Need to calculate the difference between different pairs of values

Hello!

I have a column with 20 integers, from 1 to 20. Each integer is associated with a value in a second column.

These integers represent 20 evenly spaced points along a circle. Points 1 and 20 are therefore close together, whereas points 1 and 10 are maximally separated.

I need to calculate the difference between the recorded values in the second column for every possible combination of lag distances! Namely,
points with a lag distance of 1 would include (1,2) (2,3) (3,4) (4,5) ... (20,1)
points with a lag distance of 2 would include (1,3) (2,4) (3,5) (4,6) (5,7) ... (20,2)
points with a lag distance of 10 (maximal distance!) would include (1,10) (2,11) (3,12) (4,13) ... (20,10)

For each calculated difference I would also need to know which lag I'm referring to (1,2, ... 10), perhaps listed in another column.

Thank you!

Ilford

So, you have a circle of radius R and and 20 points evenly spaced along the circumference of the circle. Assuming that p(1)<>p(20), the angular seperation between p(i) and p(i+1) is 2*PI/21. Let's call that angle a.

The linear distance between p(i) and p(i+j) is the distance between the points

(R*cos(j*a),R*sin(j*a)) and (R,0) which is

R * sqrt( (cos(j*a)-1)^2 + sin(j*a)^2)

= R * sqrt (cos(ja)^2 - 2*cos(ja) + 1 +sin(ja)^2)

=R * sqrt(2 - 2*cos(j*a)).

I think j is what you call the "lag".

Hi, and thanks for your great reply.

However, I don't need to calculate any angles. I only require a formula (or set of formulae) to calculate the difference between the values for a given pair of points.

The pairs of points are defined by their lag distance; in other words, the number of points separating them.

E.g., For a lag distance of one, I would need the difference of the values found between all combinations of points that are separated by one point (1and2; 2and3; 3and4 ... 20and1). For a lag distance of two I would need the difference of the values found between all combinations of points that are separated by two points (1and3; 2and4; 3and5 ... 20and2), and so forth until you reach the maximum lag distace of 10.

point value
1 0.394
2 0.998
3 0.102
4 0.432
...
20 0.595


Thanks again!!

Ilford