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Optical methods for number theory?

+ 1 like - 0 dislike
1400 views

I found a paper: 'A New Method of Finding the Distribution of Prime Number', says:

We stack discs and annuluses with certain rules then turn on the light to illuminate.The projection of annuluses corresponds prime number,and the projection of discs corresponds composite number.

See; http://en.cnki.com.cn/Article_en/CJFDTOTAL-HNKX201201010.htm

Are there other physics methods for number theory?

This post imported from StackExchange MathOverflow at 2014-06-19 11:37 (UCT), posted by SE-user Mike
asked Jun 18, 2014 in Mathematics by Mike (115 points) [ no revision ]
retagged Jun 19, 2014
The paper you refer to doesn't seem to be very accessible -- when I click the PDF link, I see a page asking in Chinese for a login password.

This post imported from StackExchange MathOverflow at 2014-06-19 11:37 (UCT), posted by SE-user Stefan Kohl
@StefanKohl,the paper has 4 pages,main content is in Chinese ,here you can see the first 2 pages, wenku.baidu.com/view/1d602350be23482fb4da4cc6.html?re=view, the last 2 pages are more examples.

This post imported from StackExchange MathOverflow at 2014-06-19 11:37 (UCT), posted by SE-user Mike
The diagrams in that paper are implementing a poor version of the en.wikipedia.org/wiki/Sieve_of_Eratosthenes where instead of covering multiples of the next uncovered (i.e. prime) number, they cover multiples of the next number, regardless of it's status. So two rounds after covering all multiples of $2$, they cover all multiples of $4$.

This post imported from StackExchange MathOverflow at 2014-06-19 11:37 (UCT), posted by SE-user Zack Wolske
Here is a physical implementation of the more efficient version: en.wikipedia.org/wiki/Lehmer_sieve

This post imported from StackExchange MathOverflow at 2014-06-19 11:37 (UCT), posted by SE-user Zack Wolske
@ZackWolske ,yes it is sieve of Eratosthenes.

This post imported from StackExchange MathOverflow at 2014-06-19 11:37 (UCT), posted by SE-user Mike
I would like to query the closure - have posted on meta: meta.mathoverflow.net/questions/1749

This post imported from StackExchange MathOverflow at 2014-06-19 11:37 (UCT), posted by SE-user Carl

I personally think this is an interesting question at the interface betwen math and physics, whereas for MathOverflow it seems to be a bit too "interdisciplinary" as they say ...

3 Answers

+ 6 like - 0 dislike

Probably, the best-known application of ideas from physics to computational number theory is Shor's algorithm.

You may also be interested in other examples from “unusual and physical methods for finding prime numbers”.

This post imported from StackExchange MathOverflow at 2014-06-19 11:37 (UCT), posted by SE-user Waldemar
answered Jun 18, 2014 by Waldemar (60 points) [ no revision ]
+ 4 like - 0 dislike

The physics of the Riemann Hypothesis D. Schumayer and D. A. W. Hutchinson, Rev. Mod. Phys. 83 307-330 (2011). abstract here

This post imported from StackExchange MathOverflow at 2014-06-19 11:37 (UCT), posted by SE-user Carl
answered Jun 18, 2014 by Carl (60 points) [ no revision ]
+ 1 like - 0 dislike

There's a way to use physics to calculate the digits of $\pi$. I quote from http://math.stackexchange.com/questions/138289/intuitive-reasoning-behind-pis-appearance-in-bouncing-balls

Let the mass of two balls be $M$ and $m$ respectively. Assume that $M=16\times100^nm$. Now, we will roll the ball with mass $M$ towards the lighter ball which is near a wall. How many times do the balls touch each other before the larger ball changes direction? (The large ball hits the small ball which bounces off the wall)

The solution is the first $n+1$ digits of $\pi$.

This post imported from StackExchange MathOverflow at 2014-06-19 11:37 (UCT), posted by SE-user Gerry Myerson
answered Jun 18, 2014 by Gerry Myerson (10 points) [ no revision ]

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