This can't be possible!

Geometry Level pending

How many places are there on Earth such that if you walk 10km north, then 10km west, then 10km south, you will arrive at the original place you started at?

2 0 1 ∞ \infty

Sharky Kesa by Sharky Kesa , 19, United Kingdom

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2 solutions

Prince Loomba
Jul 30, 2016

Check here for video as well as written solution

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Michael Mendrin
Jul 26, 2016

Pick any line of latitude such that an integer multiple of its distance around to the point of beginning is exactly 10k. Then pick any point 10k directly south of that latitude. You have your path that would work, one of infinitely many possible. For the most part, it just seems like walking 10k to close to either the north or south pole, going around in a circle for another 10k, and then going back to the point of beginning.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Not that it matters to the final tally, but the South Pole also fits the bill.

Brian Charlesworth - 4 years, 10 months ago

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Brian, in a while from now, the South Pole is going to be the only place where we WALK on such a path.

Michael Mendrin - 4 years, 10 months ago

For the south pole it works when starting point is exactly in the south pole, I do not see how it would work otherwise. For the north pole it works in a way that Michael described in his solution.

Maria Kozlowska - 4 years, 10 months ago

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Oh don't be a party pooper, even if you are right about this. It's true, I can't find any argument for any possible path where "starting out north" ends up putting nearly at the south pole.

Michael Mendrin - 4 years, 10 months ago

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@Michael Mendrin – I realized yesterday that we have a drought in Ontario, the pond with snapping turtles and muskrats in park nearby has less than a half of its water level. We did have heavy rain yesterday and a water level is up a little bit. I hope it is getting better in California. I am glad the South Pole is holding up.

Maria Kozlowska - 4 years, 10 months ago

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@Maria Kozlowska – We had a brief respite from the recent El Nino weather, but unfortunately the drought situation is still here. It is not looking good, and it will be terribly foolish for us to imagine that someday "things will be back to normal". Anyone who still believes that should go visit Greenland and see the rivers of ice melt-water gushing out of that place.

Is it a normal part of Earth's history for this to be happening? Oh, sure, of course it is normal. It's also been normal to have mass extinctions in Earth's history. Business as usual---let's not interfere with what's natural.

Michael Mendrin - 4 years, 10 months ago

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@Michael Mendrin – This type of approach to problems was taught by Fr. Dolindo Ruotolo

Maria Kozlowska - 4 years, 10 months ago

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