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"I've got this beautiful panoramic three-dimensional painting of Mars based on Martian photos. It's 30 feet wide. You can pick out every pebble on the Martian landscape. And who'd have dreamed you could do that?"
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This piece of technovelgy gives a great illustration of the fastest way to get from point A on the surface of the earth to another surface point B.
The ingenious solution is to dig a tunnel from one point to the other, using the force of gravity to provide some of the acceleration. The beauty of this approach is that, in a frictionless environment, you can speed the train on its way without having to apply any energy - and slow it down the same way!
The questions (for you engineers) are: what is the best shape (or curve) for the tunnel, and how can you avoid those pesky underground temperatures and pressures? See this article on the brachistochrone problem, one of the earliest problems posed in the calculus of variations. Newton solved this problem from scratch in one day in 1696; got your pencil? Ready, set ... go! Comment/Join this discussion ( 1 ) | RSS/XML | Blog This | Additional
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