Talk:Centered square number

From Wikipedia, the free encyclopedia

I don't inderstand what is meant by represents a square with a dot in the center and all other dots surrounding the center dot equidistantly.

I picture like what is shown in figurate numbers would be useful.

--- User:Karl Palmen 16 June 2004

Those are more like ASCII art than pictures. I'm fooling around with Adobe Illustrator to try to create some nice, professional-looking diagrams. In the meantime, here is some ASCII art to illustrate the concept. And if you come up with a better word description please edit the article accordingly. PrimeFan 21:03, 17 Jun 2004 (UTC)

*   *     *       *
   ***   ***     ***
    *   *****   *****
         ***   *******
          *     *****
                 ***
                  *

I've added the diagram to the main page. One can replace it with a better diagaram later if you want.

I don't regard represents a square with a dot in the center and all other dots surrounding the center dot equidistantly as a correct desription. Surely this would describe

*    *     * *      *      * *
    ***     *             *   *
     *     * *    * * *     *  
                          *   *
                    *      * *

where the applicable distances are the square roots of 0,1,2,4,5, etc.

--- User:Karl Palmen 18 June 2004

You're right about the word description. As for the diagrams, I can't figure out how to make them in Adobe Illustrator. I do have to admit that in the case of centered square numbers, ASCII art is slightly more satisfactory than it is in the case of other figurate numbers. PrimeFan 22:07, 20 Jun 2004 (UTC)

I've corrected the description and made use of the concept of taxicab geometry in so doing

distance = abs(x+y)

rather than

distance = sqrt(x^2+y^2)

Now I've thought of a diagram that shows the (x-1)^2 + x^2 formula. I'll put these in and correct the formulae.

--- User:Karl Palmen 21 June 2004