Precalculus

R = 6.378 * 10^6 m
_________________
C =2*pi*R
= 6.28*R
= 6.28 * (6.378 * 10^6 m)

C' = 2*pi*R'
= 6.28*R'
= 6.28 * (6.378*10^6m + .01m)
= 6.28 * (6.37800001 * 10^6 m)

C' - C =

tomr-
Thank you.

It was recently published in The New York Times. The Times says the answer is 6.28 cm.

It's always going to be 2 x pi x 1 cm longer, whatever the initial starting point. Isn't that obvious?

Or 6.283185307179586476925286766559 cm

No, I do not find it obvious. Though I am not denying you are right.

I think it is intuitive that if you have a series of concentric circles, that each circle going outward is longer than the circle before, and the length of disparity increases.

The circumference of a circle is given by 2 x pi x the radius, and the circumference of another circle of greater radius is going to be greater by 2 x pi x the difference. This seems as obvious to me as saying that 5 is greater by one than 4, or that three tons is two tons greater than one ton. The arithmetic is that simple.

The riddle makes the actual arithmetic, in the example case, even easier by having the band stretched so it is 1 centimetre above the surface of the imaginary smoothly spherical earth.

The radius of the earth is entirely irrelevant to the question as asked, and is in fact a red herring, since we are considering only the difference in radius between two circles, and in any case it is roughly 6,371 km and not 6.371 km as shown in the first post.

The point of the question, it seems to me, is to test for a certain kind of basic mathematical thinking, or whether you have done your 3rd grade math homework and/or paid attention in class, because if so, the answer is as obvious as 4 - 1 = 3, and if not, it will be all Greek to you or you are liable to get distracted by the earth being kind of big etc.

contrex-
Thank you. I understand now.

However, I think 3rd grade is not right. Would 3rd graders really answer correctly? The problem was posed in The New York Times as a test in precalculus for high school students.

I got that slightly wrong, I believe it would be either Grade 5 or 6. I have now seen a list of school grades in the USA. I am British and we learned about pi and how to calculate the area and circumference of a circle in the school year when we were 11 to 12.