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.
▪ Abacus: Mystery of the Bead
▪ Advanced Abacus Techniques
© October, 2008
Gary Flom Atlanta Georgia USA