Round Island Problem

A person got stuck on a round island (perfect circle).
There is a crocodile swimming nearby.
The speed of the crocodile is 4 times that of the person.
The crocodile will always run to the beach that is closest to the human.

Question:How could the human move (zig-zag, straight, etc.) to reach to the sea without encountering the crocodile?

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`2^{34}`	$2^{34}$
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Comments

I believe the answer would be to move in a spiral which radiates outwards from the center of the island, but I am at a loss for how to rigorously prove this. It also seems like the size of the island would affect the answer, though I am unsure of this as well.

David Stiff - 1 year, 2 months ago

The size of the island is not given. Either it doesn't matter, or there are different cases that should be included in the answer :P

Wenyu X - 1 year, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$