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Rajeev Kant's avatar

Why are trying to time travel … if we can fix someone in time with medicine or love or any strong force that doesnt allow someone to move from a fix point of time.

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Joshua H Sparber's avatar

Grant,

I would think intuitively that a proof for the rectangle and the box would start like this:

Take a fractal pattern like the Koch Snowflake but do not put in all the infinite lower levels.

I would believe that a series of boxes and rectangles would form, possibly depending on symmetry; say, having an even number of thorns. Then add more and more lower layers towards a geometric limit of infinite sublayers.

For such a symmetric fractal the boxes and rectangles might expand out towards a circle or converge into a circle as the thorns go infinitely down. This seems a lot like your circular geometric proof for the Basel theorem on the complex polar plane. And here symmetry might have a role to play (the usual symmetry/entropy interaction).

Further thoughts—I can see two limiting cases using the Koch Snowflake:

1) large boxes around the inside with the asymptote a circle

2) small box that diminish to dots with the asymptote a circle

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