Multi ratio comparison, is it possible?

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gundartg

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Greetings, I'm currently working on a little pet project for fun and have come across a brick wall. I came up with a way to solve this years ago but have since lost my notes on how I did it and am unable to replicate my solution

I have several 4 part ratios i.e. W:X:Y:Z

One of these ratios is the main ratio that I work with, the other ratios are the compare too ratio.
What I need to do is find the ratio that is most similar to the main ratio in proportion.

A simple add all the numbers together comparison is not going to cut it as if the main ratio is say 3:4:50:2 and two comparison ratios are 3:4:0:2 and 1:2:6:1 the comparison ratios would show as equal but the second one is most similar.
One thing of not is negative numbers can and will appear in the comparison ratio often, and while it is possible for them to appear in the main ratio it should be a very rare occurrence.

On a side note a computer will be choosing and displaying the most similar comparison ratio.
 
gundartg said:
Greetings, I'm currently working on a little pet project for fun and have come across a brick wall. I came up with a way to solve this years ago but have since lost my notes on how I did it and am unable to replicate my solution

I have several 4 part ratios i.e. W:X:Y:Z

One of these ratios is the main ratio that I work with, the other ratios are the compare too ratio.
What I need to do is find the ratio that is most similar to the main ratio in proportion.

A simple add all the numbers together comparison is not going to cut it as if the main ratio is say 3:4:50:2 and two comparison ratios are 3:4:0:2 and 1:2:6:1 the comparison ratios would show as equal but the second one is most similar.
One thing of not is negative numbers can and will appear in the comparison ratio often, and while it is possible for them to appear in the main ratio it should be a very rare occurrence.

On a side note a computer will be choosing and displaying the most similar comparison ratio.
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What are your thoughts?

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Well lets see. As I recall my method years ago involved taking the absolute value of each number in the ratio then dividing them by the lowest non zero number. I can not recall what I did after that to compare.
I've tried a simple add the numbers that didn't work, for obvious reasons.
I've considered a weighted additon comparison, but truth be told each number has equal weight.
I've considered breaking the ratio in the center to be two seperate ratios, converting those into a single number, taking each seperate number as a part of a new two part ratio and using that to compare. I could be wrong but to me that kind of results in inaccurate comparisson.

I'm stuck somewhere past the beginning but before the end, specifically at the how to compare a 4 part ratio for the one that has the most similar proportions.
 
I came up with something that kind of works, just not as accurate as I want. For each comparisson ratio I find the lowest number (absolute value) in the ratio. Then divide thes number into each part of the original comparisson ratio. Then I multiply the main ratio parts into the appropriate parts of the comparisson ratio. Then add all the parts together and take the comparisson ratio with thr highest score.

Now obviously the division stage is not necessary but it does prevent dealing with very large numbers.


How can I can go about making this more accurate?
 
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