Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Tiling the plane with checkerboard patterns
Replies: 2   Last Post: Jul 16, 2010 8:39 AM

 Search Thread: Advanced Search

 Messages: [ Previous | Next ]
 Avni Pllana Posts: 546 Registered: 12/6/04
Re: Tiling the plane with checkerboard patterns
Posted: Jul 15, 2010 7:31 AM
 Plain Text Reply

> Hello Avni, I am surprised with the discrepancy you
> have found
> in the a(6) case. I still hold hope that your
> formula does
> give the correct values for all a(n). Could it be
> that the
> discrepancy is due to Matlab's floating point
> arithmetic?
>
> Since you and Mark have both noted the effect of
> parity of n,
> I want to point out that I have reason to believe
> that what
> matters is not whether n is odd or even, but whether
> it is
> prime or composite. I don't have a fool-proof
> argument to
> support that right now; just a preliminary analysis.
> I will write about this again if I find out more.
>
> Rouben
>

Hi Rouben,

some results for n=7,8,9 are shown below:

n=7
Mat_7=[1 1 24 x x ...]
Sum_7=[1 1 24 .......]

n=8
Mat_8=[1 1 33 x x ...]
Sum_8=[1 1 63 .......]

n=9
Mat_9=[1 1 40 x x ...]
Sum_9=[1 1 40 .......]

The above results suggest that discrepancy has to with the parity of n and not with the primeness of n.

Best regards,
Avni

Date Subject Author
7/15/10 Avni Pllana
7/16/10 mark

© The Math Forum at NCTM 1994-2018. All Rights Reserved.