Wednesday, February 27, 2013

Natural Navigation Quiz



How many points are there on the earth where you could travel one mile south, then one mile east, then one mile north and end up in the same spot you started?


28 comments:

Mike Wise said...

Near the South Magnetic Pole you could stand still and let the pole travel around you.

Tillerman said...

You'll have to explain that answer a bit more Mike. I'm not sure I understand what you are saying.

O Docker said...

Instinct tells me that there is only one such place - the true north pole - but something is making me think that's not the only answer.

Tillerman said...

Maybe it's the penguins making you think like that? If I had showed a picture of a polar bear would the quiz be any easier?

O Docker said...

I'm pretty sure that Ft. McHenry is not a correct answer.

Bursledon Blogger said...

That's the same sat nav I have in my car!!

O Docker said...

Oh, now I've got it. I knew there was at least one other place on earth where this is true.

It's the magic roundabout in Swindon, England, where practically any sequence of turns will bring you back to where you started. Some people have been stuck there trying to escape for months at a time and have had to be rescued by members of the RLSS UK.

Tillerman said...

I'm pretty sure you are correct.

Tillerman said...

You are getting warm...

JP said...

Somewhere with strong E->W tidal flow

Somewhere with big spots

JP said...

So Tillerman, have you asked Mrs T how she feels about the opportunity of a fly-by visit to Mars?

John in PDX said...

My Apple map app says the rotunda at the capitol in DC.

Litoralis said...

There's the obvious one at the North Pole. Then there are all the points on a line of latitude near the South Pole that is one mile north of a line of latitude that is one mile around its circumference. From all those points, you can walk south one mile, walk one mile east around a one-mile-long line of latitude, and then one mile north back to where you started.

Baydog said...

Two?

Tillerman said...

Litoralis has part of the answer but there are some other points that he has overlooked.

Tillerman said...

I spent almost 30 years of my life at Mars. Why would I want a mere fly-by?

Litoralis said...

Also anywhere in the air or on water where there is wind or current at least a component of which is moving west. At any of those locations, you could travel south, then travel east, then travel north back to your starting point. Depending which frame of reference is used to measure the distances and speeds traveled, the eastward travel could either be at the speed of the westward component of the wind or current, less than that speed, or greater than that speed. In some cases, a pause in travel might be necessary before turning north to ensure correct alignment with the desired end point.

Anonymous said...

An infinite number. The 2 that Litoralis mentioned and all those points 1 mile north of where a line of latitude is 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, etc. long.

Tillerman said...

The full answer doesn't need to invoke air or water currents. "Travel" in the question should be understood to mean "walk" or "drive a motorized or dog-powered vehicle on land appropriate to the terrain in question." It's not a trick question. it's a very geometrical question. Well, maybe it's a bit of a trick.

There are in fact an infinite number of other answers each defining an infinite number of solutions.

That's enough clues for now. Can you solve it? 93.6% of former MIT sailing team members get this wrong.

Tillerman said...

Bingo! Anonymous 3:40 PM has it! Although I wish he or she would have added a name to their answer.

Just to clarify, when you walk east for a mile along the lines of latitude 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, etc. long. you are of course walking 2, 3, 4, 5, 6, 7, etc. times around the circle before turning north and returning to your start point.

Tillerman said...

Thanks to everyone who participated and especial thanks to O Docker who inspired this post with his picture of penguins on a post about walking. I hope he is grateful for us giving him the idea for an infinite number of 3 mile walks.

And before anyone points it out, yes, I do know that you won't see penguins at the South Pole. Or the North Pole for that matter.

Tillerman said...

My Apple map app knows where there are 14 liquor stores close to Bristol Harbor. That's good enough for me.

O Docker said...

I think perturbation theory predicts that there are also an infinite number of ways to get lost at the Swindon roundabout.

Tillerman said...

There is also a very similar Magic Roundabout at Hemel Hempstead in Hertfordshire in England, with which I am more familiar.

You really should aim to visit both of these, O Docker, on your upcoming trip to England. They are only an easy and pleasant walk from your small Belgravia hotel.

O Docker said...

The UK is such a 'walkable' country, isn't it? Nothing is more than just a few pleasant steps from Belgravia.

Tillerman said...

Exactly. Especially for someone like you O Docker, who is such a powerful advocate for the benefits of walking.

my2fish said...

the number pi?

Tillerman said...

Well if we want to get mathematical we could use pi in the answer.

As well as the North Pole the conditions are satisfied by all points on lines of latitude that are 1+1/(2*N*pi) miles from the South Pole, where N is a positive integer.

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