Vedic Square

By Kardi Teknomo, PhD.

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In the previous section, Vedic square was introduced as multiplication table of digital roots. Vedic square has very rich patterns that worth to explore further about its properties.

• Vedic square is a symmetric matrix, that is

• Quadratic pattern is lies in the diagonal of Vedic square: 1497-7941-9

• Let us use basic Vedic Square as our matrix and the element of the matrix as

General Vedic square can have any size bigger than 9 by 9. We can then derive several important basic properties for general Vedic square of any size

• Top left boundary: . This is to say that the top and left digit sums are equal to its placement.

• Bottom Right boundary: . Every multiple of 9, the Vedic square will produce 9

• Sum of columns in Vedic square: . For example, second column plus seventh column will always produce the ninth column; third column plus fifth column will produce 8 th column.

• Sum of rows in Vedic square: . For example, second row plus seventh row will always produce the ninth row; third row plus fifth row will produce 8 th row.

• Cyclical property: .

Tips: Making Vedic Square using Matlab

function V=Vedic(n, color) 

    if nargin<1 | n<9, n=9; end     % if no input or input less than 9, set n as 9 

    if nargin<2, color='prism'; end % if no input color set color as prism 

    A=[1:n];                        % this is to make n by n Vedic square 

    K=ones(n, n); 

    V=K+mod((A'*A-K),9);            % this is the Vedic square 

    imagesc(V);                     % show Vedic square as image 

    colormap(color);                % change color of image. 
                                    % Try many different color maps 
                                    % such as 'colorcube', 'flag', 'hsv(30)',
                                    % 'jet', 'summer', 'hot', 'prism', etc. 

    axis off;                       % remove the axis label 

Run this code using

>>Vedic(81, ‘hot')

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The PDF file of this tutorial is also available for download here.

This tutorial is copyrighted.

Preferable reference for this tutorial is

Teknomo, Kardi. Digital Root. http:\\people.revoledu.com\kardi\ tutorial\