Solution Visual analogue using a square As the string must be raised all along the entire circumference, one might expect several kilometres of additional string. Surprisingly, the answer is 2 or around .  Even more surprising is that the size of the sphere or circle around which the string is spanned is irrelevant, and may be anything from the size of an atom to the Milky Way — the result depends only on the amount it is raised. In the second phrasing, considering that is almost negligible compared with the circumference, the first response may be that the new position of the string will be no different from the original surface-hugging position. The answer is that a cat will easily pass through the gap, the size of which will be metres or about ., p. 2436 This diagram gives a visual analogue using a square: regardless of the size of the square, the added perimeter is the sum of the four blue arcs ' , a circle of radius equal to the offset.
Solution Visual analogue using a square As the string must be raised all along the entire circumference, one might expect several kilometres of additional string. Surprisingly, the answer is 2 or around . In the second phrasing, considering that is almost negligible compared with the circumference, the first response may be that the new position of the string will be no different from the original surface-hugging position. The answer is that a cat will easily pass through the gap, the size of which will be metres or about . Even more surprising is that the size of the sphere or circle around which the string is spanned is irrelevant, and may be anything from the size of an atom to the Milky Way — the result depends only on the amount it is raised. Moreover, as in the coin-rolling problem, the shape the string girdles need not be a circle: 2 times the offset is added when it is any simple polygon or closed curve which does not intersect itself. If the shape is complex, 2 times the offset, times the absolute value of its turning number must be added ., p. 2436 This diagram gives a visual analogue using a square: regardless of the size of the square, the added perimeter is the sum of the four blue arcs , a circle of radius equal to the offset.
A
In the second phrasing, considering that is almost negligible compared with the circumference, the first response may be that the new position of the string will be no different from the original surface-hugging position. The answer is that a cat will easily pass through the gap, the size of which will be metres or about .
R
In the second phrasing, considering that is almost negligible compared with the circumference, the first response may be that the new position of the string will be no different from the original surface-hugging position. The answer is that a cat will easily pass through the gap, the size of which will be metres or about
Moreover, as in the coin-rolling problem, the shape the string girdles need not be a circle: 2 times the offset is added when it is any simple polygon or closed curve which does not intersect itself. If the shape is complex, 2 times the offset, times the absolute value of its turning number must be added
D
'