IT TOOK A ROCKET SCIENTIST

Evaluating the responses to the rope around the equator problem has taken me right back to my classroom days except this time, most of my students are in their thirties or forties.

It has been such a delight to hear from so many of you. Before announcing the winning solution, let me explain that there are actually two ways of approaching the problem. One is to take the actual numerical difference between the radius of the enlarged circle and the radius of the Earth. The more elegant answer is an algebraic one which is displayed below.

Both methods determine the same astonishing answer of 1.59 metres. What amazes me about this answer is how such a small addition of rope can have such an the enormous impact on radius. I am also impressed by the fact that the answer remains constant whether you add 10 metres to a rope encircling a baseball or to a rope around the universe. Mr. Sturino from Brebeuf also noted that the same fundamental concept can be applied to help determine how much farther one runs on a track if moved to an outer lane.

Now for the best answers !

Peter Csizmadia, from the Brebeuf graduating class of 1984, was the first with a clear and precise version of the numerical solution. Another fine entry was that of Darek Szadkowski from the class of 2002. Darek actually submitted the algebraic answer as well after I prompted him to go beyond the numerical method.

Matthew Au, a Brebeuf alumnus from 1993, submitted the correct solution without the accompanying work. Although I didn’t suspect treachery at the time, Matthew later playfully owned up to the fact that he found the answer to the problem on the internet at: http://www.abc.net.au/science/surfingscientist/pdf/conundrum17.pdf .

I guess it’s true that you can find everything on the internet.

I also want to recognize thoughtful submissions by Tim Flanagan 1981, Kurt Tan 1998, Hodge Lai 2009 and Canice Mok 2010.

My criterion for the winning solution was that it had to be an accurate algebraic answer similar to the one outlined below. In fact, the winner of the contest, Mike Viechweg, supplied me with both the algebraic and numerical method within hours of my posting the question.

Although he graduated from Brebeuf in 1983, I still remember Mike as a quiet lad with a wonderful broad smile and an intense desire to always get the right answer. Well Mike, you’ve done it again. As well as being a mechanical engineer whose company deals with licensing amusement rides and solar array installations, Mike is also the co-founder of a small company which does work for the Canadian Space Agency which in theory makes him a rocket scientist.

No, he doesn’t win a trip for two to Aruba but I do look forward to meeting Mike soon for a lunch or dinner on me. And just maybe he can slip me some rocket fuel to get my engines firing again.



ROPE AROUND THE EQUATOR SOLUTION

Let C(1) be the circumference of the Earth at the equator
Let C(2) be the circumference of the rope with the extra 10 metres of rope added

Let r(1) be the radius of the Earth
Let r(2) be the radius of the circle formed with the extra 10 metres of rope added

Find r(2) - r(1)

Solution

The circumference of a circle is found using C = 2 pi r

Thus C(2) = 2 pi r(2) and C(1) = 2 pi r(1)

Since C(2) - C(1) = 10

2 pi r(2) - 2 pi r(1) = 10

2 pi ( r(2)- r(1) ) = 10

r(2)- r(1) = 10 / (2 pi)

r(2)- r(1) = 1.59

Hence, the rope would rise enough for a dog or a cat or even, as Mr. Sturino added, for most Italians to walk under.