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Well, the way I make it is

C= 40000000M therefore (Cx3.142857143/2=r) the Radius is 62857142.86 M

C= 40000000 + 10 is C = 40000010M therefore the radius is 62857158.57 M

62857142.86 - 62857158.57 is 15.71428571M.

Your answer of 1.6 M would be correct if the wire were only 1 M longer.

Or have I missed it completely?

err...C = 2*pi*r, so r = C/(2*pi). Dunno why you're multiplying by pi, and pi = 3.14159... by the way, not 3.142857...

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Well, the way I make it is

C= 40000000M therefore (Cx3.142857143/2=r) the Radius is 62857142.86 M

C= 40000000 + 10 is C = 40000010M therefore the radius is 62857158.57 M

62857142.86 - 62857158.57 is 15.71428571M.

Your answer of 1.6 M would be correct if the wire were only 1 M longer.

Or have I missed it completely?

err...C = 2*pi*r, so r = C/(2*pi). Dunno why you're multiplying by pi, and pi = 3.14159... by the way, not 3.142857...

Yep,

That's how I missed it!

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The way I like to think about this is imagine cutting the earth in half (along the equator) and looking at it from above-- it would appear as a circle (well, assuming the earth is perfectly spherical). With the wire being longer than the circumference of the circle, it would make a concentric circle (a circle within a circle). If both the circles shared the same midpoint, (Is that what it's called? It's been too long since I did geometry.) is the distance between the two circles longer than the height of an average human?

So the way you can get the answer is subtracting the radius of the small circle FROM the radius of the big circle, which was what sphinxteroonicat did, and compare that answer to average height of humans (in the right units, of course.)

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Hey, SO like, One time in Band Camp, We did this Math Ditto, right??!!?? lol

You guy are way beyond me here. I thought pie was 1.49 at Denny's

O.k,,, I'll shut up

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I was just going to suggest anyone being sneaky in Australia would be 'creeping under it'

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All this Math & Algebra is a complete waste of time. Common sense tells us that the earth is not a perfect sphere and hence even if the wire was exactly the same length as the earth's circumference (ie 40,000KM) you could quite comfortably walk under it in many places (or swim under it in the seas/oceans/lakes).

I know because my neighbour's cat is able to get into my garden under a concrete fence base simply by digging through under it!

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All this Math & Algebra is a complete waste of time. Common sense tells us that the earth is not a perfect sphere and hence even if the wire was exactly the same length as the earth's circumference (ie 40,000KM) you could quite comfortably walk under it in many places (or swim under it in the seas/oceans/lakes).

I know because my neighbour's cat is able to get into my garden under a concrete fence base simply by digging through under it!

AGGHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH.... Thats all I have to say ,,, AAAGGGHHHHHHHHHHHHHHHHHHHHHHHGHGHGHG....

Why does everyone find it necessary to find the FLAWS in the question? Can you not understand that they are using EARTH as an EXAMPLE for its SIZE...? Rivers, Valleys and Pot hole SHOULD NOT BE FACTORED INTO THIS... Ahhh, forget it. I need to accept the fact that Ignorance is all around us in this world...

You’re Right, forget the answer... Go look for a river to swim in... LOL

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The illusion comes from the notion that 10 meters is infinitesimally small compared to 40,000 km (so the change should be really really small). Yes, so is 1.6 meters compared to 40,000/(2*PI) km

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The illusion comes from the notion that 10 meters is infinitesimally small compared to 40,000 km (so the change should be really really small). Yes, so is 1.6 meters compared to 40,000/(2*PI) km

Well said dude.

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Well, the way I make it is

C= 40000000M therefore (Cx3.142857143/2=r) the Radius is 62857142.86 M

C= 40000000 + 10 is C = 40000010M therefore the radius is 62857158.57 M

62857142.86 - 62857158.57 is 15.71428571M.

Your answer of 1.6 M would be correct if the wire were only 1 M longer.

Or have I missed it completely?

You're about 10 (or Pi squared) times too large.

You multiplied by Pi when you should have divided: Circumference / (2 Pi) = Radius

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The illusion comes from the notion that 10 meters is infinitesimally small compared to 40,000 km (so the change should be really really small). Yes, so is 1.6 meters compared to 40,000/(2*PI) km

VERY VERY Well Said! That's what I said minus all the educated words..lol

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I think there is another way to interpret the question. Its never stated that the extra 10 meters should be evenly distributed along the circumference. So 40000 Km of wire can be used to encircle the earth and u r left with 10 meters. That wd mean a height of about 5 meters (10/2). So i guess a man can surely pass thru it...

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I do agree with Mannu. 40 000km requires a wire of at least 40 000km. You hence cover the original circumference. Now at a very location you add 10 meters of wire: simply putting it on the ground, the wires will overlap.

If you want to maximize the eventual surface available, you take from the original wire 5 meters on the left and 5 on the right to have them stick perpendicular to the ground and use your 10 meters to complete the new figure.

At the end, you have approximately 5 x 10 meters of surface available. Well enough for whatever you may think. Indeed it's not precisely 50 sq/m; the earth being a rather spheric, it's a little less.

Distributing the additional 10 meters over the entire circumference would leave a gap of 1.6m. But I'm still wondering how this new wire will stand up by itself! Thus my more pragmatic interpretation of the problem...

This was my two cents.

Stephane

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No it does not mean having a wire of 40,010 meters but 40,000.01 km. But still, the 0.01km change leaves room for children to walk around.

Ahh... That was sneaky -- I missed the conversion. I didn't read that one was Km and the other was M.

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Check the value of PI you have used. The correct value of PI is 3.1415926536. Use this and you will get the correct answer.

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