A Wall Around The Earth

[chemist]

Ok, to solve this riddle, which is not that difficult, you need some very basic knowledge of math.

Let's say that someone builds a 1 meter high wall all around the Earth, following the equator (we don't care here about the fact that there are some oceans in the way). Now, person 1 walks around the Earth on top of that wall, while person 2 walks around the Earth beside the wall. When they are finished walking, what is the difference in distance covered between the two persons? (We assume here that the equator is a perfect circle.)

Hint: The correct answer may surprise some people...

Regards

[suegha]

Oh please tell us!

[Paulbangkok]

The distances are exactly the same......................................and if that is the correct answer i really will be surprised!!!

Edited July 19, 2007 by Paulbangkok

[PattayaAddict]

Same distance ?

[suegha]

I think I have heard this or something similar before. The difference is very little, but I can't remember why. Is it because of the vast circumference of the earth?

[lanny]

The answer is about 6.25 meters (I don't remember the exact value for pi.)

You have two circles, one 2 meters greater in diameter than the other. Since the formula for the circumfrence of a circle is pi times diameter, the difference is 2 meters times pi.

[Soju]

The answer is about 6.25 meters (I don't remember the exact value for pi.)

You have two circles, one 2 meters greater in diameter than the other. Since the formula for the circumfrence of a circle is pi times diameter, the difference is 2 meters times pi.

Correct, except the part about the "exact value for pi", being nobody can remember the exact value being there's a likely infinite number of non-repeating digits beyond the decimal point. The value of pi with only the five most significant decimal places is 3.14159... so the difference is double that in meters. A lot of people probably think you need to know the actual circumference of the world in order to figure it out, but in reality you don't. If you built the same wall around the moon, around the sun, or around a basketball (if that was possible), the answer would still be the same.

[percy2]

The answer is about 6.25 meters (I don't remember the exact value for pi.)

You have two circles, one 2 meters greater in diameter than the other. Since the formula for the circumfrence of a circle is pi times diameter, the difference is 2 meters times pi.

Correct, except the part about the "exact value for pi", being nobody can remember the exact value being there's a likely infinite number of non-repeating digits beyond the decimal point. The value of pi with only the five most significant decimal places is 3.14159... so the difference is double that in meters. A lot of people probably think you need to know the actual circumference of the world in order to figure it out, but in reality you don't. If you built the same wall around the moon, around the sun, or around a basketball (if that was possible), the answer would still be the same.

If you can't remember those decimal places 22/7 will get you very close.

Cheers

[chemist]

The answer is about 6.25 meters (I don't remember the exact value for pi.)

You have two circles, one 2 meters greater in diameter than the other. Since the formula for the circumfrence of a circle is pi times diameter, the difference is 2 meters times pi.

Correct, except the part about the "exact value for pi", being nobody can remember the exact value being there's a likely infinite number of non-repeating digits beyond the decimal point. The value of pi with only the five most significant decimal places is 3.14159... so the difference is double that in meters. A lot of people probably think you need to know the actual circumference of the world in order to figure it out, but in reality you don't. If you built the same wall around the moon, around the sun, or around a basketball (if that was possible), the answer would still be the same.

Excellent, Soju and lenny . And yes, some people think that you have to know the diameter/radius (or circumference) of the Earth to solve this one. And some get surprised when they hear that the answer is only pi x 2 meters (about 6.28 m). "But the Earth is so big; how can the difference be only about 6.28 m??". An extra to you Soju, for the extended and highly correct analysis above.

To prove that the radius of the sphere around which the wall is built is of no importance, you can use the following approach:

Let's say the radius of the sphere (and the radius of the circle that constitutes the "equator" of the sphere) = R, and that the height of the wall = H. This gives that the radius of the circle that is formed by the wall = R + H.

Now, since the circumference of a circle = 2 x pi x the radius of that circle, the difference in circumference (= the difference in the distance walked in our riddle) = 2 x pi x (R + H) - 2 x pi x R = 2 x pi x R + 2 x pi x H - 2 x pi x R = 2 x pi x H.

The value of H was 1 meter in our example, and thus the answer to the problem = 2 x pi x 1 meter = about 6.28m.

Regards

[Tywais]

Perhaps a simpler way to look at the equation

(2*pi*r1) - (2*pi*r2) = x

2*pi*(r1-r2) = x

2*pi*(1) = x = 6.28

[chemist]

Perhaps a simpler way to look at the equation

(2*pi*r1) - (2*pi*r2) = x

2*pi*(r1-r2) = x

2*pi*(1) = x = 6.28

Indeed. Basically it is of course a variation of the reasoning that I used in my previous post, in which I tried to provide an "easy-to-follow" approach.

Cheers