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## Question

A perfect sphere hangs in space. The sphere has an equator, and thus a north and south pole. A point starts out on the equator. Say that the equator line is the 0°, 180° and 360° line- the point sets out at an angle of 30° on a spiral that will take the point to the north pole. If the diameter of the sphere is D (ie, the length of the equator), and the point moves at the exact unwavering speed of D/108 per minute, and nothing interrupts its path, how many hours does the point take to reach the north pole?

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No time to think - need to sleep - but can't avoid the question or the irresitible urge to post first...

I assume the 30 degrees is relative to the line of the equator. If that's the case, does it ever actually get there - unless the angle becomes something other than 30 degrees, I think it continually travels around and around and gets closer and closer, but never quite makes it to the pole.

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yeah the equator is "0 degrees" like it says in the post

and you're right ;D

only one angle will reach the point: an exact right angle, going straight up. Everything else (except for 270 degrees to the south pole I guess, depends if it "keeps going" or stops at the south pole) ends up in an infinite

logarithmic spiral which is kinda like a fractal in a way that every view of it looks the same zoomed in or out... ie, the point gets closer and closer, never actually touching the north pole. The spiral never ends...

edit: check this out too ;D

note: this is a "catch" riddle, obviously the math is very easy, don't give away the answer, hopefully I'll "catch" some ;D

Edited by unreality
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yeah the equator is "0 degrees" like it says in the post

and you're right ;D

only one angle will reach the point: an exact right angle, going straight up. Everything else (except for 270 degrees to the south pole I guess, depends if it "keeps going" or stops at the south pole) ends up in an infinite

logarithmic spiral which is kinda like a fractal in a way that every view of it looks the same zoomed in or out... ie, the point gets closer and closer, never actually touching the north pole. The spiral never ends...

edit: check this out too ;D

note: this is a "catch" riddle, obviously the math is very easy, don't give away the answer, hopefully I'll "catch" some ;D

You know, the only "true" definition of a finite spiral that actually goes somewhere requires that the angle changes with distance - for example, starting at 0 degrees and ending at 90 degrees. It feels like a spiral, and I guess it looks like one viewed from above the north pole, but because the angle never changes, it never actually gets there. Glad to know my hunch was right!

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