ABACUS: MYSTERY OF THE BEAD
The Bead Unbaffled - An Abacus Manual

 Euclidean norm of a vector

The length of a vector can be readily calculated on an abacus using the distance formula. As an example, I will compute the length of a vector in 3 dimensional space.

Let's say the coordinates of the endpoint of the vector is ( x, y, z ).

The length of the vector is : the square root of ( x^2 + y^2 + z^2 ).

So if the vector's coordinates are : ( 3, 7, 4 ) it's length is: the square root of ( 9 + 49 + 16 ) = sq rt of 74.

If the vector's coordinates are : ( 8, -5, 9 ) it's length is: the square root of ( 64 + 25 + 81 ) = sq rt of 170.

You may calculate the square root by one of the known techniques (Kato or Kojima) in bead arithmetic on whichever rods make the most sense for your particular abacus.
 

 

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▪ Advanced Abacus Techniques

© October, 2008
Gary Flom   Atlanta Georgia   USA
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