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Guru

Join Date: Apr 2010
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# Interesting Mathematical Proof

08/08/2022 6:14 PM

This is interesting. The logic kind of bends your mind...

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Guru

Join Date: Dec 2008
Location: Long Island NY
Posts: 15285
#1

### Re: Interesting Mathematical Proof

08/10/2022 1:59 PM

This seems more like a mathematician's version of the three-card Monte card trick. A non-zero probability is not identical to a probability of one.

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Guru

Join Date: Apr 2010
Location: About 4000 miles from the center of the earth (+/-100 mi)
Posts: 9253
#2

### Re: Interesting Mathematical Proof

08/11/2022 12:30 PM

Nice card trick. I don't for sure know how it's done, but did notice that both of his hands are not always in the limited field of view of the video.

I'm still trying to understand the logic of the dots and quarters puzzle in the "Probably Exists" video.

If you tile the plane with quarters, there is a 90.69 percent chance for each dot that it is covered, the percentage of area of a circle inscribed in a hexagon (see figure below). An average of 9.069 dots will be covered by a quarter for any configuration. As you move the quarters up and down, left and right, etc, some dots will be covered or uncovered. The argument is that, since the average is greater than 9, there has to be some offset that covers 10 dots.

The argument is for a random set of 10 dots. It seems that the door is still open for some "special" set of 10 dots that could survive the translation and rotation of the mass of quarters. And there are still more degrees of freedom if you remove some quarters so you can move them around individually. So, I doubt this special set exists, but I don't think that it's proven that it doesn't.

Hexagons tile plane 100%. Circles tile plane 90.69% or pi / 2*sqrt(3)

Guru

Join Date: Dec 2008
Location: Long Island NY
Posts: 15285
#3

### Re: Interesting Mathematical Proof

08/11/2022 3:24 PM

I also believe the proffered example of dots and quarters is true. I don't see how the equally proposed probability calculation and logic prove the example as true. This is the mathematical "sleight of hand" distraction I am referring to.

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"Don't disturb my circles." translation of Archimedes last words