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Vandaag is het 26 September 2023

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Long rope - math puzzle


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Suppose you have an enormous long rope. You place this rope on the soil along the equator, such that the rope forms a circle around the earth. After you have finished this big job, you increase the length of the rope by one meter. How far from the soil do yo have to attach the rope to make again a circle around the equator? Assume that the earth is a perfect sphere, without mountains etc. earth


Let's call the radius of the earth r (in meters). The length of the rope should be equal to the circumference of the earth which is 2*pi*r. Now you increase the length of the rope by 1 meter. The new length of the rope will be 2*pi*r + 1 meter. With this length you can make a circle of radius (2*pi*r + 1) / (2*pi) = r + 1/(2*pi). You therefore have to attach the rope at r + 1/(2*pi) - r = 1/(2*pi) = 0.15915 meter above the soil. The nice thing of this result is that it is independent of the radius r. So this 0.15915 meters also holds if you do the same experiment on your pencil or your car tyre.