Assume for this problem that the earth is a perfect sphere. A point \(P\) on it's surface has the following property. Starting from \(P\), suppose you travel \(1\) mile south, then \(1\) mile west and finally \(1\) mile north. Doing so takes you back to the same point \(P\). Are there any such points \(P\) other than the north pole? Choose the appropriate option:

There are no such points.

Such points for a single circle.

Such points form at least two but finitely many circles.

Such points form infinitely many distinct circles.

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewest"Such points can form infinitely many distinct circles", because one can start at a point that is 1 + x miles from the South pole, travel 1 mile south to a distance x from the South Pole, such that in travelling west 1 mile one can end up making n number of circuits coming back to exactly where one was before travelling west, and thence travel 1 mile north back to the point of beginning P. n can be any integer.

Log in to reply

Can you clarify what you mean by "making n number of circuits"?

Log in to reply

x = 1 / 2πn, where n is any integer > 0. Then n circuits or trips around will bring him back to the point where he began traveling west.

Log in to reply

There are no such points.

Log in to reply

No. Check your reasoning.

Log in to reply